LMFDB - Group of Dirichlet characters of modulus 29645

Show commands: PariGP / SageMath

sage: H = DirichletGroup(29645)

pari: g = idealstar(,29645,2)

Character group

sage: G.order() pari: g.no
Order	=	18480
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4620}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{29645}(23717,\cdot)$, $\chi_{29645}(1816,\cdot)$, $\chi_{29645}(19846,\cdot)$

First 32 of 18480 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$12$	$13$	$16$	$17$
$\chi_{29645}(1,\cdot)$	29645.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{29645}(2,\cdot)$	29645.hj	4620	yes	$1$	$1$	$e\left(\frac{1637}{4620}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{1637}{2310}\right)$	$e\left(\frac{403}{770}\right)$	$e\left(\frac{97}{1540}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{811}{924}\right)$	$e\left(\frac{149}{1540}\right)$	$e\left(\frac{482}{1155}\right)$	$e\left(\frac{793}{4620}\right)$
$\chi_{29645}(3,\cdot)$	29645.fv	420	no	$1$	$1$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{283}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{229}{420}\right)$
$\chi_{29645}(4,\cdot)$	29645.hc	2310	yes	$1$	$1$	$e\left(\frac{1637}{2310}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{482}{1155}\right)$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{97}{770}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{349}{462}\right)$	$e\left(\frac{149}{770}\right)$	$e\left(\frac{964}{1155}\right)$	$e\left(\frac{793}{2310}\right)$
$\chi_{29645}(6,\cdot)$	29645.gm	770	no	$1$	$1$	$e\left(\frac{403}{770}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{141}{385}\right)$	$e\left(\frac{439}{770}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{359}{385}\right)$	$e\left(\frac{36}{385}\right)$	$e\left(\frac{276}{385}\right)$
$\chi_{29645}(8,\cdot)$	29645.gx	1540	yes	$1$	$1$	$e\left(\frac{97}{1540}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{97}{770}\right)$	$e\left(\frac{439}{770}\right)$	$e\left(\frac{291}{1540}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{447}{1540}\right)$	$e\left(\frac{97}{385}\right)$	$e\left(\frac{793}{1540}\right)$
$\chi_{29645}(9,\cdot)$	29645.fb	210	no	$1$	$1$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{19}{210}\right)$
$\chi_{29645}(12,\cdot)$	29645.gr	924	yes	$1$	$1$	$e\left(\frac{811}{924}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{349}{462}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{709}{924}\right)$	$e\left(\frac{9}{308}\right)$	$e\left(\frac{118}{231}\right)$	$e\left(\frac{821}{924}\right)$
$\chi_{29645}(13,\cdot)$	29645.gw	1540	yes	$-1$	$1$	$e\left(\frac{149}{1540}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{149}{770}\right)$	$e\left(\frac{359}{385}\right)$	$e\left(\frac{447}{1540}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{9}{308}\right)$	$e\left(\frac{1409}{1540}\right)$	$e\left(\frac{149}{385}\right)$	$e\left(\frac{591}{1540}\right)$
$\chi_{29645}(16,\cdot)$	29645.gu	1155	no	$1$	$1$	$e\left(\frac{482}{1155}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{964}{1155}\right)$	$e\left(\frac{36}{385}\right)$	$e\left(\frac{97}{385}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{118}{231}\right)$	$e\left(\frac{149}{385}\right)$	$e\left(\frac{773}{1155}\right)$	$e\left(\frac{793}{1155}\right)$
$\chi_{29645}(17,\cdot)$	29645.hg	4620	yes	$-1$	$1$	$e\left(\frac{793}{4620}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{793}{2310}\right)$	$e\left(\frac{276}{385}\right)$	$e\left(\frac{793}{1540}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{821}{924}\right)$	$e\left(\frac{591}{1540}\right)$	$e\left(\frac{793}{1155}\right)$	$e\left(\frac{4427}{4620}\right)$
$\chi_{29645}(18,\cdot)$	29645.gf	660	no	$1$	$1$	$e\left(\frac{457}{660}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{173}{660}\right)$
$\chi_{29645}(19,\cdot)$	29645.fo	330	no	$1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{101}{330}\right)$
$\chi_{29645}(23,\cdot)$	29645.gs	924	yes	$-1$	$1$	$e\left(\frac{841}{924}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{379}{462}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{225}{308}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{901}{924}\right)$	$e\left(\frac{117}{308}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{509}{924}\right)$
$\chi_{29645}(24,\cdot)$	29645.hd	2310	yes	$1$	$1$	$e\left(\frac{268}{1155}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{536}{1155}\right)$	$e\left(\frac{159}{385}\right)$	$e\left(\frac{268}{385}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{149}{231}\right)$	$e\left(\frac{97}{770}\right)$	$e\left(\frac{1072}{1155}\right)$	$e\left(\frac{139}{2310}\right)$
$\chi_{29645}(26,\cdot)$	29645.hf	2310	no	$-1$	$1$	$e\left(\frac{521}{1155}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{1042}{1155}\right)$	$e\left(\frac{351}{770}\right)$	$e\left(\frac{136}{385}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{419}{462}\right)$	$e\left(\frac{9}{770}\right)$	$e\left(\frac{929}{1155}\right)$	$e\left(\frac{1283}{2310}\right)$
