id	sid	tid	token	lemma	pos
ejpam-2420	1	1	compile	compile	NOUN
ejpam-2420	1	2	/	/	SYM
ejpam-2420	1	3	output.dvi	output.dvi	NOUN
ejpam-2420	1	4	european	european	ADJ
ejpam-2420	1	5	journal	journal	NOUN
ejpam-2420	1	6	of	of	ADP
ejpam-2420	1	7	pure	pure	ADJ
ejpam-2420	1	8	and	and	CCONJ
ejpam-2420	1	9	applied	apply	VERB
ejpam-2420	1	10	mathematics	mathematic	NOUN
ejpam-2420	1	11	vol	vol	NOUN
ejpam-2420	1	12	.	.	PROPN
ejpam-2420	1	13	8	8	NUM
ejpam-2420	1	14	,	,	PUNCT
ejpam-2420	1	15	no	no	INTJ
ejpam-2420	1	16	.	.	NOUN
ejpam-2420	1	17	4	4	NUM
ejpam-2420	1	18	,	,	PUNCT
ejpam-2420	1	19	2015	2015	NUM
ejpam-2420	1	20	,	,	PUNCT
ejpam-2420	1	21	526	526	NUM
ejpam-2420	1	22	-	-	SYM
ejpam-2420	1	23	529	529	NUM
ejpam-2420	1	24	issn	issn	PROPN
ejpam-2420	1	25	1307	1307	NUM
ejpam-2420	1	26	-	-	SYM
ejpam-2420	1	27	5543	5543	NUM
ejpam-2420	1	28	–	–	PUNCT
ejpam-2420	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2420	1	30	on	on	ADP
ejpam-2420	1	31	class	class	NOUN
ejpam-2420	1	32	numbers	number	NOUN
ejpam-2420	1	33	of	of	ADP
ejpam-2420	1	34	real	real	ADJ
ejpam-2420	1	35	quadratic	quadratic	ADJ
ejpam-2420	1	36	fields	field	NOUN
ejpam-2420	1	37	with	with	ADP
ejpam-2420	1	38	certain	certain	ADJ
ejpam-2420	1	39	fundamental	fundamental	ADJ
ejpam-2420	1	40	discriminants	discriminant	NOUN
ejpam-2420	1	41	ayten	ayten	VERB
ejpam-2420	1	42	pekin1,∗	pekin1,∗	NOUN
ejpam-2420	1	43	,	,	PUNCT
ejpam-2420	1	44	aydın	aydın	PROPN
ejpam-2420	1	45	carus	carus	PROPN
ejpam-2420	1	46	2	2	NUM
ejpam-2420	1	47	1	1	NUM
ejpam-2420	1	48	department	department	NOUN
ejpam-2420	1	49	of	of	ADP
ejpam-2420	1	50	mathematics	mathematic	NOUN
ejpam-2420	1	51	,	,	PUNCT
ejpam-2420	1	52	faculty	faculty	NOUN
ejpam-2420	1	53	of	of	ADP
ejpam-2420	1	54	sciences	sciences	PROPN
ejpam-2420	1	55	,	,	PUNCT
ejpam-2420	1	56	istanbul	istanbul	PROPN
ejpam-2420	1	57	university	university	PROPN
ejpam-2420	1	58	,	,	PUNCT
ejpam-2420	1	59	istanbul	istanbul	PROPN
ejpam-2420	1	60	,	,	PUNCT
ejpam-2420	1	61	turkey	turkey	PROPN
ejpam-2420	1	62	2	2	NUM
ejpam-2420	1	63	department	department	NOUN
ejpam-2420	1	64	of	of	ADP
ejpam-2420	1	65	computer	computer	NOUN
ejpam-2420	1	66	engineering	engineering	NOUN
ejpam-2420	1	67	,	,	PUNCT
ejpam-2420	1	68	faculty	faculty	NOUN
ejpam-2420	1	69	of	of	ADP
ejpam-2420	1	70	engineering	engineering	NOUN
ejpam-2420	1	71	,	,	PUNCT
ejpam-2420	1	72	trakya	trakya	PROPN
ejpam-2420	1	73	university	university	NOUN
ejpam-2420	1	74	,	,	PUNCT
ejpam-2420	1	75	edirne	edirne	PROPN
ejpam-2420	1	76	,	,	PUNCT
ejpam-2420	1	77	turkey	turkey	PROPN
ejpam-2420	1	78	abstract	abstract	NOUN
ejpam-2420	1	79	.	.	PUNCT
ejpam-2420	2	1	let	let	VERB
ejpam-2420	2	2	n	n	PRON
ejpam-2420	2	3	denote	denote	VERB
ejpam-2420	2	4	the	the	DET
ejpam-2420	2	5	sets	set	NOUN
ejpam-2420	2	6	of	of	ADP
ejpam-2420	2	7	positive	positive	ADJ
ejpam-2420	2	8	integers	integer	NOUN
ejpam-2420	2	9	and	and	CCONJ
ejpam-2420	2	10	d	d	ADP
ejpam-2420	2	11	∈	∈	PROPN
ejpam-2420	2	12	n	n	VERB
ejpam-2420	2	13	be	be	AUX
ejpam-2420	2	14	square	square	ADV
ejpam-2420	2	15	free	free	ADJ
ejpam-2420	2	16	,	,	PUNCT
ejpam-2420	2	17	and	and	CCONJ
ejpam-2420	2	18	let	let	VERB
ejpam-2420	2	19	χd	χd	NOUN
ejpam-2420	2	20	,	,	PUNCT
ejpam-2420	2	21	h	h	NOUN
ejpam-2420	2	22	=	=	SYM
ejpam-2420	2	23	h(d	h(d	PROPN
ejpam-2420	2	24	)	)	PUNCT
ejpam-2420	2	25	denote	denote	VERB
ejpam-2420	2	26	the	the	DET
ejpam-2420	2	27	non	non	ADJ
ejpam-2420	2	28	-	-	ADJ
ejpam-2420	2	29	trivial	trivial	ADJ
ejpam-2420	2	30	dirichlet	dirichlet	NOUN
ejpam-2420	2	31	character	character	NOUN
ejpam-2420	2	32	,	,	PUNCT
ejpam-2420	2	33	the	the	DET
ejpam-2420	2	34	class	class	NOUN
ejpam-2420	2	35	number	number	NOUN
ejpam-2420	2	36	of	of	ADP
ejpam-2420	2	37	the	the	DET
ejpam-2420	2	38	real	real	ADJ
ejpam-2420	2	39	quadratic	quadratic	ADJ
ejpam-2420	2	40	field	field	NOUN
ejpam-2420	2	41	k	k	NOUN
ejpam-2420	3	1	=	=	PUNCT
ejpam-2420	3	2	q	q	X
ejpam-2420	3	3	(	(	PUNCT
ejpam-2420	3	4	p	p	NOUN
ejpam-2420	3	5	d	d	NOUN
ejpam-2420	3	6	)	)	PUNCT
ejpam-2420	3	7	,	,	PUNCT
ejpam-2420	3	8	respectively	respectively	ADV
ejpam-2420	3	9	.	.	PUNCT
ejpam-2420	4	1	ono	ono	PROPN
ejpam-2420	4	2	proved	prove	VERB
ejpam-2420	4	3	the	the	DET
ejpam-2420	4	4	theorem	theorem	NOUN
ejpam-2420	4	5	in	in	ADP
ejpam-2420	4	6	[	[	X
ejpam-2420	4	7	2	2	NUM
ejpam-2420	4	8	]	]	PUNCT
ejpam-2420	4	9	by	by	ADP
ejpam-2420	4	10	applying	apply	VERB
ejpam-2420	4	11	sturm	sturm	PROPN
ejpam-2420	4	12	’s	’s	PART
ejpam-2420	4	13	theorem	theorem	NOUN
ejpam-2420	4	14	on	on	ADP
ejpam-2420	4	15	the	the	DET
ejpam-2420	4	16	congruence	congruence	NOUN
ejpam-2420	4	17	of	of	ADP
ejpam-2420	4	18	modular	modular	ADJ
ejpam-2420	4	19	form	form	NOUN
ejpam-2420	4	20	to	to	PART
ejpam-2420	4	21	cohen	cohen	PROPN
ejpam-2420	4	22	’s	’s	PART
ejpam-2420	4	23	half	half	ADJ
ejpam-2420	4	24	integral	integral	ADJ
ejpam-2420	4	25	weight	weight	NOUN
ejpam-2420	4	26	modular	modular	ADJ
ejpam-2420	4	27	forms	form	NOUN
ejpam-2420	4	28	.	.	PUNCT
ejpam-2420	5	1	later	later	ADV
ejpam-2420	5	2	,	,	PUNCT
ejpam-2420	5	3	dongho	dongho	NOUN
ejpam-2420	5	4	byeon	byeon	NOUN
ejpam-2420	5	5	proved	prove	VERB
ejpam-2420	5	6	a	a	DET
ejpam-2420	5	7	theorem	theorem	NOUN
ejpam-2420	5	8	and	and	CCONJ
ejpam-2420	5	9	corollary	corollary	ADJ
ejpam-2420	5	10	in	in	ADP
ejpam-2420	5	11	[	[	X
ejpam-2420	5	12	1	1	NUM
ejpam-2420	5	13	]	]	PUNCT
ejpam-2420	5	14	by	by	ADP
ejpam-2420	5	15	refining	refine	VERB
ejpam-2420	5	16	ono	ono	PROPN
ejpam-2420	5	17	’s	’s	PART
ejpam-2420	5	18	methods	method	NOUN
ejpam-2420	5	19	.	.	PUNCT
ejpam-2420	6	1	in	in	ADP
ejpam-2420	6	2	this	this	DET
ejpam-2420	6	3	paper	paper	NOUN
ejpam-2420	6	4	,	,	PUNCT
ejpam-2420	6	5	we	we	PRON
ejpam-2420	6	6	will	will	AUX
ejpam-2420	6	7	give	give	VERB
ejpam-2420	6	8	a	a	DET
ejpam-2420	6	9	theorem	theorem	NOUN
ejpam-2420	6	10	for	for	ADP
ejpam-2420	6	11	certain	certain	ADJ
