LMFDB - Group of Dirichlet characters of modulus 230

Show commands: PariGP / SageMath

sage: H = DirichletGroup(230)

pari: g = idealstar(,230,2)

Character group

sage: G.order() pari: g.no
Order	=	88
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{44}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{230}(47,\cdot)$, $\chi_{230}(51,\cdot)$

First 32 of 88 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{230}(1,\cdot)$	230.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{230}(3,\cdot)$	230.k	44	no	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{230}(7,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{230}(9,\cdot)$	230.j	22	no	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{230}(11,\cdot)$	230.h	22	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{230}(13,\cdot)$	230.k	44	no	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{230}(17,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{230}(19,\cdot)$	230.i	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{230}(21,\cdot)$	230.h	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{230}(27,\cdot)$	230.k	44	no	$-1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{230}(29,\cdot)$	230.j	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{230}(31,\cdot)$	230.g	11	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{230}(33,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{230}(37,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{230}(39,\cdot)$	230.j	22	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{230}(41,\cdot)$	230.g	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{230}(43,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{230}(47,\cdot)$	230.f	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$i$	$-1$
$\chi_{230}(49,\cdot)$	230.j	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{230}(51,\cdot)$	230.h	22	no	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{230}(53,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{230}(57,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{230}(59,\cdot)$	230.j	22	no	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{230}(61,\cdot)$	230.h	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{230}(63,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{230}(67,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{230}(71,\cdot)$	230.g	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{230}(73,\cdot)$	230.k	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{230}(77,\cdot)$	230.k	44	no	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{230}(79,\cdot)$	230.i	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{230}(81,\cdot)$	230.g	11	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{230}(83,\cdot)$	230.l	44	no	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{15}{22}\right)$

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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	$230$
Structure	\(C_{2}\times C_{44}\)
Order	$88$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{230}(1,\cdot)\)	230.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{230}(3,\cdot)\)	230.k	44	no	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{230}(7,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{230}(9,\cdot)\)	230.j	22	no	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{230}(11,\cdot)\)	230.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{230}(13,\cdot)\)	230.k	44	no	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{230}(17,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{230}(19,\cdot)\)	230.i	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{230}(21,\cdot)\)	230.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{230}(27,\cdot)\)	230.k	44	no	\(-1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{230}(29,\cdot)\)	230.j	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{230}(31,\cdot)\)	230.g	11	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{230}(33,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{230}(37,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{230}(39,\cdot)\)	230.j	22	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{230}(41,\cdot)\)	230.g	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{230}(43,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{230}(47,\cdot)\)	230.f	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{230}(49,\cdot)\)	230.j	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{230}(51,\cdot)\)	230.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{230}(53,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{230}(57,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{230}(59,\cdot)\)	230.j	22	no	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{230}(61,\cdot)\)	230.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{230}(63,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{230}(67,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{230}(71,\cdot)\)	230.g	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{230}(73,\cdot)\)	230.k	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{230}(77,\cdot)\)	230.k	44	no	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{230}(79,\cdot)\)	230.i	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{230}(81,\cdot)\)	230.g	11	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{230}(83,\cdot)\)	230.l	44	no	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 88 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.