$\chi_{29645}(27,\cdot)$	29645.ek	140	no	$1$	$1$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{89}{140}\right)$
$\chi_{29645}(29,\cdot)$	29645.gj	770	yes	$-1$	$1$	$e\left(\frac{307}{385}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{229}{385}\right)$	$e\left(\frac{251}{770}\right)$	$e\left(\frac{151}{385}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{97}{385}\right)$	$e\left(\frac{73}{385}\right)$	$e\left(\frac{303}{385}\right)$
$\chi_{29645}(31,\cdot)$	29645.fm	330	no	$-1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{157}{330}\right)$
$\chi_{29645}(32,\cdot)$	29645.gq	924	yes	$1$	$1$	$e\left(\frac{713}{924}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{251}{462}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{97}{308}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{359}{924}\right)$	$e\left(\frac{149}{308}\right)$	$e\left(\frac{20}{231}\right)$	$e\left(\frac{793}{924}\right)$
$\chi_{29645}(34,\cdot)$	29645.ep	154	yes	$-1$	$1$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{10}{77}\right)$
$\chi_{29645}(36,\cdot)$	29645.ft	385	no	$1$	$1$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{36}{385}\right)$	$e\left(\frac{282}{385}\right)$	$e\left(\frac{54}{385}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{333}{385}\right)$	$e\left(\frac{72}{385}\right)$	$e\left(\frac{167}{385}\right)$
$\chi_{29645}(37,\cdot)$	29645.hh	4620	yes	$-1$	$1$	$e\left(\frac{2039}{4620}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{2039}{2310}\right)$	$e\left(\frac{213}{385}\right)$	$e\left(\frac{499}{1540}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{919}{924}\right)$	$e\left(\frac{703}{1540}\right)$	$e\left(\frac{884}{1155}\right)$	$e\left(\frac{31}{4620}\right)$
$\chi_{29645}(38,\cdot)$	29645.hi	4620	yes	$1$	$1$	$e\left(\frac{1273}{4620}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{1273}{2310}\right)$	$e\left(\frac{137}{770}\right)$	$e\left(\frac{1273}{1540}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{419}{924}\right)$	$e\left(\frac{471}{1540}\right)$	$e\left(\frac{118}{1155}\right)$	$e\left(\frac{2207}{4620}\right)$
$\chi_{29645}(39,\cdot)$	29645.he	2310	yes	$-1$	$1$	$e\left(\frac{307}{1155}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{614}{1155}\right)$	$e\left(\frac{597}{770}\right)$	$e\left(\frac{307}{385}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{19}{462}\right)$	$e\left(\frac{289}{385}\right)$	$e\left(\frac{73}{1155}\right)$	$e\left(\frac{1073}{1155}\right)$
$\chi_{29645}(41,\cdot)$	29645.gm	770	no	$1$	$1$	$e\left(\frac{381}{770}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{381}{385}\right)$	$e\left(\frac{97}{385}\right)$	$e\left(\frac{373}{770}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{348}{385}\right)$	$e\left(\frac{377}{385}\right)$	$e\left(\frac{67}{385}\right)$
$\chi_{29645}(43,\cdot)$	29645.fj	308	yes	$1$	$1$	$e\left(\frac{213}{308}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{23}{308}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{239}{308}\right)$	$e\left(\frac{283}{308}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{141}{308}\right)$
$\chi_{29645}(46,\cdot)$	29645.ha	2310	no	$-1$	$1$	$e\left(\frac{611}{2310}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{611}{1155}\right)$	$e\left(\frac{453}{770}\right)$	$e\left(\frac{611}{770}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{197}{231}\right)$	$e\left(\frac{367}{770}\right)$	$e\left(\frac{67}{1155}\right)$	$e\left(\frac{1669}{2310}\right)$
$\chi_{29645}(47,\cdot)$	29645.hi	4620	yes	$1$	$1$	$e\left(\frac{1091}{4620}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{1091}{2310}\right)$	$e\left(\frac{389}{770}\right)$	$e\left(\frac{1091}{1540}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{685}{924}\right)$	$e\left(\frac{1017}{1540}\right)$	$e\left(\frac{1091}{1155}\right)$	$e\left(\frac{4069}{4620}\right)$
$\chi_{29645}(48,\cdot)$	29645.fd	220	no	$1$	$1$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{51}{220}\right)$
$\chi_{29645}(51,\cdot)$	29645.ha	2310	no	$-1$	$1$	$e\left(\frac{787}{2310}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{787}{1155}\right)$	$e\left(\frac{431}{770}\right)$	$e\left(\frac{17}{770}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{169}{770}\right)$	$e\left(\frac{419}{1155}\right)$	$e\left(\frac{1163}{2310}\right)$
$\chi_{29645}(52,\cdot)$	29645.hg	4620	yes	$-1$	$1$	$e\left(\frac{3721}{4620}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{1411}{2310}\right)$	$e\left(\frac{377}{385}\right)$	$e\left(\frac{641}{1540}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{725}{924}\right)$	$e\left(\frac{167}{1540}\right)$	$e\left(\frac{256}{1155}\right)$	$e\left(\frac{3359}{4620}\right)$

