LMFDB - Group of Dirichlet characters of modulus 234446

Show commands: PariGP / SageMath

sage: H = DirichletGroup(234446)

pari: g = idealstar(,234446,2)

Character group

sage: G.order() pari: g.no
Order	=	117222
sage: H.invariants() pari: g.cyc
Structure	=	$C_{117222}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{234446}(3,\cdot)$

First 32 of 117222 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{234446}(1,\cdot)$	234446.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{234446}(3,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{1}{117222}\right)$	$e\left(\frac{5069}{5582}\right)$	$e\left(\frac{13619}{117222}\right)$	$e\left(\frac{1}{58611}\right)$	$e\left(\frac{39878}{58611}\right)$	$e\left(\frac{9251}{39074}\right)$	$e\left(\frac{53225}{58611}\right)$	$e\left(\frac{2461}{2791}\right)$	$e\left(\frac{48917}{58611}\right)$	$e\left(\frac{2270}{19537}\right)$
$\chi_{234446}(5,\cdot)$	234446.j	5582	no	$-1$	$1$	$e\left(\frac{5069}{5582}\right)$	$e\left(\frac{369}{5582}\right)$	$e\left(\frac{2117}{5582}\right)$	$e\left(\frac{2278}{2791}\right)$	$e\left(\frac{616}{2791}\right)$	$e\left(\frac{2393}{5582}\right)$	$e\left(\frac{2719}{2791}\right)$	$e\left(\frac{2147}{2791}\right)$	$e\left(\frac{2251}{2791}\right)$	$e\left(\frac{802}{2791}\right)$
$\chi_{234446}(7,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{13619}{117222}\right)$	$e\left(\frac{2117}{5582}\right)$	$e\left(\frac{31957}{117222}\right)$	$e\left(\frac{13619}{58611}\right)$	$e\left(\frac{8956}{58611}\right)$	$e\left(\frac{14793}{39074}\right)$	$e\left(\frac{29038}{58611}\right)$	$e\left(\frac{2031}{2791}\right)$	$e\left(\frac{27997}{58611}\right)$	$e\left(\frac{7596}{19537}\right)$
$\chi_{234446}(9,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{1}{58611}\right)$	$e\left(\frac{2278}{2791}\right)$	$e\left(\frac{13619}{58611}\right)$	$e\left(\frac{2}{58611}\right)$	$e\left(\frac{21145}{58611}\right)$	$e\left(\frac{9251}{19537}\right)$	$e\left(\frac{47839}{58611}\right)$	$e\left(\frac{2131}{2791}\right)$	$e\left(\frac{39223}{58611}\right)$	$e\left(\frac{4540}{19537}\right)$
$\chi_{234446}(11,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{39878}{58611}\right)$	$e\left(\frac{616}{2791}\right)$	$e\left(\frac{8956}{58611}\right)$	$e\left(\frac{21145}{58611}\right)$	$e\left(\frac{42464}{58611}\right)$	$e\left(\frac{13744}{19537}\right)$	$e\left(\frac{52814}{58611}\right)$	$e\left(\frac{2441}{2791}\right)$	$e\left(\frac{41648}{58611}\right)$	$e\left(\frac{16278}{19537}\right)$
$\chi_{234446}(13,\cdot)$	234446.n	39074	no	$-1$	$1$	$e\left(\frac{9251}{39074}\right)$	$e\left(\frac{2393}{5582}\right)$	$e\left(\frac{14793}{39074}\right)$	$e\left(\frac{9251}{19537}\right)$	$e\left(\frac{13744}{19537}\right)$	$e\left(\frac{26823}{39074}\right)$	$e\left(\frac{13001}{19537}\right)$	$e\left(\frac{1572}{2791}\right)$	$e\left(\frac{15173}{19537}\right)$	$e\left(\frac{12022}{19537}\right)$
$\chi_{234446}(15,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{53225}{58611}\right)$	$e\left(\frac{2719}{2791}\right)$	$e\left(\frac{29038}{58611}\right)$	$e\left(\frac{47839}{58611}\right)$	$e\left(\frac{52814}{58611}\right)$	$e\left(\frac{13001}{19537}\right)$	$e\left(\frac{51713}{58611}\right)$	$e\left(\frac{1817}{2791}\right)$	$e\left(\frac{37577}{58611}\right)$	$e\left(\frac{7884}{19537}\right)$
