LMFDB - Group of Dirichlet characters of modulus 104000

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(104000)

gp:g = idealstar(,104000,2)

magma:G = FullDirichletGroup(104000);

Character group

Order	=	38400	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{1200}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{104000}(74751,\cdot)$, $\chi_{104000}(58501,\cdot)$, $\chi_{104000}(77377,\cdot)$, $\chi_{104000}(64001,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 38400 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{104000}(1,\cdot)$	104000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{104000}(3,\cdot)$	104000.ben	1200	yes	$1$	$1$	$e\left(\frac{1063}{1200}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{109}{1200}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{887}{1200}\right)$	$e\left(\frac{351}{400}\right)$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{263}{400}\right)$	$e\left(\frac{883}{1200}\right)$
$\chi_{104000}(7,\cdot)$	104000.vu	120	no	$-1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{29}{120}\right)$
$\chi_{104000}(9,\cdot)$	104000.bdo	600	no	$1$	$1$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{283}{600}\right)$
$\chi_{104000}(11,\cdot)$	104000.beq	1200	yes	$1$	$1$	$e\left(\frac{109}{1200}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{1087}{1200}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{341}{1200}\right)$	$e\left(\frac{293}{400}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{109}{400}\right)$	$e\left(\frac{1069}{1200}\right)$
$\chi_{104000}(17,\cdot)$	104000.bad	300	no	$-1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{53}{300}\right)$
$\chi_{104000}(19,\cdot)$	104000.bev	1200	yes	$1$	$1$	$e\left(\frac{887}{1200}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{341}{1200}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{1063}{1200}\right)$	$e\left(\frac{199}{400}\right)$	$e\left(\frac{223}{600}\right)$	$e\left(\frac{87}{400}\right)$	$e\left(\frac{767}{1200}\right)$
$\chi_{104000}(21,\cdot)$	104000.bck	400	yes	$-1$	$1$	$e\left(\frac{351}{400}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{293}{400}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{199}{400}\right)$	$e\left(\frac{381}{400}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{253}{400}\right)$	$e\left(\frac{391}{400}\right)$
$\chi_{104000}(23,\cdot)$	104000.bdd	600	no	$1$	$1$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{223}{600}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{107}{600}\right)$
$\chi_{104000}(27,\cdot)$	104000.bcd	400	no	$1$	$1$	$e\left(\frac{263}{400}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{109}{400}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{87}{400}\right)$	$e\left(\frac{253}{400}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{83}{400}\right)$
$\chi_{104000}(29,\cdot)$	104000.bff	1200	yes	$1$	$1$	$e\left(\frac{883}{1200}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{283}{600}\right)$	$e\left(\frac{1069}{1200}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{391}{400}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{403}{1200}\right)$
$\chi_{104000}(31,\cdot)$	104000.ut	100	no	$1$	$1$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{104000}(33,\cdot)$	104000.zr	300	no	$1$	$1$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{104000}(37,\cdot)$	104000.bfc	1200	yes	$1$	$1$	$e\left(\frac{61}{1200}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{61}{600}\right)$	$e\left(\frac{1123}{1200}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{89}{1200}\right)$	$e\left(\frac{297}{400}\right)$	$e\left(\frac{419}{600}\right)$	$e\left(\frac{61}{400}\right)$	$e\left(\frac{601}{1200}\right)$
$\chi_{104000}(41,\cdot)$	104000.bdz	600	no	$-1$	$1$	$e\left(\frac{23}{600}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{239}{600}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{277}{600}\right)$	$e\left(\frac{21}{200}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{143}{600}\right)$
$\chi_{104000}(43,\cdot)$	104000.yo	240	no	$1$	$1$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{121}{240}\right)$
$\chi_{104000}(47,\cdot)$	104000.to	100	no	$-1$	$1$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{39}{100}\right)$
$\chi_{104000}(49,\cdot)$	104000.rd	60	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{104000}(51,\cdot)$	104000.sr	80	no	$-1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{104000}(53,\cdot)$	104000.bcc	400	no	$-1$	$1$	$e\left(\frac{251}{400}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{193}{400}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{99}{400}\right)$	$e\left(\frac{281}{400}\right)$	$e\left(\frac{29}{200}\right)$	$e\left(\frac{353}{400}\right)$	$e\left(\frac{391}{400}\right)$
$\chi_{104000}(57,\cdot)$	104000.ed	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{104000}(59,\cdot)$	104000.bev	1200	yes	$1$	$1$	$e\left(\frac{881}{1200}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{281}{600}\right)$	$e\left(\frac{83}{1200}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{769}{1200}\right)$	$e\left(\frac{337}{400}\right)$	$e\left(\frac{49}{600}\right)$	$e\left(\frac{81}{400}\right)$	$e\left(\frac{521}{1200}\right)$