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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 $\F_{q}$

Modulus	$29645$
Structure	\(C_{2}\times C_{2}\times C_{4620}\)
Order	$18480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(12\)	\(13\)	\(16\)	\(17\)
\(\chi_{29645}(1,\cdot)\)	29645.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{29645}(2,\cdot)\)	29645.hj	4620	yes	\(1\)	\(1\)	\(e\left(\frac{1637}{4620}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{1637}{2310}\right)\)	\(e\left(\frac{403}{770}\right)\)	\(e\left(\frac{97}{1540}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{811}{924}\right)\)	\(e\left(\frac{149}{1540}\right)\)	\(e\left(\frac{482}{1155}\right)\)	\(e\left(\frac{793}{4620}\right)\)
\(\chi_{29645}(3,\cdot)\)	29645.fv	420	no	\(1\)	\(1\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{283}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{229}{420}\right)\)
\(\chi_{29645}(4,\cdot)\)	29645.hc	2310	yes	\(1\)	\(1\)	\(e\left(\frac{1637}{2310}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{482}{1155}\right)\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{97}{770}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{349}{462}\right)\)	\(e\left(\frac{149}{770}\right)\)	\(e\left(\frac{964}{1155}\right)\)	\(e\left(\frac{793}{2310}\right)\)
\(\chi_{29645}(6,\cdot)\)	29645.gm	770	no	\(1\)	\(1\)	\(e\left(\frac{403}{770}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{141}{385}\right)\)	\(e\left(\frac{439}{770}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{359}{385}\right)\)	\(e\left(\frac{36}{385}\right)\)	\(e\left(\frac{276}{385}\right)\)
\(\chi_{29645}(8,\cdot)\)	29645.gx	1540	yes	\(1\)	\(1\)	\(e\left(\frac{97}{1540}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{97}{770}\right)\)	\(e\left(\frac{439}{770}\right)\)	\(e\left(\frac{291}{1540}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{447}{1540}\right)\)	\(e\left(\frac{97}{385}\right)\)	\(e\left(\frac{793}{1540}\right)\)
\(\chi_{29645}(9,\cdot)\)	29645.fb	210	no	\(1\)	\(1\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)
\(\chi_{29645}(12,\cdot)\)	29645.gr	924	yes	\(1\)	\(1\)	\(e\left(\frac{811}{924}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{349}{462}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{709}{924}\right)\)	\(e\left(\frac{9}{308}\right)\)	\(e\left(\frac{118}{231}\right)\)	\(e\left(\frac{821}{924}\right)\)
\(\chi_{29645}(13,\cdot)\)	29645.gw	1540	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{1540}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{149}{770}\right)\)	\(e\left(\frac{359}{385}\right)\)	\(e\left(\frac{447}{1540}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{9}{308}\right)\)	\(e\left(\frac{1409}{1540}\right)\)	\(e\left(\frac{149}{385}\right)\)	\(e\left(\frac{591}{1540}\right)\)
\(\chi_{29645}(16,\cdot)\)	29645.gu	1155	no	\(1\)	\(1\)	\(e\left(\frac{482}{1155}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{964}{1155}\right)\)	\(e\left(\frac{36}{385}\right)\)	\(e\left(\frac{97}{385}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{118}{231}\right)\)	\(e\left(\frac{149}{385}\right)\)	\(e\left(\frac{773}{1155}\right)\)	\(e\left(\frac{793}{1155}\right)\)