$\chi_{234446}(17,\cdot)$	234446.i	2791	no	$1$	$1$	$e\left(\frac{2461}{2791}\right)$	$e\left(\frac{2147}{2791}\right)$	$e\left(\frac{2031}{2791}\right)$	$e\left(\frac{2131}{2791}\right)$	$e\left(\frac{2441}{2791}\right)$	$e\left(\frac{1572}{2791}\right)$	$e\left(\frac{1817}{2791}\right)$	$e\left(\frac{2142}{2791}\right)$	$e\left(\frac{1068}{2791}\right)$	$e\left(\frac{1701}{2791}\right)$
$\chi_{234446}(19,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{48917}{58611}\right)$	$e\left(\frac{2251}{2791}\right)$	$e\left(\frac{27997}{58611}\right)$	$e\left(\frac{39223}{58611}\right)$	$e\left(\frac{41648}{58611}\right)$	$e\left(\frac{15173}{19537}\right)$	$e\left(\frac{37577}{58611}\right)$	$e\left(\frac{1068}{2791}\right)$	$e\left(\frac{40406}{58611}\right)$	$e\left(\frac{6101}{19537}\right)$
$\chi_{234446}(21,\cdot)$	234446.m	19537	no	$1$	$1$	$e\left(\frac{2270}{19537}\right)$	$e\left(\frac{802}{2791}\right)$	$e\left(\frac{7596}{19537}\right)$	$e\left(\frac{4540}{19537}\right)$	$e\left(\frac{16278}{19537}\right)$	$e\left(\frac{12022}{19537}\right)$	$e\left(\frac{7884}{19537}\right)$	$e\left(\frac{1701}{2791}\right)$	$e\left(\frac{6101}{19537}\right)$	$e\left(\frac{9866}{19537}\right)$
$\chi_{234446}(23,\cdot)$	234446.m	19537	no	$1$	$1$	$e\left(\frac{8163}{19537}\right)$	$e\left(\frac{2225}{2791}\right)$	$e\left(\frac{6367}{19537}\right)$	$e\left(\frac{16326}{19537}\right)$	$e\left(\frac{16777}{19537}\right)$	$e\left(\frac{16224}{19537}\right)$	$e\left(\frac{4201}{19537}\right)$	$e\left(\frac{2732}{2791}\right)$	$e\left(\frac{4993}{19537}\right)$	$e\left(\frac{14530}{19537}\right)$
$\chi_{234446}(25,\cdot)$	234446.i	2791	no	$1$	$1$	$e\left(\frac{2278}{2791}\right)$	$e\left(\frac{369}{2791}\right)$	$e\left(\frac{2117}{2791}\right)$	$e\left(\frac{1765}{2791}\right)$	$e\left(\frac{1232}{2791}\right)$	$e\left(\frac{2393}{2791}\right)$	$e\left(\frac{2647}{2791}\right)$	$e\left(\frac{1503}{2791}\right)$	$e\left(\frac{1711}{2791}\right)$	$e\left(\frac{1604}{2791}\right)$
$\chi_{234446}(27,\cdot)$	234446.n	39074	no	$-1$	$1$	$e\left(\frac{1}{39074}\right)$	$e\left(\frac{4043}{5582}\right)$	$e\left(\frac{13619}{39074}\right)$	$e\left(\frac{1}{19537}\right)$	$e\left(\frac{804}{19537}\right)$	$e\left(\frac{27753}{39074}\right)$	$e\left(\frac{14151}{19537}\right)$	$e\left(\frac{1801}{2791}\right)$	$e\left(\frac{9843}{19537}\right)$	$e\left(\frac{6810}{19537}\right)$
$\chi_{234446}(29,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{806}{58611}\right)$	$e\left(\frac{2381}{2791}\right)$	$e\left(\frac{16657}{58611}\right)$	$e\left(\frac{1612}{58611}\right)$	$e\left(\frac{45680}{58611}\right)$	$e\left(\frac{12709}{19537}\right)$	$e\left(\frac{50807}{58611}\right)$	$e\left(\frac{1121}{2791}\right)$	$e\left(\frac{22409}{58611}\right)$	$e\left(\frac{5821}{19537}\right)$
$\chi_{234446}(31,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{17390}{58611}\right)$	$e\left(\frac{1757}{2791}\right)$	$e\left(\frac{45970}{58611}\right)$	$e\left(\frac{34780}{58611}\right)$	$e\left(\frac{44747}{58611}\right)$	$e\left(\frac{7232}{19537}\right)$	$e\left(\frac{54287}{58611}\right)$	$e\left(\frac{1983}{2791}\right)$	$e\left(\frac{31763}{58611}\right)$	$e\left(\frac{1583}{19537}\right)$
