LMFDB - Group of Dirichlet characters of modulus 676000

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(676000)

gp:g = idealstar(,676000,2)

magma:G := FullDirichletGroup(676000);

Character group

Order	=	249600	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{7800}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{676000}(126751,\cdot)$, $\chi_{676000}(422501,\cdot)$, $\chi_{676000}(389377,\cdot)$, $\chi_{676000}(12001,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 249600 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{676000}(1,\cdot)$	676000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{676000}(3,\cdot)$	676000.bva	7800	yes	$1$	$1$	$e\left(\frac{5297}{7800}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{1397}{3900}\right)$	$e\left(\frac{4421}{7800}\right)$	$e\left(\frac{2579}{3900}\right)$	$e\left(\frac{31}{600}\right)$	$e\left(\frac{2419}{2600}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{97}{2600}\right)$	$e\left(\frac{2027}{7800}\right)$
$\chi_{676000}(7,\cdot)$	676000.blr	780	no	$-1$	$1$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{149}{780}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{691}{780}\right)$
$\chi_{676000}(9,\cdot)$	676000.bsu	3900	no	$1$	$1$	$e\left(\frac{1397}{3900}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{1397}{1950}\right)$	$e\left(\frac{521}{3900}\right)$	$e\left(\frac{629}{1950}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{1119}{1300}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{97}{1300}\right)$	$e\left(\frac{2027}{3900}\right)$
$\chi_{676000}(11,\cdot)$	676000.bvz	7800	yes	$1$	$1$	$e\left(\frac{4421}{7800}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{521}{3900}\right)$	$e\left(\frac{3053}{7800}\right)$	$e\left(\frac{368}{975}\right)$	$e\left(\frac{283}{600}\right)$	$e\left(\frac{1467}{2600}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{1821}{2600}\right)$	$e\left(\frac{3161}{7800}\right)$
$\chi_{676000}(17,\cdot)$	676000.btn	3900	no	$-1$	$1$	$e\left(\frac{2579}{3900}\right)$	$e\left(\frac{149}{780}\right)$	$e\left(\frac{629}{1950}\right)$	$e\left(\frac{368}{975}\right)$	$e\left(\frac{3631}{3900}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{277}{325}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{1279}{1300}\right)$	$e\left(\frac{191}{975}\right)$
$\chi_{676000}(19,\cdot)$	676000.bkn	600	no	$1$	$1$	$e\left(\frac{31}{600}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{283}{600}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{569}{600}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{271}{600}\right)$
$\chi_{676000}(21,\cdot)$	676000.bsm	2600	yes	$-1$	$1$	$e\left(\frac{2419}{2600}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{1119}{1300}\right)$	$e\left(\frac{1467}{2600}\right)$	$e\left(\frac{277}{325}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{2139}{2600}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{2057}{2600}\right)$	$e\left(\frac{379}{2600}\right)$
$\chi_{676000}(23,\cdot)$	676000.bev	300	no	$1$	$1$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{241}{300}\right)$
$\chi_{676000}(27,\cdot)$	676000.bsn	2600	yes	$1$	$1$	$e\left(\frac{97}{2600}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{97}{1300}\right)$	$e\left(\frac{1821}{2600}\right)$	$e\left(\frac{1279}{1300}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{2057}{2600}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{291}{2600}\right)$	$e\left(\frac{2027}{2600}\right)$
$\chi_{676000}(29,\cdot)$	676000.bvj	7800	yes	$1$	$1$	$e\left(\frac{2027}{7800}\right)$	$e\left(\frac{691}{780}\right)$	$e\left(\frac{2027}{3900}\right)$	$e\left(\frac{3161}{7800}\right)$	$e\left(\frac{191}{975}\right)$	$e\left(\frac{271}{600}\right)$	$e\left(\frac{379}{2600}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{2027}{2600}\right)$	$e\left(\frac{6407}{7800}\right)$
