LMFDB - Group of Dirichlet characters of modulus 370

Show commands: PariGP / SageMath

sage: H = DirichletGroup(370)

pari: g = idealstar(,370,2)

Character group

sage: G.order() pari: g.no
Order	=	144
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{370}(297,\cdot)$, $\chi_{370}(261,\cdot)$

First 32 of 144 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{370}(1,\cdot)$	370.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{370}(3,\cdot)$	370.y	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{370}(7,\cdot)$	370.z	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{370}(9,\cdot)$	370.x	18	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{370}(11,\cdot)$	370.l	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{370}(13,\cdot)$	370.bd	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{370}(17,\cdot)$	370.ba	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{370}(19,\cdot)$	370.bb	36	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{370}(21,\cdot)$	370.w	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{370}(23,\cdot)$	370.r	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$i$
$\chi_{370}(27,\cdot)$	370.s	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$i$
$\chi_{370}(29,\cdot)$	370.p	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$1$
$\chi_{370}(31,\cdot)$	370.f	4	no	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-i$	$-i$	$-i$	$-1$	$-i$	$-1$
$\chi_{370}(33,\cdot)$	370.z	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{370}(39,\cdot)$	370.bb	36	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{370}(41,\cdot)$	370.w	18	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{370}(43,\cdot)$	370.g	4	no	$1$	$1$	$-i$	$-i$	$-1$	$-1$	$-1$	$1$	$-i$	$-1$	$-1$	$i$
$\chi_{370}(47,\cdot)$	370.t	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$i$
$\chi_{370}(49,\cdot)$	370.x	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{370}(51,\cdot)$	370.u	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$
$\chi_{370}(53,\cdot)$	370.z	36	no	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{370}(57,\cdot)$	370.bd	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{370}(59,\cdot)$	370.bb	36	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{370}(61,\cdot)$	370.bc	36	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{370}(63,\cdot)$	370.t	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-i$
$\chi_{370}(67,\cdot)$	370.y	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{370}(69,\cdot)$	370.bb	36	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{370}(71,\cdot)$	370.o	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{370}(73,\cdot)$	370.j	4	no	$-1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$i$	$1$	$1$	$-i$	$-i$
$\chi_{370}(77,\cdot)$	370.y	36	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{370}(79,\cdot)$	370.bb	36	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{370}(81,\cdot)$	370.o	9	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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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	$370$
Structure	\(C_{4}\times C_{36}\)
Order	$144$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{370}(1,\cdot)\)	370.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{370}(3,\cdot)\)	370.y	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{370}(7,\cdot)\)	370.z	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{370}(9,\cdot)\)	370.x	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{370}(11,\cdot)\)	370.l	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{370}(13,\cdot)\)	370.bd	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{370}(17,\cdot)\)	370.ba	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{370}(19,\cdot)\)	370.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{370}(21,\cdot)\)	370.w	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{370}(23,\cdot)\)	370.r	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(i\)
\(\chi_{370}(27,\cdot)\)	370.s	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)
\(\chi_{370}(29,\cdot)\)	370.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(1\)
\(\chi_{370}(31,\cdot)\)	370.f	4	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{370}(33,\cdot)\)	370.z	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{370}(39,\cdot)\)	370.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{370}(41,\cdot)\)	370.w	18	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{370}(43,\cdot)\)	370.g	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)
\(\chi_{370}(47,\cdot)\)	370.t	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(i\)
\(\chi_{370}(49,\cdot)\)	370.x	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{370}(51,\cdot)\)	370.u	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-1\)
\(\chi_{370}(53,\cdot)\)	370.z	36	no	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{370}(57,\cdot)\)	370.bd	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{370}(59,\cdot)\)	370.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{370}(61,\cdot)\)	370.bc	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{370}(63,\cdot)\)	370.t	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-i\)
\(\chi_{370}(67,\cdot)\)	370.y	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{370}(69,\cdot)\)	370.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{370}(71,\cdot)\)	370.o	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{370}(73,\cdot)\)	370.j	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-i\)
\(\chi_{370}(77,\cdot)\)	370.y	36	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{370}(79,\cdot)\)	370.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{370}(81,\cdot)\)	370.o	9	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)

Introduction

L-functions

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Character group

First 32 of 144 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.