ejpam-2420	6	12	real	real	ADJ
ejpam-2420	6	13	quadratic	quadratic	ADJ
ejpam-2420	6	14	fields	field	NOUN
ejpam-2420	6	15	by	by	ADP
ejpam-2420	6	16	considering	consider	VERB
ejpam-2420	6	17	above	above	ADP
ejpam-2420	6	18	mentioned	mention	VERB
ejpam-2420	6	19	studies	study	NOUN
ejpam-2420	6	20	.	.	PUNCT
ejpam-2420	7	1	to	to	PART
ejpam-2420	7	2	do	do	VERB
ejpam-2420	7	3	this	this	PRON
ejpam-2420	7	4	,	,	PUNCT
ejpam-2420	7	5	we	we	PRON
ejpam-2420	7	6	shall	shall	AUX
ejpam-2420	7	7	obtain	obtain	VERB
ejpam-2420	7	8	an	an	DET
ejpam-2420	7	9	upper	upper	ADJ
ejpam-2420	7	10	bound	bind	VERB
ejpam-2420	7	11	different	different	ADV
ejpam-2420	7	12	from	from	ADP
ejpam-2420	7	13	current	current	ADJ
ejpam-2420	7	14	bounds	bound	NOUN
ejpam-2420	7	15	for	for	ADP
ejpam-2420	7	16	l(1,χd	l(1,χd	NOUN
ejpam-2420	7	17	)	)	PUNCT
ejpam-2420	7	18	and	and	CCONJ
ejpam-2420	7	19	use	use	VERB
ejpam-2420	7	20	dirichlet	dirichlet	PROPN
ejpam-2420	7	21	’s	’s	PART
ejpam-2420	7	22	class	class	NOUN
ejpam-2420	7	23	number	number	NOUN
ejpam-2420	7	24	formula	formula	NOUN
ejpam-2420	7	25	.	.	PUNCT
ejpam-2420	8	1	2010	2010	NUM
ejpam-2420	8	2	mathematics	mathematic	NOUN
ejpam-2420	8	3	subject	subject	NOUN
ejpam-2420	8	4	classifications	classification	NOUN
ejpam-2420	8	5	:	:	PUNCT
ejpam-2420	8	6	11r29	11r29	NUM
ejpam-2420	8	7	key	key	ADJ
ejpam-2420	8	8	words	word	NOUN
ejpam-2420	8	9	and	and	CCONJ
ejpam-2420	8	10	phrases	phrase	NOUN
ejpam-2420	8	11	:	:	PUNCT
ejpam-2420	8	12	class	class	NOUN
ejpam-2420	8	13	number	number	NOUN
ejpam-2420	8	14	,	,	PUNCT
ejpam-2420	8	15	real	real	ADJ
ejpam-2420	8	16	quadratic	quadratic	ADJ
ejpam-2420	8	17	number	number	NOUN
ejpam-2420	8	18	field	field	NOUN
ejpam-2420	8	19	1	1	NUM
ejpam-2420	8	20	.	.	PUNCT
ejpam-2420	9	1	introduction	introduction	NOUN
ejpam-2420	9	2	let	let	VERB
ejpam-2420	9	3	zp	zp	PROPN
ejpam-2420	9	4	,	,	PUNCT
ejpam-2420	9	5	n	n	PRON
ejpam-2420	9	6	,	,	PUNCT
ejpam-2420	9	7	q	q	PUNCT
ejpam-2420	9	8	denote	denote	VERB
ejpam-2420	9	9	the	the	DET
ejpam-2420	9	10	the	the	DET
ejpam-2420	9	11	ring	ring	NOUN
ejpam-2420	9	12	of	of	ADP
ejpam-2420	9	13	p	p	NOUN
ejpam-2420	9	14	-	-	PUNCT
ejpam-2420	9	15	adic	adic	ADJ
ejpam-2420	9	16	integers	integer	NOUN
ejpam-2420	9	17	,	,	PUNCT
ejpam-2420	9	18	positive	positive	ADJ
ejpam-2420	9	19	integers	integer	NOUN
ejpam-2420	9	20	and	and	CCONJ
ejpam-2420	9	21	rational	rational	ADJ
ejpam-2420	9	22	numbers	number	NOUN
ejpam-2420	9	23	,	,	PUNCT
ejpam-2420	9	24	respectively	respectively	ADV
ejpam-2420	9	25	.	.	PUNCT
ejpam-2420	10	1	let	let	AUX
ejpam-2420	10	2	rp(d	rp(d	NOUN
ejpam-2420	10	3	)	)	PUNCT
ejpam-2420	10	4	denote	denote	VERB
ejpam-2420	10	5	the	the	DET
ejpam-2420	10	6	p	p	NOUN
ejpam-2420	10	7	-	-	PUNCT
ejpam-2420	10	8	adic	adic	ADJ
ejpam-2420	10	9	regulator	regulator	NOUN
ejpam-2420	10	10	of	of	ADP
ejpam-2420	10	11	k	k	PROPN
ejpam-2420	10	12	,	,	PUNCT
ejpam-2420	10	13	|.|p	|.|p	PROPN
ejpam-2420	10	14	denote	denote	VERB
ejpam-2420	10	15	the	the	DET
ejpam-2420	10	16	usual	usual	ADJ
ejpam-2420	10	17	multiplicative	multiplicative	ADJ
ejpam-2420	10	18	p	p	ADJ
ejpam-2420	10	19	-	-	PUNCT
ejpam-2420	10	20	adic	adic	ADJ
ejpam-2420	10	21	valuation	valuation	NOUN
ejpam-2420	10	22	normalized	normalize	VERB
ejpam-2420	10	23	|p|p	|p|p	PROPN
ejpam-2420	10	24	=	=	SYM
ejpam-2420	10	25	1	1	NUM
ejpam-2420	10	26	p	p	NOUN
ejpam-2420	10	27	,	,	PUNCT
ejpam-2420	10	28	and	and	CCONJ
ejpam-2420	10	29	let	let	VERB
ejpam-2420	10	30	l(s	l(s	PROPN
ejpam-2420	10	31	,	,	PUNCT
ejpam-2420	10	32	χd	χd	PROPN
ejpam-2420	10	33	)	)	PUNCT
ejpam-2420	10	34	denote	denote	VERB
ejpam-2420	10	35	the	the	DET
ejpam-2420	10	36	l	l	NOUN
ejpam-2420	10	37	-	-	NOUN
ejpam-2420	10	38	function	function	NOUN
ejpam-2420	10	39	attached	attach	VERB
ejpam-2420	10	40	to	to	ADP
ejpam-2420	10	41	χd	χd	PROPN
ejpam-2420	10	42	.	.	PUNCT
ejpam-2420	11	1	throughout	throughout	ADP
ejpam-2420	11	2	d	d	PROPN
ejpam-2420	11	3	∈	∈	PROPN
ejpam-2420	11	4	n	n	PRON
ejpam-2420	11	5	will	will	AUX
ejpam-2420	11	6	be	be	AUX
ejpam-2420	11	7	assumed	assume	VERB
ejpam-2420	11	8	square	square	ADJ
ejpam-2420	11	9	free	free	ADJ
ejpam-2420	11	10	,	,	PUNCT
ejpam-2420	11	11	k	k	PROPN
ejpam-2420	11	12	=	=	PUNCT
ejpam-2420	11	13	q	q	X
ejpam-2420	11	14	(	(	PUNCT
ejpam-2420	11	15	p	p	NOUN
ejpam-2420	11	16	d	d	NOUN
ejpam-2420	11	17	)	)	PUNCT
ejpam-2420	11	18	will	will	AUX
ejpam-2420	11	19	denote	denote	VERB
ejpam-2420	11	20	the	the	DET
ejpam-2420	11	21	real	real	ADJ
ejpam-2420	11	22	quadratic	quadratic	ADJ
ejpam-2420	11	23	field	field	NOUN
ejpam-2420	11	24	,	,	PUNCT
ejpam-2420	11	25	and	and	CCONJ
ejpam-2420	11	26	the	the	DET
ejpam-2420	11	27	class	class	NOUN
ejpam-2420	11	28	number	number	NOUN
ejpam-2420	11	29	of	of	ADP
ejpam-2420	11	30	k	k	PROPN
ejpam-2420	11	31	will	will	AUX
ejpam-2420	11	32	be	be	AUX
ejpam-2420	11	33	denoted	denote	VERB
ejpam-2420	11	34	by	by	ADP
ejpam-2420	11	35	h	h	PROPN
ejpam-2420	11	36	=	=	SYM
ejpam-2420	11	37	h(d	h(d	PROPN
ejpam-2420	11	38	)	)	PUNCT
ejpam-2420	11	39	.	.	PUNCT
ejpam-2420	12	1	let	let	VERB
ejpam-2420	12	2	∆	∆	PROPN
ejpam-2420	12	3	denote	denote	VERB
ejpam-2420	12	4	the	the	DET
ejpam-2420	12	5	discriminant	discriminant	NOUN
ejpam-2420	12	6	,	,	PUNCT
ejpam-2420	12	7	ǫd	ǫd	VERB
ejpam-2420	12	8	the	the	DET
ejpam-2420	12	9	fundamental	fundamental	ADJ
ejpam-2420	12	10	unit	unit	NOUN
ejpam-2420	12	11	of	of	ADP
ejpam-2420	12	12	k	k	PROPN
ejpam-2420	12	13	.	.	PUNCT
ejpam-2420	13	1	2	2	X
ejpam-2420	13	2	.	.	X
ejpam-2420	13	3	preliminaries	preliminary	NOUN
ejpam-2420	13	4	theorem	theorem	VERB
ejpam-2420	13	5	1	1	NUM
ejpam-2420	13	6	(	(	PUNCT
ejpam-2420	13	7	[	[	X
ejpam-2420	13	8	2	2	NUM
ejpam-2420	13	9	]	]	PUNCT
ejpam-2420	13	10	)	)	PUNCT
ejpam-2420	13	11	.	.	PUNCT
ejpam-2420	14	1	let	let	VERB
ejpam-2420	14	2	p	p	PRON
ejpam-2420	14	3	>	>	X
ejpam-2420	14	4	3	3	NUM
ejpam-2420	14	5	be	be	AUX