$\chi_{676000}(31,\cdot)$	676000.bpb	1300	no	$1$	$1$	$e\left(\frac{359}{650}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{34}{325}\right)$	$e\left(\frac{1099}{1300}\right)$	$e\left(\frac{451}{650}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{333}{1300}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{427}{650}\right)$	$e\left(\frac{47}{325}\right)$
$\chi_{676000}(33,\cdot)$	676000.buk	3900	no	$1$	$1$	$e\left(\frac{959}{3900}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{959}{1950}\right)$	$e\left(\frac{3737}{3900}\right)$	$e\left(\frac{151}{3900}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{643}{1300}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{959}{1300}\right)$	$e\left(\frac{1297}{1950}\right)$
$\chi_{676000}(37,\cdot)$	676000.bvc	7800	yes	$1$	$1$	$e\left(\frac{3359}{7800}\right)$	$e\left(\frac{367}{780}\right)$	$e\left(\frac{3359}{3900}\right)$	$e\left(\frac{2837}{7800}\right)$	$e\left(\frac{3863}{3900}\right)$	$e\left(\frac{7}{600}\right)$	$e\left(\frac{2343}{2600}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{759}{2600}\right)$	$e\left(\frac{569}{7800}\right)$
$\chi_{676000}(41,\cdot)$	676000.btr	3900	no	$-1$	$1$	$e\left(\frac{3487}{3900}\right)$	$e\left(\frac{157}{780}\right)$	$e\left(\frac{1537}{1950}\right)$	$e\left(\frac{304}{975}\right)$	$e\left(\frac{1309}{1950}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{31}{325}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{887}{1300}\right)$	$e\left(\frac{1267}{3900}\right)$
$\chi_{676000}(43,\cdot)$	676000.bqq	1560	no	$1$	$1$	$e\left(\frac{1559}{1560}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{779}{780}\right)$	$e\left(\frac{587}{1560}\right)$	$e\left(\frac{23}{780}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{93}{520}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{519}{520}\right)$	$e\left(\frac{89}{1560}\right)$
$\chi_{676000}(47,\cdot)$	676000.bno	1300	no	$-1$	$1$	$e\left(\frac{1127}{1300}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{477}{650}\right)$	$e\left(\frac{411}{1300}\right)$	$e\left(\frac{1003}{1300}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{37}{1300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{781}{1300}\right)$	$e\left(\frac{258}{325}\right)$
$\chi_{676000}(49,\cdot)$	676000.bhu	390	no	$1$	$1$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{149}{390}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{301}{390}\right)$
$\chi_{676000}(51,\cdot)$	676000.bip	520	no	$-1$	$1$	$e\left(\frac{177}{520}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{491}{520}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{407}{520}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{520}\right)$	$e\left(\frac{237}{520}\right)$
$\chi_{676000}(53,\cdot)$	676000.bsk	2600	yes	$-1$	$1$	$e\left(\frac{2469}{2600}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{1169}{1300}\right)$	$e\left(\frac{717}{2600}\right)$	$e\left(\frac{933}{1300}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{1189}{2600}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{2207}{2600}\right)$	$e\left(\frac{479}{2600}\right)$
$\chi_{676000}(57,\cdot)$	676000.pq	52	no	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{52}\right)$	$1$	$e\left(\frac{3}{26}\right)$	$-i$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{676000}(59,\cdot)$	676000.bux	7800	yes	$1$	$1$	$e\left(\frac{589}{7800}\right)$	$e\left(\frac{128}{195}\right)$	$e\left(\frac{589}{3900}\right)$	$e\left(\frac{577}{7800}\right)$	$e\left(\frac{149}{1950}\right)$	$e\left(\frac{47}{600}\right)$	$e\left(\frac{1903}{2600}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{589}{2600}\right)$	$e\left(\frac{3349}{7800}\right)$