$\chi_{234446}(33,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{79757}{117222}\right)$	$e\left(\frac{719}{5582}\right)$	$e\left(\frac{31531}{117222}\right)$	$e\left(\frac{21146}{58611}\right)$	$e\left(\frac{23731}{58611}\right)$	$e\left(\frac{36739}{39074}\right)$	$e\left(\frac{47428}{58611}\right)$	$e\left(\frac{2111}{2791}\right)$	$e\left(\frac{31954}{58611}\right)$	$e\left(\frac{18548}{19537}\right)$
$\chi_{234446}(35,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{1423}{58611}\right)$	$e\left(\frac{1243}{2791}\right)$	$e\left(\frac{38207}{58611}\right)$	$e\left(\frac{2846}{58611}\right)$	$e\left(\frac{21892}{58611}\right)$	$e\left(\frac{15772}{19537}\right)$	$e\left(\frac{27526}{58611}\right)$	$e\left(\frac{1387}{2791}\right)$	$e\left(\frac{16657}{58611}\right)$	$e\left(\frac{13210}{19537}\right)$
$\chi_{234446}(37,\cdot)$	234446.m	19537	no	$1$	$1$	$e\left(\frac{14337}{19537}\right)$	$e\left(\frac{1003}{2791}\right)$	$e\left(\frac{2825}{19537}\right)$	$e\left(\frac{9137}{19537}\right)$	$e\left(\frac{236}{19537}\right)$	$e\left(\frac{4219}{19537}\right)$	$e\left(\frac{1821}{19537}\right)$	$e\left(\frac{1}{2791}\right)$	$e\left(\frac{6680}{19537}\right)$	$e\left(\frac{17162}{19537}\right)$
$\chi_{234446}(39,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{13877}{58611}\right)$	$e\left(\frac{940}{2791}\right)$	$e\left(\frac{28999}{58611}\right)$	$e\left(\frac{27754}{58611}\right)$	$e\left(\frac{22499}{58611}\right)$	$e\left(\frac{18037}{19537}\right)$	$e\left(\frac{33617}{58611}\right)$	$e\left(\frac{1242}{2791}\right)$	$e\left(\frac{35825}{58611}\right)$	$e\left(\frac{14292}{19537}\right)$
$\chi_{234446}(41,\cdot)$	234446.m	19537	no	$1$	$1$	$e\left(\frac{4451}{19537}\right)$	$e\left(\frac{1816}{2791}\right)$	$e\left(\frac{14395}{19537}\right)$	$e\left(\frac{8902}{19537}\right)$	$e\left(\frac{6666}{19537}\right)$	$e\left(\frac{15689}{19537}\right)$	$e\left(\frac{17163}{19537}\right)$	$e\left(\frac{998}{2791}\right)$	$e\left(\frac{18478}{19537}\right)$	$e\left(\frac{18846}{19537}\right)$
$\chi_{234446}(43,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{29410}{58611}\right)$	$e\left(\frac{816}{2791}\right)$	$e\left(\frac{45827}{58611}\right)$	$e\left(\frac{209}{58611}\right)$	$e\left(\frac{11740}{58611}\right)$	$e\left(\frac{19185}{19537}\right)$	$e\left(\frac{46546}{58611}\right)$	$e\left(\frac{805}{2791}\right)$	$e\left(\frac{25339}{58611}\right)$	$e\left(\frac{5542}{19537}\right)$
$\chi_{234446}(45,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{106451}{117222}\right)$	$e\left(\frac{4925}{5582}\right)$	$e\left(\frac{71695}{117222}\right)$	$e\left(\frac{47840}{58611}\right)$	$e\left(\frac{34081}{58611}\right)$	$e\left(\frac{35253}{39074}\right)$	$e\left(\frac{46327}{58611}\right)$	$e\left(\frac{1487}{2791}\right)$	$e\left(\frac{27883}{58611}\right)$	$e\left(\frac{10154}{19537}\right)$
$\chi_{234446}(47,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{3058}{58611}\right)$	$e\left(\frac{2579}{2791}\right)$	$e\left(\frac{33092}{58611}\right)$	$e\left(\frac{6116}{58611}\right)$	$e\left(\frac{13477}{58611}\right)$	$e\left(\frac{19519}{19537}\right)$	$e\left(\frac{57217}{58611}\right)$	$e\left(\frac{2404}{2791}\right)$	$e\left(\frac{25828}{58611}\right)$	$e\left(\frac{12050}{19537}\right)$
$\chi_{234446}(49,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{13619}{58611}\right)$	$e\left(\frac{2117}{2791}\right)$	$e\left(\frac{31957}{58611}\right)$	$e\left(\frac{27238}{58611}\right)$	$e\left(\frac{17912}{58611}\right)$	$e\left(\frac{14793}{19537}\right)$	$e\left(\frac{58076}{58611}\right)$	$e\left(\frac{1271}{2791}\right)$	$e\left(\frac{55994}{58611}\right)$	$e\left(\frac{15192}{19537}\right)$