ejpam-2420	14	6	prime	prime	ADJ
ejpam-2420	14	7	.	.	PUNCT
ejpam-2420	15	1	if	if	SCONJ
ejpam-2420	15	2	there	there	PRON
ejpam-2420	15	3	is	be	VERB
ejpam-2420	15	4	a	a	DET
ejpam-2420	15	5	fundamental	fundamental	ADJ
ejpam-2420	15	6	discriminant	discriminant	NOUN
ejpam-2420	15	7	d0	d0	PROPN
ejpam-2420	15	8	coprime	coprime	ADV
ejpam-2420	15	9	to	to	ADP
ejpam-2420	15	10	p	p	NOUN
ejpam-2420	15	11	for	for	ADP
ejpam-2420	15	12	which	which	PRON
ejpam-2420	15	13	∗corresponding	∗corresponde	VERB
ejpam-2420	15	14	author	author	NOUN
ejpam-2420	15	15	.	.	PUNCT
ejpam-2420	16	1	email	email	NOUN
ejpam-2420	16	2	addresses	address	NOUN
ejpam-2420	16	3	:	:	PUNCT
ejpam-2420	16	4	aypekin@istanbul.edu.tr	aypekin@istanbul.edu.tr	PROPN
ejpam-2420	16	5	(	(	PUNCT
ejpam-2420	16	6	a.	a.	NOUN
ejpam-2420	16	7	pekin	pekin	PROPN
ejpam-2420	16	8	)	)	PUNCT
ejpam-2420	16	9	,	,	PUNCT
ejpam-2420	16	10	aydinc@trakya.edu.tr	aydinc@trakya.edu.tr	PROPN
ejpam-2420	16	11	(	(	PUNCT
ejpam-2420	16	12	a.	a.	NOUN
ejpam-2420	16	13	carus	carus	PROPN
ejpam-2420	16	14	)	)	PUNCT
ejpam-2420	16	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2420	17	1	526	526	NUM
ejpam-2420	17	2	c	c	X
ejpam-2420	17	3	©	©	NOUN
ejpam-2420	17	4	2015	2015	NUM
ejpam-2420	17	5	ejpam	ejpam	NOUN
ejpam-2420	17	6	all	all	DET
ejpam-2420	17	7	rights	right	NOUN
ejpam-2420	17	8	reserved	reserve	VERB
ejpam-2420	17	9	.	.	PUNCT
ejpam-2420	18	1	a.	a.	NOUN
ejpam-2420	18	2	pekin	pekin	PROPN
ejpam-2420	18	3	,	,	PUNCT
ejpam-2420	18	4	a.	a.	PROPN
ejpam-2420	18	5	carus	carus	PROPN
ejpam-2420	18	6	/	/	SYM
ejpam-2420	18	7	eur	eur	PROPN
ejpam-2420	18	8	.	.	PUNCT
ejpam-2420	19	1	j.	j.	PROPN
ejpam-2420	19	2	pure	pure	PROPN
ejpam-2420	19	3	appl	appl	PROPN
ejpam-2420	19	4	.	.	PROPN
ejpam-2420	19	5	math	math	PROPN
ejpam-2420	19	6	,	,	PUNCT
ejpam-2420	19	7	8	8	NUM
ejpam-2420	19	8	(	(	PUNCT
ejpam-2420	19	9	2015	2015	NUM
ejpam-2420	19	10	)	)	PUNCT
ejpam-2420	19	11	,	,	PUNCT
ejpam-2420	19	12	526	526	NUM
ejpam-2420	19	13	-	-	SYM
ejpam-2420	19	14	529	529	NUM
ejpam-2420	19	15	527	527	NUM
ejpam-2420	19	16	(	(	PUNCT
ejpam-2420	19	17	i	i	NOUN
ejpam-2420	19	18	)	)	PUNCT
ejpam-2420	19	19	(	(	PUNCT
ejpam-2420	19	20	−1	−1	NOUN
ejpam-2420	19	21	)	)	PUNCT
ejpam-2420	19	22	p−1	p−1	PROPN
ejpam-2420	19	23	2	2	NUM
ejpam-2420	19	24	d0	d0	NOUN
ejpam-2420	19	25	>	>	X
ejpam-2420	19	26	0	0	PUNCT
ejpam-2420	19	27	(	(	PUNCT
ejpam-2420	19	28	ii	ii	NOUN
ejpam-2420	19	29	)	)	PUNCT
ejpam-2420	19	30	|b	|b	PROPN
ejpam-2420	19	31	�	�	PROPN
ejpam-2420	19	32	p−1	p−1	PROPN
ejpam-2420	19	33	2	2	NUM
ejpam-2420	19	34	,	,	PUNCT
ejpam-2420	19	35	χd0	χd0	NOUN
ejpam-2420	19	36	�	�	NOUN
ejpam-2420	19	37	|=	|=	VERB
ejpam-2420	19	38	1	1	NUM
ejpam-2420	19	39	then	then	ADV
ejpam-2420	19	40	#	#	PROPN
ejpam-2420	19	41	§	§	PROPN
ejpam-2420	19	42	0	0	NUM
ejpam-2420	19	43	<	<	X
ejpam-2420	19	44	d	d	X
ejpam-2420	19	45	<	<	X
ejpam-2420	19	46	x	x	X
ejpam-2420	19	47	|	|	NOUN
ejpam-2420	19	48	h(d	h(d	PROPN
ejpam-2420	19	49	)	)	PUNCT
ejpam-2420	19	50	6≡	6≡	NUM
ejpam-2420	19	51	0	0	NUM
ejpam-2420	20	1	(	(	PUNCT
ejpam-2420	20	2	mod	mod	PROPN
ejpam-2420	20	3	p	p	X
ejpam-2420	20	4	)	)	PUNCT
ejpam-2420	20	5	,	,	PUNCT
ejpam-2420	20	6	χd(p	χd(p	SCONJ
ejpam-2420	20	7	)	)	PUNCT
ejpam-2420	20	8	=	=	SYM
ejpam-2420	20	9	0	0	NUM
ejpam-2420	20	10	,	,	PUNCT
ejpam-2420	20	11	|rp(d)p	|rp(d)p	NOUN
ejpam-2420	21	1	d	d	NOUN
ejpam-2420	21	2	|	|	ADV
ejpam-2420	21	3	p	p	NOUN
ejpam-2420	21	4	=	=	NOUN
ejpam-2420	21	5	1	1	NUM
ejpam-2420	21	6	ª	ª	PROPN
ejpam-2420	21	7	≫p	≫p	PROPN
ejpam-2420	21	8	p	p	X
ejpam-2420	21	9	x	x	X
ejpam-2420	21	10	logx	logx	PROPN
ejpam-2420	21	11	.	.	PUNCT
ejpam-2420	22	1	here	here	ADV
ejpam-2420	22	2	b	b	X
ejpam-2420	22	3	(	(	PUNCT
ejpam-2420	22	4	p−1	p−1	PROPN
ejpam-2420	22	5	2	2	NUM
ejpam-2420	22	6	,	,	PUNCT
ejpam-2420	22	7	χd0	χd0	NOUN
ejpam-2420	22	8	)	)	PUNCT
ejpam-2420	22	9	is	be	AUX
ejpam-2420	22	10	the	the	DET
ejpam-2420	22	11	p−1	p−1	PROPN
ejpam-2420	22	12	2	2	NUM
ejpam-2420	22	13	st	st	NOUN
ejpam-2420	22	14	generalized	generalize	VERB
ejpam-2420	22	15	bernoulli	bernoulli	NOUN
ejpam-2420	22	16	number	number	NOUN
ejpam-2420	22	17	with	with	ADP
ejpam-2420	22	18	character	character	NOUN
ejpam-2420	22	19	χd0	χd0	NOUN
ejpam-2420	22	20	.	.	PUNCT
ejpam-2420	23	1	d.	d.	PROPN
ejpam-2420	23	2	byeon	byeon	PROPN
ejpam-2420	23	3	given	give	VERB
ejpam-2420	23	4	in	in	ADP
ejpam-2420	23	5	[	[	X
ejpam-2420	23	6	1	1	X
ejpam-2420	23	7	]	]	X
ejpam-2420	23	8	the	the	DET
ejpam-2420	23	9	following	follow	VERB
ejpam-2420	23	10	theorems	theorem	NOUN
ejpam-2420	23	11	by	by	ADP
ejpam-2420	23	12	refining	refine	VERB
ejpam-2420	23	13	ono	ono	PROPN
ejpam-2420	23	14	’s	’s	PART
ejpam-2420	23	15	theorem	theorem	NOUN
ejpam-2420	23	16	above	above	ADV
ejpam-2420	23	17	mentioned	mention	VERB
ejpam-2420	23	18	for	for	ADP
ejpam-2420	23	19	any	any	DET
ejpam-2420	23	20	prime	prime	NOUN
ejpam-2420	23	21	p	p	X
ejpam-2420	23	22	>	>	X
ejpam-2420	23	23	3	3	NUM
ejpam-2420	23	24	.	.	PUNCT
ejpam-2420	23	25	theorem	theorem	NOUN
ejpam-2420	23	26	2	2	NUM
ejpam-2420	23	27	.	.	PUNCT
ejpam-2420	24	1	let	let	VERB
ejpam-2420	24	2	p	p	PRON
ejpam-2420	24	3	>	>	X
ejpam-2420	24	4	3	3	NUM
ejpam-2420	24	5	be	be	AUX
ejpam-2420	24	6	prime	prime	ADJ
ejpam-2420	24	7	.	.	PUNCT
ejpam-2420	25	1	(	(	PUNCT
ejpam-2420	25	2	a	a	X
ejpam-2420	25	3	)	)	PUNCT
ejpam-2420	25	4	if	if	SCONJ
ejpam-2420	25	5	p	p	PRON
ejpam-2420	25	6	≡	≡	PROPN
ejpam-2420	25	7	1	1	NUM
ejpam-2420	25	8	(	(	PUNCT
ejpam-2420	25	9	mod	mod	NOUN
ejpam-2420	25	10	4	4	NUM
ejpam-2420	25	11	)	)	PUNCT
ejpam-2420	25	12	,	,	PUNCT
ejpam-2420	25	13	then	then	ADV
ejpam-2420	25	14	the	the	DET
ejpam-2420	25	15	fundamental	fundamental	ADJ
ejpam-2420	25	16	discriminant	discriminant	NOUN
ejpam-2420	25	17	d0	d0	PROPN
ejpam-2420	25	18	>	>	X
ejpam-2420	25	19	0	0	NUM
ejpam-2420	25	20	of	of	ADP
ejpam-2420	25	21	the	the	DET
ejpam-2420	25	22	real	real	ADJ