$\chi_{676000}(61,\cdot)$	676000.bvk	7800	yes	$1$	$1$	$e\left(\frac{2551}{7800}\right)$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{2551}{3900}\right)$	$e\left(\frac{6793}{7800}\right)$	$e\left(\frac{791}{1950}\right)$	$e\left(\frac{23}{600}\right)$	$e\left(\frac{1827}{2600}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{2551}{2600}\right)$	$e\left(\frac{5791}{7800}\right)$
$\chi_{676000}(63,\cdot)$	676000.bsy	3900	no	$-1$	$1$	$e\left(\frac{2377}{3900}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{427}{1950}\right)$	$e\left(\frac{511}{3900}\right)$	$e\left(\frac{2003}{3900}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{979}{1300}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{1077}{1300}\right)$	$e\left(\frac{791}{1950}\right)$
$\chi_{676000}(67,\cdot)$	676000.bvq	7800	yes	$-1$	$1$	$e\left(\frac{7373}{7800}\right)$	$e\left(\frac{529}{780}\right)$	$e\left(\frac{3473}{3900}\right)$	$e\left(\frac{5339}{7800}\right)$	$e\left(\frac{2411}{3900}\right)$	$e\left(\frac{529}{600}\right)$	$e\left(\frac{1621}{2600}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{2173}{2600}\right)$	$e\left(\frac{5243}{7800}\right)$
$\chi_{676000}(69,\cdot)$	676000.bvn	7800	yes	$1$	$1$	$e\left(\frac{7273}{7800}\right)$	$e\left(\frac{599}{780}\right)$	$e\left(\frac{3373}{3900}\right)$	$e\left(\frac{1639}{7800}\right)$	$e\left(\frac{934}{975}\right)$	$e\left(\frac{329}{600}\right)$	$e\left(\frac{1821}{2600}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{2073}{2600}\right)$	$e\left(\frac{493}{7800}\right)$
$\chi_{676000}(71,\cdot)$	676000.btu	3900	no	$1$	$1$	$e\left(\frac{731}{3900}\right)$	$e\left(\frac{131}{780}\right)$	$e\left(\frac{731}{1950}\right)$	$e\left(\frac{902}{975}\right)$	$e\left(\frac{1517}{1950}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{231}{650}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{731}{1300}\right)$	$e\left(\frac{2021}{3900}\right)$
$\chi_{676000}(73,\cdot)$	676000.bpe	1300	no	$1$	$1$	$e\left(\frac{103}{650}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{103}{325}\right)$	$e\left(\frac{379}{650}\right)$	$e\left(\frac{209}{1300}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{643}{650}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{309}{650}\right)$	$e\left(\frac{971}{1300}\right)$
$\chi_{676000}(77,\cdot)$	676000.brq	2600	yes	$-1$	$1$	$e\left(\frac{2127}{2600}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{827}{1300}\right)$	$e\left(\frac{1011}{2600}\right)$	$e\left(\frac{739}{1300}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{1187}{2600}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{1181}{2600}\right)$	$e\left(\frac{757}{2600}\right)$
$\chi_{676000}(79,\cdot)$	676000.blc	650	no	$-1$	$1$	$e\left(\frac{531}{650}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{206}{325}\right)$	$e\left(\frac{54}{325}\right)$	$e\left(\frac{209}{650}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{311}{650}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{293}{650}\right)$	$e\left(\frac{321}{650}\right)$
$\chi_{676000}(81,\cdot)$	676000.bqy	1950	no	$1$	$1$	$e\left(\frac{1397}{1950}\right)$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{422}{975}\right)$	$e\left(\frac{521}{1950}\right)$	$e\left(\frac{629}{975}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{469}{650}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{97}{650}\right)$	$e\left(\frac{77}{1950}\right)$
$\chi_{676000}(83,\cdot)$	676000.bsh	2600	yes	$-1$	$1$	$e\left(\frac{2351}{2600}\right)$	$e\left(\frac{173}{260}\right)$	$e\left(\frac{1051}{1300}\right)$	$e\left(\frac{693}{2600}\right)$	$e\left(\frac{7}{1300}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{1481}{2600}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1853}{2600}\right)$	$e\left(\frac{2141}{2600}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$676000$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{7800}\)