$\chi_{234446}(51,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{103363}{117222}\right)$	$e\left(\frac{3781}{5582}\right)$	$e\left(\frac{98921}{117222}\right)$	$e\left(\frac{44752}{58611}\right)$	$e\left(\frac{32528}{58611}\right)$	$e\left(\frac{31259}{39074}\right)$	$e\left(\frac{32771}{58611}\right)$	$e\left(\frac{1812}{2791}\right)$	$e\left(\frac{12734}{58611}\right)$	$e\left(\frac{14177}{19537}\right)$
$\chi_{234446}(53,\cdot)$	234446.o	58611	no	$1$	$1$	$e\left(\frac{54491}{58611}\right)$	$e\left(\frac{773}{2791}\right)$	$e\left(\frac{39058}{58611}\right)$	$e\left(\frac{50371}{58611}\right)$	$e\left(\frac{37157}{58611}\right)$	$e\left(\frac{2567}{19537}\right)$	$e\left(\frac{12113}{58611}\right)$	$e\left(\frac{766}{2791}\right)$	$e\left(\frac{50378}{58611}\right)$	$e\left(\frac{11646}{19537}\right)$
$\chi_{234446}(55,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{68983}{117222}\right)$	$e\left(\frac{1601}{5582}\right)$	$e\left(\frac{62369}{117222}\right)$	$e\left(\frac{10372}{58611}\right)$	$e\left(\frac{55400}{58611}\right)$	$e\left(\frac{5165}{39074}\right)$	$e\left(\frac{51302}{58611}\right)$	$e\left(\frac{1797}{2791}\right)$	$e\left(\frac{30308}{58611}\right)$	$e\left(\frac{2355}{19537}\right)$
$\chi_{234446}(57,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{97835}{117222}\right)$	$e\left(\frac{3989}{5582}\right)$	$e\left(\frac{69613}{117222}\right)$	$e\left(\frac{39224}{58611}\right)$	$e\left(\frac{22915}{58611}\right)$	$e\left(\frac{523}{39074}\right)$	$e\left(\frac{32191}{58611}\right)$	$e\left(\frac{738}{2791}\right)$	$e\left(\frac{30712}{58611}\right)$	$e\left(\frac{8371}{19537}\right)$
$\chi_{234446}(59,\cdot)$	234446.l	16746	no	$-1$	$1$	$e\left(\frac{12797}{16746}\right)$	$e\left(\frac{2579}{5582}\right)$	$e\left(\frac{6721}{16746}\right)$	$e\left(\frac{4424}{8373}\right)$	$e\left(\frac{1162}{8373}\right)$	$e\left(\frac{1991}{5582}\right)$	$e\left(\frac{1894}{8373}\right)$	$e\left(\frac{1202}{2791}\right)$	$e\left(\frac{250}{8373}\right)$	$e\left(\frac{462}{2791}\right)$
$\chi_{234446}(61,\cdot)$	234446.k	8373	no	$1$	$1$	$e\left(\frac{3356}{8373}\right)$	$e\left(\frac{142}{2791}\right)$	$e\left(\frac{5530}{8373}\right)$	$e\left(\frac{6712}{8373}\right)$	$e\left(\frac{1445}{8373}\right)$	$e\left(\frac{2063}{2791}\right)$	$e\left(\frac{3782}{8373}\right)$	$e\left(\frac{2076}{2791}\right)$	$e\left(\frac{455}{8373}\right)$	$e\left(\frac{171}{2791}\right)$
$\chi_{234446}(63,\cdot)$	234446.p	117222	no	$-1$	$1$	$e\left(\frac{13621}{117222}\right)$	$e\left(\frac{1091}{5582}\right)$	$e\left(\frac{59195}{117222}\right)$	$e\left(\frac{13621}{58611}\right)$	$e\left(\frac{30101}{58611}\right)$	$e\left(\frac{33295}{39074}\right)$	$e\left(\frac{18266}{58611}\right)$	$e\left(\frac{1371}{2791}\right)$	$e\left(\frac{8609}{58611}\right)$	$e\left(\frac{12136}{19537}\right)$

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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	$234446$
Structure	\(C_{117222}\)