ejpam-2420	25	23	quadratic	quadratic	ADJ
ejpam-2420	25	24	field	field	NOUN
ejpam-2420	25	25	q	q	NOUN
ejpam-2420	25	26	(	(	PUNCT
ejpam-2420	25	27	p	p	NOUN
ejpam-2420	25	28	p−	p−	NOUN
ejpam-2420	25	29	2	2	NUM
ejpam-2420	25	30	)	)	PUNCT
ejpam-2420	25	31	satisfies	satisfy	VERB
ejpam-2420	25	32	the	the	DET
ejpam-2420	25	33	conditions	condition	NOUN
ejpam-2420	25	34	(	(	PUNCT
ejpam-2420	25	35	i	i	NOUN
ejpam-2420	25	36	)	)	PUNCT
ejpam-2420	25	37	and	and	CCONJ
ejpam-2420	25	38	(	(	PUNCT
ejpam-2420	25	39	ii	ii	NOUN
ejpam-2420	25	40	)	)	PUNCT
ejpam-2420	25	41	.	.	PUNCT
ejpam-2420	26	1	(	(	PUNCT
ejpam-2420	26	2	b	b	X
ejpam-2420	26	3	)	)	PUNCT
ejpam-2420	26	4	if	if	SCONJ
ejpam-2420	26	5	p	p	PRON
ejpam-2420	26	6	≡	≡	PROPN
ejpam-2420	26	7	3	3	NUM
ejpam-2420	26	8	(	(	PUNCT
ejpam-2420	26	9	mod	mod	NOUN
ejpam-2420	26	10	4	4	NUM
ejpam-2420	26	11	)	)	PUNCT
ejpam-2420	26	12	,	,	PUNCT
ejpam-2420	26	13	then	then	ADV
ejpam-2420	26	14	the	the	DET
ejpam-2420	26	15	fundamental	fundamental	ADJ
ejpam-2420	26	16	discriminant	discriminant	NOUN
ejpam-2420	26	17	d0	d0	NOUN
ejpam-2420	26	18	<	<	X
ejpam-2420	26	19	0	0	NUM
ejpam-2420	26	20	of	of	ADP
ejpam-2420	26	21	the	the	DET
ejpam-2420	26	22	real	real	ADJ
ejpam-2420	26	23	quadratic	quadratic	ADJ
ejpam-2420	26	24	field	field	NOUN
ejpam-2420	26	25	q	q	NOUN
ejpam-2420	26	26	(	(	PUNCT
ejpam-2420	26	27	p−(p−	p−(p−	VERB
ejpam-2420	26	28	4	4	NUM
ejpam-2420	26	29	)	)	PUNCT
ejpam-2420	26	30	satisfies	satisfy	VERB
ejpam-2420	26	31	the	the	DET
ejpam-2420	26	32	conditions	condition	NOUN
ejpam-2420	26	33	(	(	PUNCT
ejpam-2420	26	34	i	i	NOUN
ejpam-2420	26	35	)	)	PUNCT
ejpam-2420	26	36	and	and	CCONJ
ejpam-2420	26	37	(	(	PUNCT
ejpam-2420	26	38	ii	ii	NOUN
ejpam-2420	26	39	)	)	PUNCT
ejpam-2420	26	40	.	.	PUNCT
ejpam-2420	27	1	theorem	theorem	NOUN
ejpam-2420	27	2	3	3	X
ejpam-2420	27	3	.	.	PUNCT
ejpam-2420	28	1	let	let	VERB
ejpam-2420	28	2	p	p	PRON
ejpam-2420	28	3	>	>	X
ejpam-2420	28	4	3	3	NUM
ejpam-2420	28	5	be	be	AUX
ejpam-2420	28	6	prime	prime	ADJ
ejpam-2420	28	7	.	.	PUNCT
ejpam-2420	29	1	then	then	ADV
ejpam-2420	29	2	#	#	PROPN
ejpam-2420	29	3	§	§	PROPN
ejpam-2420	29	4	0	0	NUM
ejpam-2420	29	5	<	<	X
ejpam-2420	29	6	d	d	X
ejpam-2420	29	7	<	<	X
ejpam-2420	29	8	x	x	X
ejpam-2420	29	9	|	|	NOUN
ejpam-2420	29	10	h(d	h(d	PROPN
ejpam-2420	29	11	)	)	PUNCT
ejpam-2420	29	12	6≡	6≡	NUM
ejpam-2420	29	13	0	0	NUM
ejpam-2420	30	1	(	(	PUNCT
ejpam-2420	30	2	mod	mod	PROPN
ejpam-2420	30	3	p	p	X
ejpam-2420	30	4	)	)	PUNCT
ejpam-2420	30	5	,	,	PUNCT
ejpam-2420	30	6	χd(p	χd(p	SCONJ
ejpam-2420	30	7	)	)	PUNCT
ejpam-2420	30	8	=	=	SYM
ejpam-2420	30	9	δ	δ	PROPN
ejpam-2420	30	10	,	,	PUNCT
ejpam-2420	30	11	|rp(d)|p	|rp(d)|p	PUNCT
ejpam-2420	30	12	=	=	SYM
ejpam-2420	31	1	1	1	NUM
ejpam-2420	31	2	p	p	NOUN
ejpam-2420	31	3	ª	ª	X
ejpam-2420	31	4	≫p	≫p	PRON
ejpam-2420	31	5	p	p	X
ejpam-2420	31	6	x	x	X
ejpam-2420	31	7	logx	logx	NOUN
ejpam-2420	31	8	.	.	PUNCT
ejpam-2420	32	1	3	3	X
ejpam-2420	32	2	.	.	X
ejpam-2420	32	3	main	main	ADJ
ejpam-2420	32	4	theorem	theorem	ADJ
ejpam-2420	32	5	main	main	ADJ
ejpam-2420	32	6	theorem	theorem	NOUN
ejpam-2420	32	7	.	.	PUNCT
ejpam-2420	33	1	let	let	VERB
ejpam-2420	33	2	p	p	PRON
ejpam-2420	33	3	>	>	X
ejpam-2420	33	4	3	3	NUM
ejpam-2420	33	5	be	be	AUX
ejpam-2420	33	6	a	a	DET
ejpam-2420	33	7	prime	prime	NOUN
ejpam-2420	33	8	.	.	PUNCT
ejpam-2420	34	1	if	if	SCONJ
ejpam-2420	34	2	p	p	DET
ejpam-2420	34	3	≡	≡	PROPN
ejpam-2420	34	4	3	3	NUM
ejpam-2420	34	5	(	(	PUNCT
ejpam-2420	34	6	mod	mod	NOUN
ejpam-2420	34	7	4	4	NUM
ejpam-2420	34	8	)	)	PUNCT
ejpam-2420	34	9	,	,	PUNCT
ejpam-2420	34	10	then	then	ADV
ejpam-2420	34	11	the	the	DET
ejpam-2420	34	12	fundamental	fundamental	ADJ
ejpam-2420	34	13	discriminant	discriminant	NOUN
ejpam-2420	34	14	d0	d0	PROPN
ejpam-2420	34	15	>	>	X
ejpam-2420	34	16	0	0	NUM
ejpam-2420	34	17	of	of	ADP
ejpam-2420	34	18	the	the	DET
ejpam-2420	34	19	real	real	ADJ
ejpam-2420	34	20	quadratic	quadratic	ADJ
ejpam-2420	34	21	fields	field	NOUN
ejpam-2420	34	22	k	k	X
ejpam-2420	35	1	=	=	NOUN
ejpam-2420	35	2	q	q	X
ejpam-2420	35	3	(	(	PUNCT
ejpam-2420	35	4	p	p	NOUN
ejpam-2420	35	5	p2	p2	PROPN
ejpam-2420	35	6	−	−	PROPN
ejpam-2420	35	7	4	4	NUM
ejpam-2420	35	8	)	)	PUNCT
ejpam-2420	35	9	and	and	CCONJ
ejpam-2420	35	10	k	k	X
ejpam-2420	35	11	=	=	NOUN
ejpam-2420	35	12	q	q	X
ejpam-2420	35	13	(	(	PUNCT
ejpam-2420	35	14	p	p	NOUN
ejpam-2420	35	15	p2	p2	PROPN
ejpam-2420	35	16	−	−	PROPN
ejpam-2420	35	17	2	2	NUM
ejpam-2420	35	18	)	)	PUNCT
ejpam-2420	35	19	satisfies	satisfy	VERB
ejpam-2420	35	20	the	the	DET
ejpam-2420	35	21	conditions	condition	NOUN
ejpam-2420	35	22	(	(	PUNCT
ejpam-2420	35	23	i	i	NOUN
ejpam-2420	35	24	)	)	PUNCT
ejpam-2420	35	25	and	and	CCONJ
ejpam-2420	35	26	(	(	PUNCT
ejpam-2420	35	27	ii	ii	NOUN
ejpam-2420	35	28	)	)	PUNCT
ejpam-2420	35	29	.	.	PUNCT
ejpam-2420	36	1	in	in	ADP
ejpam-2420	36	2	order	order	NOUN
ejpam-2420	36	3	to	to	PART
ejpam-2420	36	4	prove	prove	VERB
ejpam-2420	36	5	the	the	DET
ejpam-2420	36	6	main	main	ADJ
ejpam-2420	36	7	theorem	theorem	NOUN
ejpam-2420	36	8	we	we	PRON
ejpam-2420	36	9	need	need	VERB
ejpam-2420	36	10	the	the	DET
ejpam-2420	36	11	following	follow	VERB
ejpam-2420	36	12	lemmas	lemmas	NOUN
ejpam-2420	36	13	.	.	PUNCT
ejpam-2420	37	1	lemma	lemma	PROPN
ejpam-2420	37	2	1	1	X
ejpam-2420	37	3	.	.	PUNCT
ejpam-2420	38	1	assume	assume	VERB
ejpam-2420	38	2	d	d	X
ejpam-2420	38	3	is	be	AUX
ejpam-2420	38	4	a	a	DET
ejpam-2420	38	5	prime	prime	NOUN
ejpam-2420	38	6	.	.	PUNCT
ejpam-2420	39	1	(	(	PUNCT
ejpam-2420	39	2	i	i	NOUN
ejpam-2420	39	3	)	)	PUNCT
ejpam-2420	39	4	if	if	SCONJ
ejpam-2420	39	5	d	d	PROPN
ejpam-2420	39	6	≡	≡	PROPN
ejpam-2420	39	7	1	1	NUM
ejpam-2420	39	8	(	(	PUNCT
ejpam-2420	39	9	mod	mod	NOUN
ejpam-2420	39	10	4	4	NUM
ejpam-2420	39	11	)	)	PUNCT
ejpam-2420	39	12	,	,	PUNCT
ejpam-2420	39	13	we	we	PRON
ejpam-2420	39	14	have	have	VERB
ejpam-2420	39	15	ǫd	ǫd	NUM