Order	$249600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{676000}(1,\cdot)\)	676000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{676000}(3,\cdot)\)	676000.bva	7800	yes	\(1\)	\(1\)	\(e\left(\frac{5297}{7800}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{1397}{3900}\right)\)	\(e\left(\frac{4421}{7800}\right)\)	\(e\left(\frac{2579}{3900}\right)\)	\(e\left(\frac{31}{600}\right)\)	\(e\left(\frac{2419}{2600}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{97}{2600}\right)\)	\(e\left(\frac{2027}{7800}\right)\)
\(\chi_{676000}(7,\cdot)\)	676000.blr	780	no	\(-1\)	\(1\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{149}{780}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{691}{780}\right)\)
\(\chi_{676000}(9,\cdot)\)	676000.bsu	3900	no	\(1\)	\(1\)	\(e\left(\frac{1397}{3900}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{1397}{1950}\right)\)	\(e\left(\frac{521}{3900}\right)\)	\(e\left(\frac{629}{1950}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{1119}{1300}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{97}{1300}\right)\)	\(e\left(\frac{2027}{3900}\right)\)
\(\chi_{676000}(11,\cdot)\)	676000.bvz	7800	yes	\(1\)	\(1\)	\(e\left(\frac{4421}{7800}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{521}{3900}\right)\)	\(e\left(\frac{3053}{7800}\right)\)	\(e\left(\frac{368}{975}\right)\)	\(e\left(\frac{283}{600}\right)\)	\(e\left(\frac{1467}{2600}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{1821}{2600}\right)\)	\(e\left(\frac{3161}{7800}\right)\)
\(\chi_{676000}(17,\cdot)\)	676000.btn	3900	no	\(-1\)	\(1\)	\(e\left(\frac{2579}{3900}\right)\)	\(e\left(\frac{149}{780}\right)\)	\(e\left(\frac{629}{1950}\right)\)	\(e\left(\frac{368}{975}\right)\)	\(e\left(\frac{3631}{3900}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{277}{325}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{1279}{1300}\right)\)	\(e\left(\frac{191}{975}\right)\)
\(\chi_{676000}(19,\cdot)\)	676000.bkn	600	no	\(1\)	\(1\)	\(e\left(\frac{31}{600}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{283}{600}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{569}{600}\right)\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{271}{600}\right)\)
\(\chi_{676000}(21,\cdot)\)	676000.bsm	2600	yes	\(-1\)	\(1\)	\(e\left(\frac{2419}{2600}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{1119}{1300}\right)\)	\(e\left(\frac{1467}{2600}\right)\)	\(e\left(\frac{277}{325}\right)\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{2139}{2600}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{2057}{2600}\right)\)	\(e\left(\frac{379}{2600}\right)\)
\(\chi_{676000}(23,\cdot)\)	676000.bev	300	no	\(1\)	\(1\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{241}{300}\right)\)
\(\chi_{676000}(27,\cdot)\)	676000.bsn	2600	yes	\(1\)	\(1\)	\(e\left(\frac{97}{2600}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{97}{1300}\right)\)	\(e\left(\frac{1821}{2600}\right)\)	\(e\left(\frac{1279}{1300}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{2057}{2600}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{291}{2600}\right)\)	\(e\left(\frac{2027}{2600}\right)\)
\(\chi_{676000}(29,\cdot)\)	676000.bvj	7800	yes	\(1\)	\(1\)	\(e\left(\frac{2027}{7800}\right)\)	\(e\left(\frac{691}{780}\right)\)	\(e\left(\frac{2027}{3900}\right)\)	\(e\left(\frac{3161}{7800}\right)\)	\(e\left(\frac{191}{975}\right)\)	\(e\left(\frac{271}{600}\right)\)	\(e\left(\frac{379}{2600}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{2027}{2600}\right)\)	\(e\left(\frac{6407}{7800}\right)\)
\(\chi_{676000}(31,\cdot)\)	676000.bpb	1300	no	\(1\)	\(1\)	\(e\left(\frac{359}{650}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{34}{325}\right)\)	\(e\left(\frac{1099}{1300}\right)\)	\(e\left(\frac{451}{650}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{333}{1300}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{427}{650}\right)\)	\(e\left(\frac{47}{325}\right)\)