$\chi_{104000}(61,\cdot)$	104000.bei	1200	yes	$1$	$1$	$e\left(\frac{179}{1200}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{197}{1200}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{871}{1200}\right)$	$e\left(\frac{383}{400}\right)$	$e\left(\frac{391}{600}\right)$	$e\left(\frac{179}{400}\right)$	$e\left(\frac{539}{1200}\right)$
$\chi_{104000}(63,\cdot)$	104000.bbj	300	no	$-1$	$1$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{104000}(67,\cdot)$	104000.bee	1200	yes	$-1$	$1$	$e\left(\frac{367}{1200}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{367}{600}\right)$	$e\left(\frac{1081}{1200}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{683}{1200}\right)$	$e\left(\frac{259}{400}\right)$	$e\left(\frac{593}{600}\right)$	$e\left(\frac{367}{400}\right)$	$e\left(\frac{547}{1200}\right)$
$\chi_{104000}(69,\cdot)$	104000.beh	1200	yes	$1$	$1$	$e\left(\frac{617}{1200}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{17}{600}\right)$	$e\left(\frac{431}{1200}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{133}{1200}\right)$	$e\left(\frac{109}{400}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{1097}{1200}\right)$
$\chi_{104000}(71,\cdot)$	104000.bed	600	no	$1$	$1$	$e\left(\frac{49}{600}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{551}{600}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{49}{200}\right)$	$e\left(\frac{109}{600}\right)$
$\chi_{104000}(73,\cdot)$	104000.xn	200	no	$1$	$1$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{109}{200}\right)$
$\chi_{104000}(77,\cdot)$	104000.bcb	400	yes	$-1$	$1$	$e\left(\frac{33}{400}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{219}{400}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{17}{400}\right)$	$e\left(\frac{323}{400}\right)$	$e\left(\frac{7}{200}\right)$	$e\left(\frac{99}{400}\right)$	$e\left(\frac{53}{400}\right)$
$\chi_{104000}(79,\cdot)$	104000.vb	100	no	$-1$	$1$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{59}{100}\right)$
$\chi_{104000}(81,\cdot)$	104000.zt	300	no	$1$	$1$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{283}{300}\right)$
$\chi_{104000}(83,\cdot)$	104000.bbz	400	yes	$-1$	$1$	$e\left(\frac{329}{400}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{247}{400}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{21}{400}\right)$	$e\left(\frac{199}{400}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{187}{400}\right)$	$e\left(\frac{189}{400}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$104000$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{1200}\)
Order	$38400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{104000}(1,\cdot)\)	104000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{104000}(3,\cdot)\)	104000.ben	1200	yes	\(1\)	\(1\)	\(e\left(\frac{1063}{1200}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{463}{600}\right)\)	\(e\left(\frac{109}{1200}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{887}{1200}\right)\)	\(e\left(\frac{351}{400}\right)\)	\(e\left(\frac{377}{600}\right)\)	\(e\left(\frac{263}{400}\right)\)	\(e\left(\frac{883}{1200}\right)\)
\(\chi_{104000}(7,\cdot)\)	104000.vu	120	no	\(-1\)	\(1\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)
\(\chi_{104000}(9,\cdot)\)	104000.bdo	600	no	\(1\)	\(1\)	\(e\left(\frac{463}{600}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{109}{600}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{287}{600}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{283}{600}\right)\)
\(\chi_{104000}(11,\cdot)\)	104000.beq	1200	yes	\(1\)	\(1\)	\(e\left(\frac{109}{1200}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{109}{600}\right)\)	\(e\left(\frac{1087}{1200}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{341}{1200}\right)\)	\(e\left(\frac{293}{400}\right)\)	\(e\left(\frac{161}{600}\right)\)	\(e\left(\frac{109}{400}\right)\)	\(e\left(\frac{1069}{1200}\right)\)
\(\chi_{104000}(17,\cdot)\)	104000.bad	300	no	\(-1\)	\(1\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{53}{300}\right)\)
\(\chi_{104000}(19,\cdot)\)	104000.bev	1200	yes	\(1\)	\(1\)	\(e\left(\frac{887}{1200}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{287}{600}\right)\)	\(e\left(\frac{341}{1200}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{1063}{1200}\right)\)	\(e\left(\frac{199}{400}\right)\)	\(e\left(\frac{223}{600}\right)\)	\(e\left(\frac{87}{400}\right)\)	\(e\left(\frac{767}{1200}\right)\)
\(\chi_{104000}(21,\cdot)\)	104000.bck	400	yes	\(-1\)	\(1\)	\(e\left(\frac{351}{400}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{293}{400}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{199}{400}\right)\)	\(e\left(\frac{381}{400}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{253}{400}\right)\)	\(e\left(\frac{391}{400}\right)\)
\(\chi_{104000}(23,\cdot)\)	104000.bdd	600	no	\(1\)	\(1\)	\(e\left(\frac{377}{600}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{161}{600}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{223}{600}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{107}{600}\right)\)
\(\chi_{104000}(27,\cdot)\)	104000.bcd	400	no	\(1\)	\(1\)	\(e\left(\frac{263}{400}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{109}{400}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{87}{400}\right)\)	\(e\left(\frac{253}{400}\right)\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{389}{400}\right)\)	\(e\left(\frac{83}{400}\right)\)