ejpam-2420	39	16	>	>	X
ejpam-2420	39	17	¨	¨	PROPN
ejpam-2420	39	18	‖pd∓	‖pd∓	PROPN
ejpam-2420	40	1	1‖	1‖	NUM
ejpam-2420	41	1	if	if	SCONJ
ejpam-2420	41	2	d	d	NOUN
ejpam-2420	41	3	=	=	SYM
ejpam-2420	41	4	n2	n2	NOUN
ejpam-2420	41	5	∓	∓	PROPN
ejpam-2420	41	6	4	4	NUM
ejpam-2420	41	7	,	,	PUNCT
ejpam-2420	41	8	(	(	PUNCT
ejpam-2420	41	9	n	n	X
ejpam-2420	41	10	∈	∈	PROPN
ejpam-2420	41	11	z	z	PROPN
ejpam-2420	41	12	)	)	PUNCT
ejpam-2420	41	13	,	,	PUNCT
ejpam-2420	42	1	‖p4d∓	‖p4d∓	NUM
ejpam-2420	42	2	1‖	1‖	NUM
ejpam-2420	42	3	otherwise	otherwise	ADV
ejpam-2420	42	4	,	,	PUNCT
ejpam-2420	42	5	where	where	SCONJ
ejpam-2420	42	6	”	"	PUNCT
ejpam-2420	42	7	‖	‖	PROPN
ejpam-2420	42	8	∗	∗	NOUN
ejpam-2420	42	9	‖	‖	PROPN
ejpam-2420	42	10	”	"	PUNCT
ejpam-2420	42	11	represents	represent	VERB
ejpam-2420	42	12	great	great	ADJ
ejpam-2420	42	13	value	value	NOUN
ejpam-2420	42	14	function	function	NOUN
ejpam-2420	42	15	of	of	ADP
ejpam-2420	42	16	a	a	DET
ejpam-2420	42	17	real	real	ADJ
ejpam-2420	42	18	number	number	NOUN
ejpam-2420	42	19	.	.	PUNCT
ejpam-2420	43	1	(	(	PUNCT
ejpam-2420	43	2	ii	ii	NOUN
ejpam-2420	43	3	)	)	PUNCT
ejpam-2420	43	4	if	if	SCONJ
ejpam-2420	43	5	d	d	PROPN
ejpam-2420	43	6	≡	≡	PROPN
ejpam-2420	43	7	3	3	NUM
ejpam-2420	43	8	(	(	PUNCT
ejpam-2420	43	9	mod	mod	NOUN
ejpam-2420	43	10	4	4	NUM
ejpam-2420	43	11	)	)	PUNCT
ejpam-2420	43	12	,	,	PUNCT
ejpam-2420	43	13	we	we	PRON
ejpam-2420	43	14	have	have	VERB
ejpam-2420	43	15	ǫd	ǫd	NUM
ejpam-2420	43	16	>	>	X
ejpam-2420	44	1	¨	¨	NOUN
ejpam-2420	44	2	2d∓	2d∓	NUM
ejpam-2420	44	3	1	1	NUM
ejpam-2420	44	4	if	if	SCONJ
ejpam-2420	44	5	d	d	NOUN
ejpam-2420	44	6	=	=	SYM
ejpam-2420	44	7	n2	n2	NOUN
ejpam-2420	44	8	∓	∓	PROPN
ejpam-2420	44	9	2	2	NUM
ejpam-2420	44	10	,	,	PUNCT
ejpam-2420	44	11	8d∓	8d∓	NUM
ejpam-2420	44	12	1	1	NUM
ejpam-2420	44	13	otherwise	otherwise	ADV
ejpam-2420	44	14	.	.	PUNCT
ejpam-2420	45	1	a.	a.	NOUN
ejpam-2420	45	2	pekin	pekin	PROPN
ejpam-2420	45	3	,	,	PUNCT
ejpam-2420	45	4	a.	a.	PROPN
ejpam-2420	45	5	carus	carus	PROPN
ejpam-2420	45	6	/	/	SYM
ejpam-2420	45	7	eur	eur	PROPN
ejpam-2420	45	8	.	.	PUNCT
ejpam-2420	46	1	j.	j.	PROPN
ejpam-2420	46	2	pure	pure	PROPN
ejpam-2420	46	3	appl	appl	PROPN
ejpam-2420	46	4	.	.	PROPN
ejpam-2420	46	5	math	math	PROPN
ejpam-2420	46	6	,	,	PUNCT
ejpam-2420	46	7	8	8	NUM
ejpam-2420	46	8	(	(	PUNCT
ejpam-2420	46	9	2015	2015	NUM
ejpam-2420	46	10	)	)	PUNCT
ejpam-2420	46	11	,	,	PUNCT
ejpam-2420	46	12	526	526	NUM
ejpam-2420	46	13	-	-	SYM
ejpam-2420	46	14	529	529	NUM
ejpam-2420	46	15	528	528	NUM
ejpam-2420	46	16	proof	proof	NOUN
ejpam-2420	46	17	.	.	PUNCT
ejpam-2420	47	1	(	(	PUNCT
ejpam-2420	47	2	i	i	NOUN
ejpam-2420	47	3	)	)	PUNCT
ejpam-2420	47	4	let	let	VERB
ejpam-2420	47	5	ǫd	ǫd	NUM
ejpam-2420	47	6	=	=	SYM
ejpam-2420	47	7	t+u	t+u	X
ejpam-2420	47	8	p	p	X
ejpam-2420	47	9	d	d	PROPN
ejpam-2420	47	10	2	2	NUM
ejpam-2420	47	11	>	>	SYM
ejpam-2420	47	12	1	1	NUM
ejpam-2420	47	13	be	be	AUX
ejpam-2420	47	14	the	the	DET
ejpam-2420	47	15	fundamental	fundamental	ADJ
ejpam-2420	47	16	unit	unit	NOUN
ejpam-2420	47	17	of	of	ADP
ejpam-2420	47	18	k	k	PROPN
ejpam-2420	48	1	=	=	NOUN
ejpam-2420	48	2	q	q	X
ejpam-2420	48	3	(	(	PUNCT
ejpam-2420	48	4	p	p	NOUN
ejpam-2420	48	5	d	d	NOUN
ejpam-2420	48	6	)	)	PUNCT
ejpam-2420	48	7	.	.	PUNCT
ejpam-2420	49	1	since	since	SCONJ
ejpam-2420	49	2	ǫd	ǫd	NOUN
ejpam-2420	49	3	is	be	AUX
ejpam-2420	49	4	equal	equal	ADJ
ejpam-2420	49	5	to	to	ADP
ejpam-2420	49	6	the	the	DET
ejpam-2420	49	7	fundamental	fundamental	ADJ
ejpam-2420	49	8	solution	solution	NOUN
ejpam-2420	49	9	of	of	ADP
ejpam-2420	49	10	the	the	DET
ejpam-2420	49	11	pell	pell	NOUN
ejpam-2420	49	12	’s	’s	PART
ejpam-2420	49	13	equation	equation	NOUN
ejpam-2420	50	1	x2	x2	INTJ
ejpam-2420	50	2	−	−	PROPN
ejpam-2420	51	1	d	d	NOUN
ejpam-2420	51	2	y2	y2	NOUN
ejpam-2420	51	3	=	=	SYM
ejpam-2420	51	4	∓4	∓4	PROPN
ejpam-2420	51	5	,	,	PUNCT
ejpam-2420	51	6	then	then	ADV
ejpam-2420	51	7	we	we	PRON
ejpam-2420	51	8	can	can	AUX
ejpam-2420	51	9	write	write	VERB
ejpam-2420	51	10	ǫd	ǫd	NUM
ejpam-2420	51	11	2	2	NUM
ejpam-2420	51	12	=	=	SYM
ejpam-2420	51	13	(	(	PUNCT
ejpam-2420	51	14	t	t	PROPN
ejpam-2420	51	15	+	+	CCONJ
ejpam-2420	51	16	u	u	NOUN
ejpam-2420	51	17	p	p	PROPN
ejpam-2420	51	18	d	d	PROPN
ejpam-2420	51	19	2	2	NUM
ejpam-2420	51	20	)	)	PUNCT
ejpam-2420	51	21	2	2	NUM
ejpam-2420	51	22	=	=	SYM
ejpam-2420	51	23	1	1	NUM
ejpam-2420	51	24	4	4	NUM
ejpam-2420	51	25	(	(	PUNCT
ejpam-2420	51	26	p	p	NOUN
ejpam-2420	51	27	du2	du2	PROPN
ejpam-2420	51	28	∓	∓	NOUN
ejpam-2420	51	29	4	4	NUM
ejpam-2420	51	30	+	+	SYM
ejpam-2420	51	31	u	u	NOUN
ejpam-2420	51	32	p	p	PROPN
ejpam-2420	51	33	d	d	PROPN
ejpam-2420	51	34	)	)	PUNCT
ejpam-2420	51	35	2	2	NUM
ejpam-2420	51	36	>	>	PUNCT
ejpam-2420	51	37	du2	du2	PROPN
ejpam-2420	51	38	∓	∓	PROPN
ejpam-2420	51	39	1p	1p	NUM
ejpam-2420	51	40	2	2	NUM
ejpam-2420	51	41	≥	≥	NOUN
ejpam-2420	51	42	(	(	PUNCT
ejpam-2420	51	43	d∓1p	d∓1p	ADJ
ejpam-2420	51	44	2	2	NUM
ejpam-2420	51	45	if	if	SCONJ
ejpam-2420	51	46	u=	u=	ADJ
ejpam-2420	51	47	1	1	NUM
ejpam-2420	51	48	,	,	PUNCT
ejpam-2420	51	49	4d∓1p	4d∓1p	NUM
ejpam-2420	51	50	2	2	NUM
ejpam-2420	51	51	if	if	SCONJ
ejpam-2420	51	52	u	u	NOUN
ejpam-2420	51	53	>	>	X
ejpam-2420	51	54	1	1	NUM
ejpam-2420	51	55	.	.	PUNCT
ejpam-2420	52	1	and	and	CCONJ
ejpam-2420	52	2	ǫd	ǫd	VERB
ejpam-2420	52	3	>	>	X
ejpam-2420	52	4	¨	¨	PROPN
ejpam-2420	52	5	‖pd∓	‖pd∓	PROPN
ejpam-2420	52	6	1‖	1‖	NUM
ejpam-2420	53	1	if	if	SCONJ
ejpam-2420	53	2	d	d	NOUN
ejpam-2420	53	3	=	=	SYM
ejpam-2420	53	4	n2	n2	NOUN
ejpam-2420	53	5	∓	∓	PROPN
ejpam-2420	53	6	4	4	NUM
ejpam-2420	53	7	‖p4d∓	‖p4d∓	NUM
ejpam-2420	53	8	1‖	1‖	NUM
ejpam-2420	53	9	otherwise	otherwise	ADV
ejpam-2420	53	10	.	.	PUNCT
ejpam-2420	54	1	(	(	PUNCT
ejpam-2420	54	2	ii	ii	NOUN
ejpam-2420	54	3	)	)	PUNCT
ejpam-2420	54	4	if	if	SCONJ
ejpam-2420	54	5	d	d	PROPN
ejpam-2420	54	6	≡	≡	PROPN
ejpam-2420	54	7	3	3	NUM