Order	$117222$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{234446}(1,\cdot)\)	234446.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{234446}(3,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{1}{117222}\right)\)	\(e\left(\frac{5069}{5582}\right)\)	\(e\left(\frac{13619}{117222}\right)\)	\(e\left(\frac{1}{58611}\right)\)	\(e\left(\frac{39878}{58611}\right)\)	\(e\left(\frac{9251}{39074}\right)\)	\(e\left(\frac{53225}{58611}\right)\)	\(e\left(\frac{2461}{2791}\right)\)	\(e\left(\frac{48917}{58611}\right)\)	\(e\left(\frac{2270}{19537}\right)\)
\(\chi_{234446}(5,\cdot)\)	234446.j	5582	no	\(-1\)	\(1\)	\(e\left(\frac{5069}{5582}\right)\)	\(e\left(\frac{369}{5582}\right)\)	\(e\left(\frac{2117}{5582}\right)\)	\(e\left(\frac{2278}{2791}\right)\)	\(e\left(\frac{616}{2791}\right)\)	\(e\left(\frac{2393}{5582}\right)\)	\(e\left(\frac{2719}{2791}\right)\)	\(e\left(\frac{2147}{2791}\right)\)	\(e\left(\frac{2251}{2791}\right)\)	\(e\left(\frac{802}{2791}\right)\)
\(\chi_{234446}(7,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{13619}{117222}\right)\)	\(e\left(\frac{2117}{5582}\right)\)	\(e\left(\frac{31957}{117222}\right)\)	\(e\left(\frac{13619}{58611}\right)\)	\(e\left(\frac{8956}{58611}\right)\)	\(e\left(\frac{14793}{39074}\right)\)	\(e\left(\frac{29038}{58611}\right)\)	\(e\left(\frac{2031}{2791}\right)\)	\(e\left(\frac{27997}{58611}\right)\)	\(e\left(\frac{7596}{19537}\right)\)
\(\chi_{234446}(9,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{1}{58611}\right)\)	\(e\left(\frac{2278}{2791}\right)\)	\(e\left(\frac{13619}{58611}\right)\)	\(e\left(\frac{2}{58611}\right)\)	\(e\left(\frac{21145}{58611}\right)\)	\(e\left(\frac{9251}{19537}\right)\)	\(e\left(\frac{47839}{58611}\right)\)	\(e\left(\frac{2131}{2791}\right)\)	\(e\left(\frac{39223}{58611}\right)\)	\(e\left(\frac{4540}{19537}\right)\)
\(\chi_{234446}(11,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{39878}{58611}\right)\)	\(e\left(\frac{616}{2791}\right)\)	\(e\left(\frac{8956}{58611}\right)\)	\(e\left(\frac{21145}{58611}\right)\)	\(e\left(\frac{42464}{58611}\right)\)	\(e\left(\frac{13744}{19537}\right)\)	\(e\left(\frac{52814}{58611}\right)\)	\(e\left(\frac{2441}{2791}\right)\)	\(e\left(\frac{41648}{58611}\right)\)	\(e\left(\frac{16278}{19537}\right)\)
\(\chi_{234446}(13,\cdot)\)	234446.n	39074	no	\(-1\)	\(1\)	\(e\left(\frac{9251}{39074}\right)\)	\(e\left(\frac{2393}{5582}\right)\)	\(e\left(\frac{14793}{39074}\right)\)	\(e\left(\frac{9251}{19537}\right)\)	\(e\left(\frac{13744}{19537}\right)\)	\(e\left(\frac{26823}{39074}\right)\)	\(e\left(\frac{13001}{19537}\right)\)	\(e\left(\frac{1572}{2791}\right)\)	\(e\left(\frac{15173}{19537}\right)\)	\(e\left(\frac{12022}{19537}\right)\)
\(\chi_{234446}(15,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{53225}{58611}\right)\)	\(e\left(\frac{2719}{2791}\right)\)	\(e\left(\frac{29038}{58611}\right)\)	\(e\left(\frac{47839}{58611}\right)\)	\(e\left(\frac{52814}{58611}\right)\)	\(e\left(\frac{13001}{19537}\right)\)	\(e\left(\frac{51713}{58611}\right)\)	\(e\left(\frac{1817}{2791}\right)\)	\(e\left(\frac{37577}{58611}\right)\)	\(e\left(\frac{7884}{19537}\right)\)
\(\chi_{234446}(17,\cdot)\)	234446.i	2791	no	\(1\)	\(1\)	\(e\left(\frac{2461}{2791}\right)\)	\(e\left(\frac{2147}{2791}\right)\)	\(e\left(\frac{2031}{2791}\right)\)	\(e\left(\frac{2131}{2791}\right)\)	\(e\left(\frac{2441}{2791}\right)\)	\(e\left(\frac{1572}{2791}\right)\)	\(e\left(\frac{1817}{2791}\right)\)	\(e\left(\frac{2142}{2791}\right)\)	\(e\left(\frac{1068}{2791}\right)\)	\(e\left(\frac{1701}{2791}\right)\)