\(\chi_{676000}(33,\cdot)\)	676000.buk	3900	no	\(1\)	\(1\)	\(e\left(\frac{959}{3900}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{959}{1950}\right)\)	\(e\left(\frac{3737}{3900}\right)\)	\(e\left(\frac{151}{3900}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{643}{1300}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{959}{1300}\right)\)	\(e\left(\frac{1297}{1950}\right)\)
\(\chi_{676000}(37,\cdot)\)	676000.bvc	7800	yes	\(1\)	\(1\)	\(e\left(\frac{3359}{7800}\right)\)	\(e\left(\frac{367}{780}\right)\)	\(e\left(\frac{3359}{3900}\right)\)	\(e\left(\frac{2837}{7800}\right)\)	\(e\left(\frac{3863}{3900}\right)\)	\(e\left(\frac{7}{600}\right)\)	\(e\left(\frac{2343}{2600}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{759}{2600}\right)\)	\(e\left(\frac{569}{7800}\right)\)
\(\chi_{676000}(41,\cdot)\)	676000.btr	3900	no	\(-1\)	\(1\)	\(e\left(\frac{3487}{3900}\right)\)	\(e\left(\frac{157}{780}\right)\)	\(e\left(\frac{1537}{1950}\right)\)	\(e\left(\frac{304}{975}\right)\)	\(e\left(\frac{1309}{1950}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{31}{325}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{887}{1300}\right)\)	\(e\left(\frac{1267}{3900}\right)\)
\(\chi_{676000}(43,\cdot)\)	676000.bqq	1560	no	\(1\)	\(1\)	\(e\left(\frac{1559}{1560}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{779}{780}\right)\)	\(e\left(\frac{587}{1560}\right)\)	\(e\left(\frac{23}{780}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{93}{520}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{519}{520}\right)\)	\(e\left(\frac{89}{1560}\right)\)
\(\chi_{676000}(47,\cdot)\)	676000.bno	1300	no	\(-1\)	\(1\)	\(e\left(\frac{1127}{1300}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{477}{650}\right)\)	\(e\left(\frac{411}{1300}\right)\)	\(e\left(\frac{1003}{1300}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{37}{1300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{781}{1300}\right)\)	\(e\left(\frac{258}{325}\right)\)
\(\chi_{676000}(49,\cdot)\)	676000.bhu	390	no	\(1\)	\(1\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{149}{390}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{301}{390}\right)\)
\(\chi_{676000}(51,\cdot)\)	676000.bip	520	no	\(-1\)	\(1\)	\(e\left(\frac{177}{520}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{491}{520}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{407}{520}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{520}\right)\)	\(e\left(\frac{237}{520}\right)\)
\(\chi_{676000}(53,\cdot)\)	676000.bsk	2600	yes	\(-1\)	\(1\)	\(e\left(\frac{2469}{2600}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{1169}{1300}\right)\)	\(e\left(\frac{717}{2600}\right)\)	\(e\left(\frac{933}{1300}\right)\)	\(e\left(\frac{87}{200}\right)\)	\(e\left(\frac{1189}{2600}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{2207}{2600}\right)\)	\(e\left(\frac{479}{2600}\right)\)
\(\chi_{676000}(57,\cdot)\)	676000.pq	52	no	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(-i\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{676000}(59,\cdot)\)	676000.bux	7800	yes	\(1\)	\(1\)	\(e\left(\frac{589}{7800}\right)\)	\(e\left(\frac{128}{195}\right)\)	\(e\left(\frac{589}{3900}\right)\)	\(e\left(\frac{577}{7800}\right)\)	\(e\left(\frac{149}{1950}\right)\)	\(e\left(\frac{47}{600}\right)\)	\(e\left(\frac{1903}{2600}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{589}{2600}\right)\)	\(e\left(\frac{3349}{7800}\right)\)
\(\chi_{676000}(61,\cdot)\)	676000.bvk	7800	yes	\(1\)	\(1\)	\(e\left(\frac{2551}{7800}\right)\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{2551}{3900}\right)\)	\(e\left(\frac{6793}{7800}\right)\)	\(e\left(\frac{791}{1950}\right)\)	\(e\left(\frac{23}{600}\right)\)	\(e\left(\frac{1827}{2600}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{2551}{2600}\right)\)	\(e\left(\frac{5791}{7800}\right)\)