\(\chi_{29645}(17,\cdot)\)	29645.hg	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{793}{4620}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{793}{2310}\right)\)	\(e\left(\frac{276}{385}\right)\)	\(e\left(\frac{793}{1540}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{821}{924}\right)\)	\(e\left(\frac{591}{1540}\right)\)	\(e\left(\frac{793}{1155}\right)\)	\(e\left(\frac{4427}{4620}\right)\)
\(\chi_{29645}(18,\cdot)\)	29645.gf	660	no	\(1\)	\(1\)	\(e\left(\frac{457}{660}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{173}{660}\right)\)
\(\chi_{29645}(19,\cdot)\)	29645.fo	330	no	\(1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)
\(\chi_{29645}(23,\cdot)\)	29645.gs	924	yes	\(-1\)	\(1\)	\(e\left(\frac{841}{924}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{379}{462}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{225}{308}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{901}{924}\right)\)	\(e\left(\frac{117}{308}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{509}{924}\right)\)
\(\chi_{29645}(24,\cdot)\)	29645.hd	2310	yes	\(1\)	\(1\)	\(e\left(\frac{268}{1155}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{536}{1155}\right)\)	\(e\left(\frac{159}{385}\right)\)	\(e\left(\frac{268}{385}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{149}{231}\right)\)	\(e\left(\frac{97}{770}\right)\)	\(e\left(\frac{1072}{1155}\right)\)	\(e\left(\frac{139}{2310}\right)\)
\(\chi_{29645}(26,\cdot)\)	29645.hf	2310	no	\(-1\)	\(1\)	\(e\left(\frac{521}{1155}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{1042}{1155}\right)\)	\(e\left(\frac{351}{770}\right)\)	\(e\left(\frac{136}{385}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{419}{462}\right)\)	\(e\left(\frac{9}{770}\right)\)	\(e\left(\frac{929}{1155}\right)\)	\(e\left(\frac{1283}{2310}\right)\)
\(\chi_{29645}(27,\cdot)\)	29645.ek	140	no	\(1\)	\(1\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{89}{140}\right)\)
\(\chi_{29645}(29,\cdot)\)	29645.gj	770	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{385}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{229}{385}\right)\)	\(e\left(\frac{251}{770}\right)\)	\(e\left(\frac{151}{385}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{97}{385}\right)\)	\(e\left(\frac{73}{385}\right)\)	\(e\left(\frac{303}{385}\right)\)
\(\chi_{29645}(31,\cdot)\)	29645.fm	330	no	\(-1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)
\(\chi_{29645}(32,\cdot)\)	29645.gq	924	yes	\(1\)	\(1\)	\(e\left(\frac{713}{924}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{251}{462}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{97}{308}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{359}{924}\right)\)	\(e\left(\frac{149}{308}\right)\)	\(e\left(\frac{20}{231}\right)\)	\(e\left(\frac{793}{924}\right)\)
\(\chi_{29645}(34,\cdot)\)	29645.ep	154	yes	\(-1\)	\(1\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)
\(\chi_{29645}(36,\cdot)\)	29645.ft	385	no	\(1\)	\(1\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{36}{385}\right)\)	\(e\left(\frac{282}{385}\right)\)	\(e\left(\frac{54}{385}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{333}{385}\right)\)	\(e\left(\frac{72}{385}\right)\)	\(e\left(\frac{167}{385}\right)\)
\(\chi_{29645}(37,\cdot)\)	29645.hh	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{2039}{4620}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{2039}{2310}\right)\)	\(e\left(\frac{213}{385}\right)\)	\(e\left(\frac{499}{1540}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{919}{924}\right)\)	\(e\left(\frac{703}{1540}\right)\)	\(e\left(\frac{884}{1155}\right)\)	\(e\left(\frac{31}{4620}\right)\)