\(\chi_{234446}(19,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{48917}{58611}\right)\)	\(e\left(\frac{2251}{2791}\right)\)	\(e\left(\frac{27997}{58611}\right)\)	\(e\left(\frac{39223}{58611}\right)\)	\(e\left(\frac{41648}{58611}\right)\)	\(e\left(\frac{15173}{19537}\right)\)	\(e\left(\frac{37577}{58611}\right)\)	\(e\left(\frac{1068}{2791}\right)\)	\(e\left(\frac{40406}{58611}\right)\)	\(e\left(\frac{6101}{19537}\right)\)
\(\chi_{234446}(21,\cdot)\)	234446.m	19537	no	\(1\)	\(1\)	\(e\left(\frac{2270}{19537}\right)\)	\(e\left(\frac{802}{2791}\right)\)	\(e\left(\frac{7596}{19537}\right)\)	\(e\left(\frac{4540}{19537}\right)\)	\(e\left(\frac{16278}{19537}\right)\)	\(e\left(\frac{12022}{19537}\right)\)	\(e\left(\frac{7884}{19537}\right)\)	\(e\left(\frac{1701}{2791}\right)\)	\(e\left(\frac{6101}{19537}\right)\)	\(e\left(\frac{9866}{19537}\right)\)
\(\chi_{234446}(23,\cdot)\)	234446.m	19537	no	\(1\)	\(1\)	\(e\left(\frac{8163}{19537}\right)\)	\(e\left(\frac{2225}{2791}\right)\)	\(e\left(\frac{6367}{19537}\right)\)	\(e\left(\frac{16326}{19537}\right)\)	\(e\left(\frac{16777}{19537}\right)\)	\(e\left(\frac{16224}{19537}\right)\)	\(e\left(\frac{4201}{19537}\right)\)	\(e\left(\frac{2732}{2791}\right)\)	\(e\left(\frac{4993}{19537}\right)\)	\(e\left(\frac{14530}{19537}\right)\)
\(\chi_{234446}(25,\cdot)\)	234446.i	2791	no	\(1\)	\(1\)	\(e\left(\frac{2278}{2791}\right)\)	\(e\left(\frac{369}{2791}\right)\)	\(e\left(\frac{2117}{2791}\right)\)	\(e\left(\frac{1765}{2791}\right)\)	\(e\left(\frac{1232}{2791}\right)\)	\(e\left(\frac{2393}{2791}\right)\)	\(e\left(\frac{2647}{2791}\right)\)	\(e\left(\frac{1503}{2791}\right)\)	\(e\left(\frac{1711}{2791}\right)\)	\(e\left(\frac{1604}{2791}\right)\)
\(\chi_{234446}(27,\cdot)\)	234446.n	39074	no	\(-1\)	\(1\)	\(e\left(\frac{1}{39074}\right)\)	\(e\left(\frac{4043}{5582}\right)\)	\(e\left(\frac{13619}{39074}\right)\)	\(e\left(\frac{1}{19537}\right)\)	\(e\left(\frac{804}{19537}\right)\)	\(e\left(\frac{27753}{39074}\right)\)	\(e\left(\frac{14151}{19537}\right)\)	\(e\left(\frac{1801}{2791}\right)\)	\(e\left(\frac{9843}{19537}\right)\)	\(e\left(\frac{6810}{19537}\right)\)
\(\chi_{234446}(29,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{806}{58611}\right)\)	\(e\left(\frac{2381}{2791}\right)\)	\(e\left(\frac{16657}{58611}\right)\)	\(e\left(\frac{1612}{58611}\right)\)	\(e\left(\frac{45680}{58611}\right)\)	\(e\left(\frac{12709}{19537}\right)\)	\(e\left(\frac{50807}{58611}\right)\)	\(e\left(\frac{1121}{2791}\right)\)	\(e\left(\frac{22409}{58611}\right)\)	\(e\left(\frac{5821}{19537}\right)\)
\(\chi_{234446}(31,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{17390}{58611}\right)\)	\(e\left(\frac{1757}{2791}\right)\)	\(e\left(\frac{45970}{58611}\right)\)	\(e\left(\frac{34780}{58611}\right)\)	\(e\left(\frac{44747}{58611}\right)\)	\(e\left(\frac{7232}{19537}\right)\)	\(e\left(\frac{54287}{58611}\right)\)	\(e\left(\frac{1983}{2791}\right)\)	\(e\left(\frac{31763}{58611}\right)\)	\(e\left(\frac{1583}{19537}\right)\)
\(\chi_{234446}(33,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{79757}{117222}\right)\)	\(e\left(\frac{719}{5582}\right)\)	\(e\left(\frac{31531}{117222}\right)\)	\(e\left(\frac{21146}{58611}\right)\)	\(e\left(\frac{23731}{58611}\right)\)	\(e\left(\frac{36739}{39074}\right)\)	\(e\left(\frac{47428}{58611}\right)\)	\(e\left(\frac{2111}{2791}\right)\)	\(e\left(\frac{31954}{58611}\right)\)	\(e\left(\frac{18548}{19537}\right)\)
