LMFDB - Group of Dirichlet characters of modulus 916

Show commands: PariGP / SageMath

sage: H = DirichletGroup(916)

pari: g = idealstar(,916,2)

Character group

sage: G.order() pari: g.no
Order	=	456
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{228}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{916}(459,\cdot)$, $\chi_{916}(693,\cdot)$

First 32 of 456 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{916}(1,\cdot)$	916.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{916}(3,\cdot)$	916.t	114	yes	$-1$	$1$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{916}(5,\cdot)$	916.v	114	no	$1$	$1$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{15}{38}\right)$
$\chi_{916}(7,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{63}{76}\right)$
$\chi_{916}(9,\cdot)$	916.q	57	no	$1$	$1$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{916}(11,\cdot)$	916.o	38	yes	$-1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{31}{38}\right)$
$\chi_{916}(13,\cdot)$	916.r	76	no	$-1$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{49}{76}\right)$
$\chi_{916}(15,\cdot)$	916.o	38	yes	$-1$	$1$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{29}{38}\right)$
$\chi_{916}(17,\cdot)$	916.m	19	no	$1$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{916}(19,\cdot)$	916.t	114	yes	$-1$	$1$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{916}(21,\cdot)$	916.r	76	no	$-1$	$1$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{15}{76}\right)$
$\chi_{916}(23,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{45}{76}\right)$
$\chi_{916}(25,\cdot)$	916.q	57	no	$1$	$1$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{916}(27,\cdot)$	916.p	38	yes	$-1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{916}(29,\cdot)$	916.x	228	no	$-1$	$1$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{25}{76}\right)$
$\chi_{916}(31,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{5}{76}\right)$
$\chi_{916}(33,\cdot)$	916.v	114	no	$1$	$1$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{7}{38}\right)$
$\chi_{916}(35,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{17}{76}\right)$
$\chi_{916}(37,\cdot)$	916.q	57	no	$1$	$1$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{916}(39,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{1}{76}\right)$
$\chi_{916}(41,\cdot)$	916.x	228	no	$-1$	$1$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{157}{228}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{39}{76}\right)$
$\chi_{916}(43,\cdot)$	916.p	38	yes	$-1$	$1$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{916}(45,\cdot)$	916.v	114	no	$1$	$1$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{5}{38}\right)$
$\chi_{916}(47,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{75}{76}\right)$
$\chi_{916}(49,\cdot)$	916.v	114	no	$1$	$1$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{25}{38}\right)$
$\chi_{916}(51,\cdot)$	916.t	114	yes	$-1$	$1$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{916}(53,\cdot)$	916.m	19	no	$1$	$1$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{916}(55,\cdot)$	916.t	114	yes	$-1$	$1$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{916}(57,\cdot)$	916.m	19	no	$1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{916}(59,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{61}{76}\right)$
$\chi_{916}(61,\cdot)$	916.m	19	no	$1$	$1$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{916}(63,\cdot)$	916.w	228	yes	$1$	$1$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{43}{76}\right)$

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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	$916$
Structure	\(C_{2}\times C_{228}\)
Order	$456$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{916}(1,\cdot)\)	916.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{916}(3,\cdot)\)	916.t	114	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{916}(5,\cdot)\)	916.v	114	no	\(1\)	\(1\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)
\(\chi_{916}(7,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{63}{76}\right)\)
\(\chi_{916}(9,\cdot)\)	916.q	57	no	\(1\)	\(1\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{916}(11,\cdot)\)	916.o	38	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)
\(\chi_{916}(13,\cdot)\)	916.r	76	no	\(-1\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{49}{76}\right)\)
\(\chi_{916}(15,\cdot)\)	916.o	38	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{29}{38}\right)\)
\(\chi_{916}(17,\cdot)\)	916.m	19	no	\(1\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{916}(19,\cdot)\)	916.t	114	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{916}(21,\cdot)\)	916.r	76	no	\(-1\)	\(1\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{15}{76}\right)\)
\(\chi_{916}(23,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{45}{76}\right)\)
\(\chi_{916}(25,\cdot)\)	916.q	57	no	\(1\)	\(1\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{916}(27,\cdot)\)	916.p	38	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{916}(29,\cdot)\)	916.x	228	no	\(-1\)	\(1\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{25}{76}\right)\)
\(\chi_{916}(31,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{5}{76}\right)\)
\(\chi_{916}(33,\cdot)\)	916.v	114	no	\(1\)	\(1\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{7}{38}\right)\)
\(\chi_{916}(35,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{17}{76}\right)\)
\(\chi_{916}(37,\cdot)\)	916.q	57	no	\(1\)	\(1\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{916}(39,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{1}{76}\right)\)
\(\chi_{916}(41,\cdot)\)	916.x	228	no	\(-1\)	\(1\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{157}{228}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{39}{76}\right)\)
\(\chi_{916}(43,\cdot)\)	916.p	38	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{916}(45,\cdot)\)	916.v	114	no	\(1\)	\(1\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{5}{38}\right)\)
\(\chi_{916}(47,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{75}{76}\right)\)
\(\chi_{916}(49,\cdot)\)	916.v	114	no	\(1\)	\(1\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{25}{38}\right)\)
\(\chi_{916}(51,\cdot)\)	916.t	114	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{916}(53,\cdot)\)	916.m	19	no	\(1\)	\(1\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{916}(55,\cdot)\)	916.t	114	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{916}(57,\cdot)\)	916.m	19	no	\(1\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{916}(59,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{61}{76}\right)\)
\(\chi_{916}(61,\cdot)\)	916.m	19	no	\(1\)	\(1\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{916}(63,\cdot)\)	916.w	228	yes	\(1\)	\(1\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{43}{76}\right)\)

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L-functions

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First 32 of 456 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.