LMFDB - Group of Dirichlet characters of modulus 94

Show commands: PariGP / SageMath

sage: H = DirichletGroup(94)

pari: g = idealstar(,94,2)

Character group

sage: G.order() pari: g.no
Order	=	46
sage: H.invariants() pari: g.cyc
Structure	=	$C_{46}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{94}(5,\cdot)$

First 32 of 46 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{94}(1,\cdot)$	94.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{94}(3,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{94}(5,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{94}(7,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{94}(9,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{94}(11,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{94}(13,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{94}(15,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{94}(17,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{94}(19,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{94}(21,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{18}{23}\right)$
$\chi_{94}(23,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{94}(25,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{94}(27,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{19}{23}\right)$
$\chi_{94}(29,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{94}(31,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{94}(33,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{94}(35,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{7}{23}\right)$
$\chi_{94}(37,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{94}(39,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{94}(41,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{94}(43,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{94}(45,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{94}(49,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{94}(51,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{94}(53,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{94}(55,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{94}(57,\cdot)$	94.d	46	no	$-1$	$1$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{94}(59,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{7}{23}\right)$
$\chi_{94}(61,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{94}(63,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{94}(65,\cdot)$	94.c	23	no	$1$	$1$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{13}{23}\right)$

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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	$94$
Structure	\(C_{46}\)
Order	$46$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{94}(1,\cdot)\)	94.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{94}(3,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{94}(5,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{94}(7,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{94}(9,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{94}(11,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{94}(13,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{94}(15,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{94}(17,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{94}(19,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{94}(21,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)
\(\chi_{94}(23,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{94}(25,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{94}(27,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)
\(\chi_{94}(29,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{94}(31,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{94}(33,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{94}(35,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)
\(\chi_{94}(37,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{94}(39,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{94}(41,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{94}(43,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{94}(45,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{94}(49,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{94}(51,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{94}(53,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{94}(55,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{94}(57,\cdot)\)	94.d	46	no	\(-1\)	\(1\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{94}(59,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)
\(\chi_{94}(61,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{94}(63,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{94}(65,\cdot)\)	94.c	23	no	\(1\)	\(1\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)

Introduction

L-functions

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Character group

First 32 of 46 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.