\(\chi_{234446}(35,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{1423}{58611}\right)\)	\(e\left(\frac{1243}{2791}\right)\)	\(e\left(\frac{38207}{58611}\right)\)	\(e\left(\frac{2846}{58611}\right)\)	\(e\left(\frac{21892}{58611}\right)\)	\(e\left(\frac{15772}{19537}\right)\)	\(e\left(\frac{27526}{58611}\right)\)	\(e\left(\frac{1387}{2791}\right)\)	\(e\left(\frac{16657}{58611}\right)\)	\(e\left(\frac{13210}{19537}\right)\)
\(\chi_{234446}(37,\cdot)\)	234446.m	19537	no	\(1\)	\(1\)	\(e\left(\frac{14337}{19537}\right)\)	\(e\left(\frac{1003}{2791}\right)\)	\(e\left(\frac{2825}{19537}\right)\)	\(e\left(\frac{9137}{19537}\right)\)	\(e\left(\frac{236}{19537}\right)\)	\(e\left(\frac{4219}{19537}\right)\)	\(e\left(\frac{1821}{19537}\right)\)	\(e\left(\frac{1}{2791}\right)\)	\(e\left(\frac{6680}{19537}\right)\)	\(e\left(\frac{17162}{19537}\right)\)
\(\chi_{234446}(39,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{13877}{58611}\right)\)	\(e\left(\frac{940}{2791}\right)\)	\(e\left(\frac{28999}{58611}\right)\)	\(e\left(\frac{27754}{58611}\right)\)	\(e\left(\frac{22499}{58611}\right)\)	\(e\left(\frac{18037}{19537}\right)\)	\(e\left(\frac{33617}{58611}\right)\)	\(e\left(\frac{1242}{2791}\right)\)	\(e\left(\frac{35825}{58611}\right)\)	\(e\left(\frac{14292}{19537}\right)\)
\(\chi_{234446}(41,\cdot)\)	234446.m	19537	no	\(1\)	\(1\)	\(e\left(\frac{4451}{19537}\right)\)	\(e\left(\frac{1816}{2791}\right)\)	\(e\left(\frac{14395}{19537}\right)\)	\(e\left(\frac{8902}{19537}\right)\)	\(e\left(\frac{6666}{19537}\right)\)	\(e\left(\frac{15689}{19537}\right)\)	\(e\left(\frac{17163}{19537}\right)\)	\(e\left(\frac{998}{2791}\right)\)	\(e\left(\frac{18478}{19537}\right)\)	\(e\left(\frac{18846}{19537}\right)\)
\(\chi_{234446}(43,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{29410}{58611}\right)\)	\(e\left(\frac{816}{2791}\right)\)	\(e\left(\frac{45827}{58611}\right)\)	\(e\left(\frac{209}{58611}\right)\)	\(e\left(\frac{11740}{58611}\right)\)	\(e\left(\frac{19185}{19537}\right)\)	\(e\left(\frac{46546}{58611}\right)\)	\(e\left(\frac{805}{2791}\right)\)	\(e\left(\frac{25339}{58611}\right)\)	\(e\left(\frac{5542}{19537}\right)\)
\(\chi_{234446}(45,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{106451}{117222}\right)\)	\(e\left(\frac{4925}{5582}\right)\)	\(e\left(\frac{71695}{117222}\right)\)	\(e\left(\frac{47840}{58611}\right)\)	\(e\left(\frac{34081}{58611}\right)\)	\(e\left(\frac{35253}{39074}\right)\)	\(e\left(\frac{46327}{58611}\right)\)	\(e\left(\frac{1487}{2791}\right)\)	\(e\left(\frac{27883}{58611}\right)\)	\(e\left(\frac{10154}{19537}\right)\)
\(\chi_{234446}(47,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{3058}{58611}\right)\)	\(e\left(\frac{2579}{2791}\right)\)	\(e\left(\frac{33092}{58611}\right)\)	\(e\left(\frac{6116}{58611}\right)\)	\(e\left(\frac{13477}{58611}\right)\)	\(e\left(\frac{19519}{19537}\right)\)	\(e\left(\frac{57217}{58611}\right)\)	\(e\left(\frac{2404}{2791}\right)\)	\(e\left(\frac{25828}{58611}\right)\)	\(e\left(\frac{12050}{19537}\right)\)
\(\chi_{234446}(49,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{13619}{58611}\right)\)	\(e\left(\frac{2117}{2791}\right)\)	\(e\left(\frac{31957}{58611}\right)\)	\(e\left(\frac{27238}{58611}\right)\)	\(e\left(\frac{17912}{58611}\right)\)	\(e\left(\frac{14793}{19537}\right)\)	\(e\left(\frac{58076}{58611}\right)\)	\(e\left(\frac{1271}{2791}\right)\)	\(e\left(\frac{55994}{58611}\right)\)	\(e\left(\frac{15192}{19537}\right)\)