ejpam-2420	54	8	(	(	PUNCT
ejpam-2420	54	9	mod	mod	NOUN
ejpam-2420	54	10	4	4	NUM
ejpam-2420	54	11	)	)	PUNCT
ejpam-2420	54	12	,	,	PUNCT
ejpam-2420	54	13	then	then	ADV
ejpam-2420	54	14	we	we	PRON
ejpam-2420	54	15	have	have	VERB
ejpam-2420	54	16	ǫ2	ǫ2	NOUN
ejpam-2420	54	17	d	d	NOUN
ejpam-2420	54	18	=	=	PUNCT
ejpam-2420	54	19	(	(	PUNCT
ejpam-2420	54	20	t+u	t+u	NUM
ejpam-2420	54	21	p	p	X
ejpam-2420	54	22	d	d	PROPN
ejpam-2420	54	23	2	2	NUM
ejpam-2420	54	24	)	)	PUNCT
ejpam-2420	54	25	2	2	NUM
ejpam-2420	54	26	from	from	ADP
ejpam-2420	54	27	the	the	DET
ejpam-2420	54	28	least	least	ADV
ejpam-2420	54	29	positive	positive	ADJ
ejpam-2420	54	30	integer	integer	NOUN
ejpam-2420	54	31	solution	solution	NOUN
ejpam-2420	54	32	(	(	PUNCT
ejpam-2420	54	33	x	x	X
ejpam-2420	54	34	,	,	PUNCT
ejpam-2420	54	35	y	y	PROPN
ejpam-2420	54	36	)	)	PUNCT
ejpam-2420	54	37	=	=	SYM
ejpam-2420	54	38	(	(	PUNCT
ejpam-2420	54	39	t	t	PROPN
ejpam-2420	54	40	,	,	PUNCT
ejpam-2420	54	41	u	u	NOUN
ejpam-2420	54	42	)	)	PUNCT
ejpam-2420	54	43	of	of	ADP
ejpam-2420	54	44	pell	pell	PROPN
ejpam-2420	54	45	’s	’s	PART
ejpam-2420	54	46	equation	equation	NOUN
ejpam-2420	55	1	x2	x2	INTJ
ejpam-2420	55	2	−	−	PROPN
ejpam-2420	56	1	d	d	NOUN
ejpam-2420	56	2	y2	y2	NOUN
ejpam-2420	56	3	=	=	PUNCT
ejpam-2420	56	4	∓1	∓1	PROPN
ejpam-2420	57	1	[	[	X
ejpam-2420	57	2	4	4	NUM
ejpam-2420	57	3	]	]	PUNCT
ejpam-2420	57	4	.	.	PUNCT
ejpam-2420	58	1	similarly	similarly	ADV
ejpam-2420	58	2	,	,	PUNCT
ejpam-2420	58	3	we	we	PRON
ejpam-2420	58	4	can	can	AUX
ejpam-2420	58	5	write	write	VERB
ejpam-2420	58	6	ǫd	ǫd	NUM
ejpam-2420	58	7	>	>	PUNCT
ejpam-2420	58	8	¨	¨	NOUN
ejpam-2420	58	9	2d∓	2d∓	NUM
ejpam-2420	58	10	1	1	NUM
ejpam-2420	58	11	if	if	SCONJ
ejpam-2420	58	12	d	d	NOUN
ejpam-2420	58	13	=	=	SYM
ejpam-2420	58	14	n2	n2	NOUN
ejpam-2420	58	15	∓	∓	PROPN
ejpam-2420	58	16	2	2	NUM
ejpam-2420	58	17	for	for	ADP
ejpam-2420	58	18	some	some	DET
ejpam-2420	58	19	odd	odd	ADJ
ejpam-2420	58	20	integer	integer	NOUN
ejpam-2420	58	21	n	n	CCONJ
ejpam-2420	58	22	,	,	PUNCT
ejpam-2420	58	23	8d∓	8d∓	NUM
ejpam-2420	58	24	1	1	NUM
ejpam-2420	58	25	in	in	ADP
ejpam-2420	58	26	the	the	DET
ejpam-2420	58	27	other	other	ADJ
ejpam-2420	58	28	cases	case	NOUN
ejpam-2420	58	29	.	.	PUNCT
ejpam-2420	59	1	lemma	lemma	PROPN
ejpam-2420	59	2	2	2	X
ejpam-2420	59	3	.	.	PUNCT
ejpam-2420	60	1	let	let	VERB
ejpam-2420	60	2	d	d	X
ejpam-2420	60	3	∈	∈	PROPN
ejpam-2420	60	4	n	n	AUX
ejpam-2420	60	5	be	be	AUX
ejpam-2420	60	6	square	square	ADV
ejpam-2420	60	7	free	free	ADJ
ejpam-2420	60	8	,	,	PUNCT
ejpam-2420	60	9	then	then	ADV
ejpam-2420	60	10	h(d	h(d	PRON
ejpam-2420	60	11	)	)	PUNCT
ejpam-2420	60	12	<	<	X
ejpam-2420	61	1	p	p	X
ejpam-2420	61	2	d.	d.	PROPN
ejpam-2420	61	3	in	in	ADP
ejpam-2420	61	4	order	order	NOUN
ejpam-2420	61	5	to	to	PART
ejpam-2420	61	6	prove	prove	VERB
ejpam-2420	61	7	this	this	PRON
ejpam-2420	61	8	we	we	PRON
ejpam-2420	61	9	need	need	VERB
ejpam-2420	61	10	the	the	DET
ejpam-2420	61	11	following	follow	VERB
ejpam-2420	61	12	lemma	lemma	PROPN
ejpam-2420	62	1	[	[	X
ejpam-2420	62	2	3	3	NUM
ejpam-2420	62	3	]	]	PUNCT
ejpam-2420	62	4	.	.	PUNCT
ejpam-2420	63	1	lemma	lemma	PROPN
ejpam-2420	63	2	3	3	X
ejpam-2420	63	3	.	.	PUNCT
ejpam-2420	63	4	let	let	VERB
ejpam-2420	63	5	γ	γ	NOUN
ejpam-2420	63	6	be	be	AUX
ejpam-2420	63	7	euler	euler	NOUN
ejpam-2420	63	8	’s	’s	NOUN
ejpam-2420	63	9	constant	constant	ADJ
ejpam-2420	63	10	,	,	PUNCT
ejpam-2420	63	11	then	then	ADV
ejpam-2420	63	12	|l(1,χd)|	|l(1,χd)|	NUM
ejpam-2420	63	13	≤	≤	NOUN
ejpam-2420	63	14	¨	¨	NOUN
ejpam-2420	63	15	1	1	NUM
ejpam-2420	63	16	4(log∆+	4(log∆+	NUM
ejpam-2420	63	17	2	2	NUM
ejpam-2420	63	18	+	+	NUM
ejpam-2420	63	19	γ−	γ−	PROPN
ejpam-2420	63	20	logπ	logπ	NOUN
ejpam-2420	63	21	)	)	PUNCT
ejpam-2420	63	22	if	if	SCONJ
ejpam-2420	63	23	2	2	NUM
ejpam-2420	63	24	|∆	|∆	NOUN
ejpam-2420	63	25	,	,	PUNCT
ejpam-2420	63	26	1	1	NUM
ejpam-2420	63	27	2(log∆+	2(log∆+	NUM
ejpam-2420	63	28	2	2	NUM
ejpam-2420	63	29	+	+	NUM
ejpam-2420	63	30	γ−	γ−	NUM
ejpam-2420	63	31	log4π	log4π	ADV
ejpam-2420	63	32	)	)	PUNCT
ejpam-2420	63	33	otherwise	otherwise	ADV
ejpam-2420	63	34	.	.	PUNCT
ejpam-2420	64	1	proof	proof	NOUN
ejpam-2420	64	2	.	.	PUNCT
ejpam-2420	65	1	[	[	X
ejpam-2420	65	2	lemma	lemma	PROPN
ejpam-2420	65	3	2	2	NUM
ejpam-2420	65	4	]	]	PUNCT
ejpam-2420	65	5	by	by	ADP
ejpam-2420	65	6	dirichlet	dirichlet	PROPN
ejpam-2420	65	7	’s	’s	PART
ejpam-2420	65	8	class	class	NOUN
ejpam-2420	65	9	number	number	NOUN
ejpam-2420	65	10	formula	formula	NOUN
ejpam-2420	65	11	,	,	PUNCT
ejpam-2420	65	12	we	we	PRON
ejpam-2420	65	13	have	have	VERB
ejpam-2420	65	14	h(d	h(d	PRON
ejpam-2420	65	15	)	)	PUNCT
ejpam-2420	66	1	=	=	PUNCT
ejpam-2420	67	1	p	p	NOUN
ejpam-2420	67	2	∆	∆	PROPN
ejpam-2420	67	3	2logǫd	2logǫd	NUM
ejpam-2420	67	4	|l(1,χd)|	|l(1,χd)|	NUM
ejpam-2420	67	5	where	where	SCONJ
ejpam-2420	67	6	∆	∆	PROPN
ejpam-2420	67	7	is	be	AUX
ejpam-2420	67	8	a	a	DET
ejpam-2420	67	9	fundamental	fundamental	ADJ
ejpam-2420	67	10	discriminant	discriminant	NOUN
ejpam-2420	67	11	of	of	ADP
ejpam-2420	67	12	a	a	DET
ejpam-2420	67	13	quadratic	quadratic	ADJ
ejpam-2420	67	14	field	field	NOUN
ejpam-2420	67	15	defined	define	VERB
ejpam-2420	67	16	by	by	ADP
ejpam-2420	67	17	∆=	∆=	NOUN
ejpam-2420	67	18	¨	¨	NOUN
ejpam-2420	67	19	4d	4d	NUM
ejpam-2420	67	20	if	if	SCONJ
ejpam-2420	67	21	d	d	PROPN
ejpam-2420	67	22	≡	≡	PROPN
ejpam-2420	67	23	2,3	2,3	NUM
ejpam-2420	67	24	(	(	PUNCT
ejpam-2420	67	25	mod	mod	PROPN
ejpam-2420	67	26	4	4	NUM
ejpam-2420	67	27	)	)	PUNCT
ejpam-2420	67	28	,	,	PUNCT
ejpam-2420	68	1	d	d	X
ejpam-2420	68	2	if	if	SCONJ
ejpam-2420	68	3	d	d	PROPN
ejpam-2420	68	4	≡	≡	PROPN
ejpam-2420	68	5	1	1	NUM
ejpam-2420	68	6	(	(	PUNCT
ejpam-2420	68	7	mod	mod	NOUN
ejpam-2420	68	8	4	4	NUM
ejpam-2420	68	9	)	)	PUNCT
ejpam-2420	68	10	.	.	PUNCT
ejpam-2420	69	1	first	first	ADV
ejpam-2420	69	2	,	,	PUNCT
ejpam-2420	69	3	we	we	PRON