\(\chi_{104000}(29,\cdot)\)	104000.bff	1200	yes	\(1\)	\(1\)	\(e\left(\frac{883}{1200}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{283}{600}\right)\)	\(e\left(\frac{1069}{1200}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{391}{400}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{403}{1200}\right)\)
\(\chi_{104000}(31,\cdot)\)	104000.ut	100	no	\(1\)	\(1\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{104000}(33,\cdot)\)	104000.zr	300	no	\(1\)	\(1\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{104000}(37,\cdot)\)	104000.bfc	1200	yes	\(1\)	\(1\)	\(e\left(\frac{61}{1200}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{61}{600}\right)\)	\(e\left(\frac{1123}{1200}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{89}{1200}\right)\)	\(e\left(\frac{297}{400}\right)\)	\(e\left(\frac{419}{600}\right)\)	\(e\left(\frac{61}{400}\right)\)	\(e\left(\frac{601}{1200}\right)\)
\(\chi_{104000}(41,\cdot)\)	104000.bdz	600	no	\(-1\)	\(1\)	\(e\left(\frac{23}{600}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{239}{600}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{277}{600}\right)\)	\(e\left(\frac{21}{200}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{143}{600}\right)\)
\(\chi_{104000}(43,\cdot)\)	104000.yo	240	no	\(1\)	\(1\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)
\(\chi_{104000}(47,\cdot)\)	104000.to	100	no	\(-1\)	\(1\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{104000}(49,\cdot)\)	104000.rd	60	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{104000}(51,\cdot)\)	104000.sr	80	no	\(-1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{104000}(53,\cdot)\)	104000.bcc	400	no	\(-1\)	\(1\)	\(e\left(\frac{251}{400}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{193}{400}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{99}{400}\right)\)	\(e\left(\frac{281}{400}\right)\)	\(e\left(\frac{29}{200}\right)\)	\(e\left(\frac{353}{400}\right)\)	\(e\left(\frac{391}{400}\right)\)
\(\chi_{104000}(57,\cdot)\)	104000.ed	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{104000}(59,\cdot)\)	104000.bev	1200	yes	\(1\)	\(1\)	\(e\left(\frac{881}{1200}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{281}{600}\right)\)	\(e\left(\frac{83}{1200}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{769}{1200}\right)\)	\(e\left(\frac{337}{400}\right)\)	\(e\left(\frac{49}{600}\right)\)	\(e\left(\frac{81}{400}\right)\)	\(e\left(\frac{521}{1200}\right)\)
\(\chi_{104000}(61,\cdot)\)	104000.bei	1200	yes	\(1\)	\(1\)	\(e\left(\frac{179}{1200}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{179}{600}\right)\)	\(e\left(\frac{197}{1200}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{871}{1200}\right)\)	\(e\left(\frac{383}{400}\right)\)	\(e\left(\frac{391}{600}\right)\)	\(e\left(\frac{179}{400}\right)\)	\(e\left(\frac{539}{1200}\right)\)
\(\chi_{104000}(63,\cdot)\)	104000.bbj	300	no	\(-1\)	\(1\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{104000}(67,\cdot)\)	104000.bee	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{367}{1200}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{367}{600}\right)\)	\(e\left(\frac{1081}{1200}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{683}{1200}\right)\)	\(e\left(\frac{259}{400}\right)\)	\(e\left(\frac{593}{600}\right)\)	\(e\left(\frac{367}{400}\right)\)	\(e\left(\frac{547}{1200}\right)\)
\(\chi_{104000}(69,\cdot)\)	104000.beh	1200	yes	\(1\)	\(1\)	\(e\left(\frac{617}{1200}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{17}{600}\right)\)	\(e\left(\frac{431}{1200}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{133}{1200}\right)\)	\(e\left(\frac{109}{400}\right)\)	\(e\left(\frac{193}{600}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{1097}{1200}\right)\)
\(\chi_{104000}(71,\cdot)\)	104000.bed	600	no	\(1\)	\(1\)	\(e\left(\frac{49}{600}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{157}{600}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{551}{600}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{49}{200}\right)\)	\(e\left(\frac{109}{600}\right)\)
\(\chi_{104000}(73,\cdot)\)	104000.xn	200	no	\(1\)	\(1\)	\(e\left(\frac{99}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{109}{200}\right)\)
\(\chi_{104000}(77,\cdot)\)	104000.bcb	400	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{400}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{219}{400}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{17}{400}\right)\)	\(e\left(\frac{323}{400}\right)\)	\(e\left(\frac{7}{200}\right)\)	\(e\left(\frac{99}{400}\right)\)	\(e\left(\frac{53}{400}\right)\)
\(\chi_{104000}(79,\cdot)\)	104000.vb	100	no	\(-1\)	\(1\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)
\(\chi_{104000}(81,\cdot)\)	104000.zt	300	no	\(1\)	\(1\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)
\(\chi_{104000}(83,\cdot)\)	104000.bbz	400	yes	\(-1\)	\(1\)	\(e\left(\frac{329}{400}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{247}{400}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{21}{400}\right)\)	\(e\left(\frac{199}{400}\right)\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{187}{400}\right)\)	\(e\left(\frac{189}{400}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.