\(\chi_{234446}(51,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{103363}{117222}\right)\)	\(e\left(\frac{3781}{5582}\right)\)	\(e\left(\frac{98921}{117222}\right)\)	\(e\left(\frac{44752}{58611}\right)\)	\(e\left(\frac{32528}{58611}\right)\)	\(e\left(\frac{31259}{39074}\right)\)	\(e\left(\frac{32771}{58611}\right)\)	\(e\left(\frac{1812}{2791}\right)\)	\(e\left(\frac{12734}{58611}\right)\)	\(e\left(\frac{14177}{19537}\right)\)
\(\chi_{234446}(53,\cdot)\)	234446.o	58611	no	\(1\)	\(1\)	\(e\left(\frac{54491}{58611}\right)\)	\(e\left(\frac{773}{2791}\right)\)	\(e\left(\frac{39058}{58611}\right)\)	\(e\left(\frac{50371}{58611}\right)\)	\(e\left(\frac{37157}{58611}\right)\)	\(e\left(\frac{2567}{19537}\right)\)	\(e\left(\frac{12113}{58611}\right)\)	\(e\left(\frac{766}{2791}\right)\)	\(e\left(\frac{50378}{58611}\right)\)	\(e\left(\frac{11646}{19537}\right)\)
\(\chi_{234446}(55,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{68983}{117222}\right)\)	\(e\left(\frac{1601}{5582}\right)\)	\(e\left(\frac{62369}{117222}\right)\)	\(e\left(\frac{10372}{58611}\right)\)	\(e\left(\frac{55400}{58611}\right)\)	\(e\left(\frac{5165}{39074}\right)\)	\(e\left(\frac{51302}{58611}\right)\)	\(e\left(\frac{1797}{2791}\right)\)	\(e\left(\frac{30308}{58611}\right)\)	\(e\left(\frac{2355}{19537}\right)\)
\(\chi_{234446}(57,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{97835}{117222}\right)\)	\(e\left(\frac{3989}{5582}\right)\)	\(e\left(\frac{69613}{117222}\right)\)	\(e\left(\frac{39224}{58611}\right)\)	\(e\left(\frac{22915}{58611}\right)\)	\(e\left(\frac{523}{39074}\right)\)	\(e\left(\frac{32191}{58611}\right)\)	\(e\left(\frac{738}{2791}\right)\)	\(e\left(\frac{30712}{58611}\right)\)	\(e\left(\frac{8371}{19537}\right)\)
\(\chi_{234446}(59,\cdot)\)	234446.l	16746	no	\(-1\)	\(1\)	\(e\left(\frac{12797}{16746}\right)\)	\(e\left(\frac{2579}{5582}\right)\)	\(e\left(\frac{6721}{16746}\right)\)	\(e\left(\frac{4424}{8373}\right)\)	\(e\left(\frac{1162}{8373}\right)\)	\(e\left(\frac{1991}{5582}\right)\)	\(e\left(\frac{1894}{8373}\right)\)	\(e\left(\frac{1202}{2791}\right)\)	\(e\left(\frac{250}{8373}\right)\)	\(e\left(\frac{462}{2791}\right)\)
\(\chi_{234446}(61,\cdot)\)	234446.k	8373	no	\(1\)	\(1\)	\(e\left(\frac{3356}{8373}\right)\)	\(e\left(\frac{142}{2791}\right)\)	\(e\left(\frac{5530}{8373}\right)\)	\(e\left(\frac{6712}{8373}\right)\)	\(e\left(\frac{1445}{8373}\right)\)	\(e\left(\frac{2063}{2791}\right)\)	\(e\left(\frac{3782}{8373}\right)\)	\(e\left(\frac{2076}{2791}\right)\)	\(e\left(\frac{455}{8373}\right)\)	\(e\left(\frac{171}{2791}\right)\)
\(\chi_{234446}(63,\cdot)\)	234446.p	117222	no	\(-1\)	\(1\)	\(e\left(\frac{13621}{117222}\right)\)	\(e\left(\frac{1091}{5582}\right)\)	\(e\left(\frac{59195}{117222}\right)\)	\(e\left(\frac{13621}{58611}\right)\)	\(e\left(\frac{30101}{58611}\right)\)	\(e\left(\frac{33295}{39074}\right)\)	\(e\left(\frac{18266}{58611}\right)\)	\(e\left(\frac{1371}{2791}\right)\)	\(e\left(\frac{8609}{58611}\right)\)	\(e\left(\frac{12136}{19537}\right)\)

Introduction

L-functions

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Character group

First 32 of 117222 characters

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