ejpam-2420	69	4	consider	consider	VERB
ejpam-2420	69	5	the	the	DET
ejpam-2420	69	6	case	case	NOUN
ejpam-2420	69	7	d	d	X
ejpam-2420	69	8	≡	≡	PROPN
ejpam-2420	69	9	1	1	NUM
ejpam-2420	69	10	(	(	PUNCT
ejpam-2420	69	11	mod	mod	NOUN
ejpam-2420	69	12	4	4	NUM
ejpam-2420	69	13	)	)	PUNCT
ejpam-2420	69	14	and	and	CCONJ
ejpam-2420	69	15	d	d	NOUN
ejpam-2420	69	16	=	=	SYM
ejpam-2420	69	17	n2	n2	NOUN
ejpam-2420	69	18	∓	∓	PROPN
ejpam-2420	69	19	4	4	NUM
ejpam-2420	69	20	.	.	PUNCT
ejpam-2420	70	1	thus	thus	ADV
ejpam-2420	70	2	,	,	PUNCT
ejpam-2420	70	3	by	by	ADP
ejpam-2420	70	4	the	the	DET
ejpam-2420	70	5	upper	upper	ADJ
ejpam-2420	70	6	bound	bind	VERB
ejpam-2420	70	7	for	for	ADP
ejpam-2420	70	8	l(1,χd	l(1,χd	PROPN
ejpam-2420	70	9	)	)	PUNCT
ejpam-2420	70	10	in	in	ADP
ejpam-2420	70	11	lemma	lemma	PROPN
ejpam-2420	70	12	3	3	NUM
ejpam-2420	70	13	,	,	PUNCT
ejpam-2420	70	14	and	and	CCONJ
ejpam-2420	70	15	from	from	ADP
ejpam-2420	70	16	lemma	lemma	PROPN
ejpam-2420	70	17	1	1	NUM
ejpam-2420	70	18	we	we	PRON
ejpam-2420	70	19	have	have	VERB
ejpam-2420	70	20	that	that	PRON
ejpam-2420	70	21	h(d	h(d	PROPN
ejpam-2420	70	22	)	)	PUNCT
ejpam-2420	70	23	<	<	X
ejpam-2420	71	1	p	p	X
ejpam-2420	71	2	d(logd+	d(logd+	NOUN
ejpam-2420	71	3	1,478	1,478	NUM
ejpam-2420	71	4	)	)	PUNCT
ejpam-2420	71	5	4log‖pd∓	4log‖pd∓	NOUN
ejpam-2420	72	1	1‖	1‖	NUM
ejpam-2420	73	1	=	=	PUNCT
ejpam-2420	74	1	p	p	NOUN
ejpam-2420	74	2	d(logd+	d(logd+	NOUN
ejpam-2420	74	3	1,478	1,478	NUM
ejpam-2420	74	4	)	)	PUNCT
ejpam-2420	74	5	2log‖(d∓	2log‖(d∓	NUM
ejpam-2420	75	1	1)‖	1)‖	NUM
ejpam-2420	75	2	<	<	X
ejpam-2420	75	3	p	p	X
ejpam-2420	75	4	d	d	PROPN
ejpam-2420	75	5	,	,	PUNCT
ejpam-2420	75	6	(	(	PUNCT
ejpam-2420	75	7	d	d	X
ejpam-2420	75	8	>	>	X
ejpam-2420	75	9	5	5	NUM
ejpam-2420	75	10	)	)	PUNCT
ejpam-2420	75	11	.	.	PUNCT
ejpam-2420	76	1	moreover	moreover	ADV
ejpam-2420	76	2	,	,	PUNCT
ejpam-2420	76	3	we	we	PRON
ejpam-2420	76	4	can	can	AUX
ejpam-2420	76	5	write	write	VERB
ejpam-2420	76	6	h(d	h(d	PROPN
ejpam-2420	76	7	)	)	PUNCT
ejpam-2420	76	8	≤	≤	NUM
ejpam-2420	77	1	‖	‖	PROPN
ejpam-2420	77	2	p	p	PROPN
ejpam-2420	77	3	d(logd+1,478	d(logd+1,478	PROPN
ejpam-2420	77	4	)	)	PUNCT
ejpam-2420	77	5	2log(d∓1	2log(d∓1	NUM
ejpam-2420	77	6	)	)	PUNCT
ejpam-2420	77	7	‖	‖	PROPN
ejpam-2420	77	8	where	where	SCONJ
ejpam-2420	77	9	"	"	PUNCT
ejpam-2420	77	10	‖x‖	‖x‖	PROPN
ejpam-2420	77	11	"	"	PUNCT
ejpam-2420	77	12	is	be	AUX
ejpam-2420	77	13	the	the	DET
ejpam-2420	77	14	greatest	great	ADJ
ejpam-2420	77	15	integer	integer	NOUN
ejpam-2420	77	16	less	less	ADJ
ejpam-2420	77	17	than	than	ADP
ejpam-2420	77	18	or	or	CCONJ
ejpam-2420	77	19	equal	equal	ADJ
ejpam-2420	77	20	to	to	ADP
ejpam-2420	77	21	x	x	X
ejpam-2420	77	22	.	.	PUNCT
ejpam-2420	78	1	it	it	PRON
ejpam-2420	78	2	is	be	AUX
ejpam-2420	78	3	also	also	ADV
ejpam-2420	78	4	h(d	h(d	PROPN
ejpam-2420	78	5	)	)	PUNCT
ejpam-2420	78	6	<	<	X
ejpam-2420	79	1	p	p	X
ejpam-2420	79	2	d	d	PROPN
ejpam-2420	79	3	for	for	ADP
ejpam-2420	79	4	d	d	PROPN
ejpam-2420	79	5	6=	6=	PROPN
ejpam-2420	79	6	n2	n2	PROPN
ejpam-2420	79	7	∓	∓	PROPN
ejpam-2420	79	8	4	4	NUM
ejpam-2420	79	9	.	.	PUNCT
ejpam-2420	79	10	references	reference	NOUN
ejpam-2420	79	11	529	529	NUM
ejpam-2420	79	12	now	now	ADV
ejpam-2420	79	13	,	,	PUNCT
ejpam-2420	79	14	we	we	PRON
ejpam-2420	79	15	consider	consider	VERB
ejpam-2420	79	16	the	the	DET
ejpam-2420	79	17	case	case	NOUN
ejpam-2420	79	18	d	d	X
ejpam-2420	79	19	≡	≡	PROPN
ejpam-2420	79	20	3	3	NUM
ejpam-2420	79	21	(	(	PUNCT
ejpam-2420	79	22	mod	mod	NOUN
ejpam-2420	79	23	4	4	NUM
ejpam-2420	79	24	)	)	PUNCT
ejpam-2420	79	25	and	and	CCONJ
ejpam-2420	79	26	d	d	NOUN
ejpam-2420	79	27	=	=	SYM
ejpam-2420	79	28	n2	n2	PROPN
ejpam-2420	79	29	∓	∓	PROPN
ejpam-2420	79	30	2	2	NUM
ejpam-2420	79	31	(	(	PUNCT
ejpam-2420	79	32	n	n	X
ejpam-2420	79	33	∈	∈	PROPN
ejpam-2420	79	34	z	z	NOUN
ejpam-2420	79	35	is	be	AUX
ejpam-2420	79	36	odd	odd	ADJ
ejpam-2420	79	37	)	)	PUNCT
ejpam-2420	79	38	.	.	PUNCT
ejpam-2420	80	1	similarly	similarly	ADV
ejpam-2420	80	2	,	,	PUNCT
ejpam-2420	80	3	by	by	ADP
ejpam-2420	80	4	applying	apply	VERB
ejpam-2420	80	5	lemmas	lemmas	PROPN
ejpam-2420	80	6	1	1	NUM
ejpam-2420	80	7	,	,	PUNCT
ejpam-2420	80	8	3	3	NUM
ejpam-2420	80	9	and	and	CCONJ
ejpam-2420	80	10	using	use	VERB
ejpam-2420	80	11	class	class	NOUN
ejpam-2420	80	12	number	number	NOUN
ejpam-2420	80	13	formula	formula	NOUN
ejpam-2420	80	14	,	,	PUNCT
ejpam-2420	80	15	we	we	PRON
ejpam-2420	80	16	get	get	VERB
ejpam-2420	80	17	h(d	h(d	PRON
ejpam-2420	80	18	)	)	PUNCT
ejpam-2420	80	19	<	<	X
ejpam-2420	81	1	p	p	X
ejpam-2420	81	2	d(log4d+	d(log4d+	NOUN
ejpam-2420	81	3	1,478	1,478	NUM
ejpam-2420	81	4	)	)	PUNCT
ejpam-2420	81	5	2log(2d∓	2log(2d∓	NUM
ejpam-2420	81	6	1	1	NUM
ejpam-2420	81	7	)	)	PUNCT
ejpam-2420	81	8	<	<	X
ejpam-2420	81	9	p	p	PROPN
ejpam-2420	81	10	d	d	NOUN
ejpam-2420	81	11	and	and	CCONJ
ejpam-2420	81	12	h(d)≤	h(d)≤	ADJ
ejpam-2420	81	13	‖	‖	PROPN
ejpam-2420	81	14	p	p	NOUN
ejpam-2420	81	15	d(log4d+	d(log4d+	NOUN
ejpam-2420	81	16	1,478	1,478	NUM
ejpam-2420	81	17	)	)	PUNCT
ejpam-2420	81	18	2log(2d∓	2log(2d∓	NUM
ejpam-2420	81	19	1	1	NUM
ejpam-2420	81	20	)	)	PUNCT
ejpam-2420	81	21	‖	‖	PROPN
ejpam-2420	82	1	it	it	PRON
ejpam-2420	82	2	is	be	AUX
ejpam-2420	82	3	also	also	ADV
ejpam-2420	82	4	true	true	ADJ
ejpam-2420	82	5	for	for	ADP
ejpam-2420	82	6	d	d	PROPN
ejpam-2420	82	7	6=	6=	PROPN
ejpam-2420	82	8	n2	n2	PROPN
ejpam-2420	82	9	∓	∓	PROPN
ejpam-2420	82	10	2	2	NUM
ejpam-2420	82	11	.	.	NOUN
ejpam-2420	82	12	4	4	NUM
ejpam-2420	82	13	.	.	X
ejpam-2420	83	1	proof	proof	NOUN
ejpam-2420	83	2	of	of	ADP
ejpam-2420	83	3	main	main	ADJ
ejpam-2420	83	4	theorem	theorem	NOUN
ejpam-2420	83	5	specially	specially	ADV
ejpam-2420	83	6	,	,	PUNCT
ejpam-2420	83	7	if	if	SCONJ
ejpam-2420	83	8	we	we	PRON
ejpam-2420	83	9	write	write	VERB
ejpam-2420	83	10	ds	ds	NOUN
ejpam-2420	83	11	depend	depend	VERB