\(\chi_{29645}(38,\cdot)\)	29645.hi	4620	yes	\(1\)	\(1\)	\(e\left(\frac{1273}{4620}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{1273}{2310}\right)\)	\(e\left(\frac{137}{770}\right)\)	\(e\left(\frac{1273}{1540}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{419}{924}\right)\)	\(e\left(\frac{471}{1540}\right)\)	\(e\left(\frac{118}{1155}\right)\)	\(e\left(\frac{2207}{4620}\right)\)
\(\chi_{29645}(39,\cdot)\)	29645.he	2310	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{1155}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{614}{1155}\right)\)	\(e\left(\frac{597}{770}\right)\)	\(e\left(\frac{307}{385}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{19}{462}\right)\)	\(e\left(\frac{289}{385}\right)\)	\(e\left(\frac{73}{1155}\right)\)	\(e\left(\frac{1073}{1155}\right)\)
\(\chi_{29645}(41,\cdot)\)	29645.gm	770	no	\(1\)	\(1\)	\(e\left(\frac{381}{770}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{381}{385}\right)\)	\(e\left(\frac{97}{385}\right)\)	\(e\left(\frac{373}{770}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{348}{385}\right)\)	\(e\left(\frac{377}{385}\right)\)	\(e\left(\frac{67}{385}\right)\)
\(\chi_{29645}(43,\cdot)\)	29645.fj	308	yes	\(1\)	\(1\)	\(e\left(\frac{213}{308}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{23}{308}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{239}{308}\right)\)	\(e\left(\frac{283}{308}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{141}{308}\right)\)
\(\chi_{29645}(46,\cdot)\)	29645.ha	2310	no	\(-1\)	\(1\)	\(e\left(\frac{611}{2310}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{611}{1155}\right)\)	\(e\left(\frac{453}{770}\right)\)	\(e\left(\frac{611}{770}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{197}{231}\right)\)	\(e\left(\frac{367}{770}\right)\)	\(e\left(\frac{67}{1155}\right)\)	\(e\left(\frac{1669}{2310}\right)\)
\(\chi_{29645}(47,\cdot)\)	29645.hi	4620	yes	\(1\)	\(1\)	\(e\left(\frac{1091}{4620}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{1091}{2310}\right)\)	\(e\left(\frac{389}{770}\right)\)	\(e\left(\frac{1091}{1540}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{685}{924}\right)\)	\(e\left(\frac{1017}{1540}\right)\)	\(e\left(\frac{1091}{1155}\right)\)	\(e\left(\frac{4069}{4620}\right)\)
\(\chi_{29645}(48,\cdot)\)	29645.fd	220	no	\(1\)	\(1\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{51}{220}\right)\)
\(\chi_{29645}(51,\cdot)\)	29645.ha	2310	no	\(-1\)	\(1\)	\(e\left(\frac{787}{2310}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{787}{1155}\right)\)	\(e\left(\frac{431}{770}\right)\)	\(e\left(\frac{17}{770}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{169}{770}\right)\)	\(e\left(\frac{419}{1155}\right)\)	\(e\left(\frac{1163}{2310}\right)\)
\(\chi_{29645}(52,\cdot)\)	29645.hg	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{3721}{4620}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{1411}{2310}\right)\)	\(e\left(\frac{377}{385}\right)\)	\(e\left(\frac{641}{1540}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{725}{924}\right)\)	\(e\left(\frac{167}{1540}\right)\)	\(e\left(\frac{256}{1155}\right)\)	\(e\left(\frac{3359}{4620}\right)\)

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L-functions

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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.