\(\chi_{676000}(63,\cdot)\)	676000.bsy	3900	no	\(-1\)	\(1\)	\(e\left(\frac{2377}{3900}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{427}{1950}\right)\)	\(e\left(\frac{511}{3900}\right)\)	\(e\left(\frac{2003}{3900}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{979}{1300}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{1077}{1300}\right)\)	\(e\left(\frac{791}{1950}\right)\)
\(\chi_{676000}(67,\cdot)\)	676000.bvq	7800	yes	\(-1\)	\(1\)	\(e\left(\frac{7373}{7800}\right)\)	\(e\left(\frac{529}{780}\right)\)	\(e\left(\frac{3473}{3900}\right)\)	\(e\left(\frac{5339}{7800}\right)\)	\(e\left(\frac{2411}{3900}\right)\)	\(e\left(\frac{529}{600}\right)\)	\(e\left(\frac{1621}{2600}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{2173}{2600}\right)\)	\(e\left(\frac{5243}{7800}\right)\)
\(\chi_{676000}(69,\cdot)\)	676000.bvn	7800	yes	\(1\)	\(1\)	\(e\left(\frac{7273}{7800}\right)\)	\(e\left(\frac{599}{780}\right)\)	\(e\left(\frac{3373}{3900}\right)\)	\(e\left(\frac{1639}{7800}\right)\)	\(e\left(\frac{934}{975}\right)\)	\(e\left(\frac{329}{600}\right)\)	\(e\left(\frac{1821}{2600}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{2073}{2600}\right)\)	\(e\left(\frac{493}{7800}\right)\)
\(\chi_{676000}(71,\cdot)\)	676000.btu	3900	no	\(1\)	\(1\)	\(e\left(\frac{731}{3900}\right)\)	\(e\left(\frac{131}{780}\right)\)	\(e\left(\frac{731}{1950}\right)\)	\(e\left(\frac{902}{975}\right)\)	\(e\left(\frac{1517}{1950}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{231}{650}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{731}{1300}\right)\)	\(e\left(\frac{2021}{3900}\right)\)
\(\chi_{676000}(73,\cdot)\)	676000.bpe	1300	no	\(1\)	\(1\)	\(e\left(\frac{103}{650}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{103}{325}\right)\)	\(e\left(\frac{379}{650}\right)\)	\(e\left(\frac{209}{1300}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{643}{650}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{309}{650}\right)\)	\(e\left(\frac{971}{1300}\right)\)
\(\chi_{676000}(77,\cdot)\)	676000.brq	2600	yes	\(-1\)	\(1\)	\(e\left(\frac{2127}{2600}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{827}{1300}\right)\)	\(e\left(\frac{1011}{2600}\right)\)	\(e\left(\frac{739}{1300}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{1187}{2600}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{1181}{2600}\right)\)	\(e\left(\frac{757}{2600}\right)\)
\(\chi_{676000}(79,\cdot)\)	676000.blc	650	no	\(-1\)	\(1\)	\(e\left(\frac{531}{650}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{206}{325}\right)\)	\(e\left(\frac{54}{325}\right)\)	\(e\left(\frac{209}{650}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{311}{650}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{293}{650}\right)\)	\(e\left(\frac{321}{650}\right)\)
\(\chi_{676000}(81,\cdot)\)	676000.bqy	1950	no	\(1\)	\(1\)	\(e\left(\frac{1397}{1950}\right)\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{422}{975}\right)\)	\(e\left(\frac{521}{1950}\right)\)	\(e\left(\frac{629}{975}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{469}{650}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{97}{650}\right)\)	\(e\left(\frac{77}{1950}\right)\)
\(\chi_{676000}(83,\cdot)\)	676000.bsh	2600	yes	\(-1\)	\(1\)	\(e\left(\frac{2351}{2600}\right)\)	\(e\left(\frac{173}{260}\right)\)	\(e\left(\frac{1051}{1300}\right)\)	\(e\left(\frac{693}{2600}\right)\)	\(e\left(\frac{7}{1300}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{1481}{2600}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1853}{2600}\right)\)	\(e\left(\frac{2141}{2600}\right)\)

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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.