ejpam-2420	83	12	on	on	ADP
ejpam-2420	83	13	prime	prime	ADJ
ejpam-2420	83	14	p	p	NOUN
ejpam-2420	83	15	in	in	ADP
ejpam-2420	83	16	the	the	DET
ejpam-2420	83	17	forms	form	NOUN
ejpam-2420	83	18	of	of	ADP
ejpam-2420	83	19	d	d	PROPN
ejpam-2420	83	20	=	=	SYM
ejpam-2420	83	21	p2−4	p2−4	PROPN
ejpam-2420	83	22	,	,	PUNCT
ejpam-2420	83	23	d	d	PROPN
ejpam-2420	83	24	=	=	PRON
ejpam-2420	84	1	p2−2	p2−2	X
ejpam-2420	85	1	we	we	PRON
ejpam-2420	85	2	can	can	AUX
ejpam-2420	85	3	immediately	immediately	ADV
ejpam-2420	85	4	prove	prove	VERB
ejpam-2420	85	5	that	that	SCONJ
ejpam-2420	85	6	h(d	h(d	PROPN
ejpam-2420	85	7	)	)	PUNCT
ejpam-2420	85	8	<	<	X
ejpam-2420	86	1	p	p	NOUN
ejpam-2420	86	2	for	for	ADP
ejpam-2420	86	3	the	the	DET
ejpam-2420	86	4	class	class	NOUN
ejpam-2420	86	5	numbers	number	NOUN
ejpam-2420	86	6	of	of	ADP
ejpam-2420	86	7	real	real	ADJ
ejpam-2420	86	8	quadratic	quadratic	ADJ
ejpam-2420	86	9	fields	field	NOUN
ejpam-2420	86	10	k	k	X
ejpam-2420	87	1	=	=	SYM
ejpam-2420	87	2	q	q	X
ejpam-2420	87	3	(	(	PUNCT
ejpam-2420	87	4	p	p	NOUN
ejpam-2420	87	5	p2	p2	PROPN
ejpam-2420	87	6	−	−	PROPN
ejpam-2420	87	7	4	4	NUM
ejpam-2420	87	8	)	)	PUNCT
ejpam-2420	87	9	,	,	PUNCT
ejpam-2420	87	10	k	k	X
ejpam-2420	88	1	=	=	PUNCT
ejpam-2420	88	2	q	q	X
ejpam-2420	88	3	(	(	PUNCT
ejpam-2420	88	4	p	p	NOUN
ejpam-2420	88	5	p2	p2	PROPN
ejpam-2420	88	6	−	−	PROPN
ejpam-2420	88	7	2	2	NUM
ejpam-2420	88	8	)	)	PUNCT
ejpam-2420	88	9	from	from	ADP
ejpam-2420	88	10	lemma	lemma	PROPN
ejpam-2420	88	11	2	2	NUM
ejpam-2420	88	12	.	.	PUNCT
ejpam-2420	88	13	therefore	therefore	ADV
ejpam-2420	88	14	we	we	PRON
ejpam-2420	88	15	have	have	VERB
ejpam-2420	88	16	h(d	h(d	PROPN
ejpam-2420	88	17	)	)	PUNCT
ejpam-2420	88	18	6≡	6≡	NUM
ejpam-2420	88	19	0	0	NUM
ejpam-2420	89	1	(	(	PUNCT
ejpam-2420	89	2	mod	mod	PROPN
ejpam-2420	89	3	p	p	X
ejpam-2420	89	4	)	)	PUNCT
ejpam-2420	90	1	and	and	CCONJ
ejpam-2420	90	2	it	it	PRON
ejpam-2420	90	3	is	be	AUX
ejpam-2420	90	4	clear	clear	ADJ
ejpam-2420	90	5	that	that	SCONJ
ejpam-2420	90	6	|rp(d)p	|rp(d)p	VERB
ejpam-2420	91	1	d	d	NOUN
ejpam-2420	91	2	|	|	ADV
ejpam-2420	91	3	p	p	NOUN
ejpam-2420	91	4	=	=	NOUN
ejpam-2420	91	5	1	1	NUM
ejpam-2420	91	6	for	for	ADP
ejpam-2420	91	7	above	above	ADV
ejpam-2420	91	8	mentioned	mention	VERB
ejpam-2420	91	9	real	real	ADJ
ejpam-2420	91	10	quadratic	quadratic	ADJ
ejpam-2420	91	11	fields	field	NOUN
ejpam-2420	91	12	.	.	PUNCT
ejpam-2420	92	1	references	reference	NOUN
ejpam-2420	92	2	[	[	X
ejpam-2420	92	3	1	1	NUM
ejpam-2420	92	4	]	]	PUNCT
ejpam-2420	92	5	d.	d.	PROPN
ejpam-2420	92	6	byeon	byeon	PROPN
ejpam-2420	92	7	.	.	PUNCT
ejpam-2420	93	1	existence	existence	NOUN
ejpam-2420	93	2	of	of	ADP
ejpam-2420	93	3	certain	certain	ADJ
ejpam-2420	93	4	fundamental	fundamental	ADJ
ejpam-2420	93	5	discriminants	discriminant	NOUN
ejpam-2420	93	6	and	and	CCONJ
ejpam-2420	93	7	class	class	NOUN
ejpam-2420	93	8	numbers	number	NOUN
ejpam-2420	93	9	of	of	ADP
ejpam-2420	93	10	real	real	ADJ
ejpam-2420	93	11	quadratic	quadratic	ADJ
ejpam-2420	93	12	fields	field	NOUN
ejpam-2420	93	13	.	.	PUNCT
ejpam-2420	94	1	journal	journal	NOUN
ejpam-2420	94	2	of	of	ADP
ejpam-2420	94	3	number	number	NOUN
ejpam-2420	94	4	theory	theory	NOUN
ejpam-2420	94	5	,	,	PUNCT
ejpam-2420	94	6	98(2):432	98(2):432	NUM
ejpam-2420	94	7	–	–	PUNCT
ejpam-2420	94	8	437	437	NUM
ejpam-2420	94	9	,	,	PUNCT
ejpam-2420	94	10	2003	2003	NUM
ejpam-2420	94	11	.	.	PUNCT
ejpam-2420	95	1	[	[	X
ejpam-2420	95	2	2	2	X
ejpam-2420	95	3	]	]	X
ejpam-2420	95	4	o.	o.	PROPN
ejpam-2420	95	5	ken	ken	PROPN
ejpam-2420	95	6	.	.	PROPN
ejpam-2420	95	7	indivisibility	indivisibility	NOUN
ejpam-2420	95	8	of	of	ADP
ejpam-2420	95	9	class	class	NOUN
ejpam-2420	95	10	numbers	number	NOUN
ejpam-2420	95	11	of	of	ADP
ejpam-2420	95	12	real	real	ADJ
ejpam-2420	95	13	quadratic	quadratic	ADJ
ejpam-2420	95	14	fields	field	NOUN
ejpam-2420	95	15	.	.	PUNCT
ejpam-2420	96	1	compositio	compositio	PROPN
ejpam-2420	96	2	mathematica	mathematica	PROPN
ejpam-2420	96	3	,	,	PUNCT
ejpam-2420	96	4	119(1):1–11	119(1):1–11	PROPN
ejpam-2420	96	5	,	,	PUNCT
ejpam-2420	96	6	1999	1999	NUM
ejpam-2420	96	7	.	.	PUNCT
ejpam-2420	97	1	[	[	X
ejpam-2420	97	2	3	3	X
ejpam-2420	97	3	]	]	PUNCT
ejpam-2420	97	4	s.	s.	PROPN
ejpam-2420	97	5	louboutin	louboutin	PROPN
ejpam-2420	97	6	.	.	PUNCT
ejpam-2420	98	1	majorations	majoration	NOUN
ejpam-2420	98	2	explicites	explicite	NOUN
ejpam-2420	98	3	de	de	X
ejpam-2420	98	4	|l(1,χ)|	|l(1,χ)|	X
ejpam-2420	98	5	(	(	PUNCT
ejpam-2420	98	6	troisième	troisième	X
ejpam-2420	98	7	partie	partie	NOUN
ejpam-2420	98	8	)	)	PUNCT
ejpam-2420	98	9	.	.	PUNCT
ejpam-2420	99	1	comptes	compte	VERB
ejpam-2420	99	2	rendus	rendus	PROPN
ejpam-2420	99	3	de	de	PROPN
ejpam-2420	99	4	l’académie	l’académie	PROPN
ejpam-2420	99	5	des	des	PROPN
ejpam-2420	99	6	sciences	sciences	PROPN
ejpam-2420	99	7	series	series	PROPN
ejpam-2420	99	8	i	i	PRON
ejpam-2420	99	9	mathematics	mathematic	NOUN
ejpam-2420	99	10	,	,	PUNCT
ejpam-2420	99	11	332(2):95	332(2):95	NUM
ejpam-2420	99	12	–	–	PUNCT
ejpam-2420	99	13	98	98	NUM
ejpam-2420	99	14	,	,	PUNCT
ejpam-2420	99	15	2001	2001	NUM
ejpam-2420	99	16	.	.	PUNCT
ejpam-2420	100	1	[	[	X
ejpam-2420	100	2	4	4	NUM
ejpam-2420	100	3	]	]	X
ejpam-2420	100	4	r.a	r.a	PROPN
ejpam-2420	100	5	mollin	mollin	NOUN
ejpam-2420	100	6	.	.	PUNCT
ejpam-2420	101	1	diophantine	diophantine	VERB
ejpam-2420	101	2	equations	equation	NOUN
ejpam-2420	101	3	and	and	CCONJ
ejpam-2420	101	4	class	class	NOUN
ejpam-2420	101	5	numbers	number	NOUN
ejpam-2420	101	6	.	.	PUNCT
ejpam-2420	102	1	journal	journal	NOUN
ejpam-2420	102	2	of	of	ADP
ejpam-2420	102	3	number	number	NOUN
ejpam-2420	102	4	theory	theory	NOUN
ejpam-2420	102	5	,	,	PUNCT
ejpam-2420	102	6	24(1):7	24(1):7	PROPN
ejpam-2420	102	7	–	–	PUNCT
ejpam-2420	102	8	19	19	NUM
ejpam-2420	102	9	,	,	PUNCT
ejpam-2420	102	10	1986	1986	NUM
ejpam-2420	102	11	.	.	PUNCT