LMFDB - Group of Dirichlet characters of modulus 290

sage:H = DirichletGroup(290)

pari:g = idealstar(,290,2)

Character group

sage:G.order() pari:g.no
Order	=	112
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{28}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{290}(117,\cdot)$, $\chi_{290}(31,\cdot)$

First 32 of 112 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{290}(1,\cdot)$	290.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{290}(3,\cdot)$	290.o	28	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{290}(7,\cdot)$	290.q	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{28}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{290}(9,\cdot)$	290.l	14	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{290}(11,\cdot)$	290.p	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$-i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{290}(13,\cdot)$	290.r	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{290}(17,\cdot)$	290.e	4	no	$1$	$1$	$-1$	$i$	$1$	$-i$	$i$	$1$	$i$	$-i$	$-i$	$-1$
$\chi_{290}(19,\cdot)$	290.s	28	no	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{7}\right)$	$i$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{290}(21,\cdot)$	290.p	28	no	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$-i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{290}(23,\cdot)$	290.q	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{28}\right)$	$-i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{290}(27,\cdot)$	290.o	28	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{290}(31,\cdot)$	290.p	28	no	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{290}(33,\cdot)$	290.r	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{290}(37,\cdot)$	290.o	28	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{290}(39,\cdot)$	290.s	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$-i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{290}(41,\cdot)$	290.i	4	no	$-1$	$1$	$i$	$1$	$-1$	$i$	$-1$	$i$	$i$	$i$	$1$	$-i$
$\chi_{290}(43,\cdot)$	290.o	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{290}(47,\cdot)$	290.o	28	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{290}(49,\cdot)$	290.n	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{290}(51,\cdot)$	290.m	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{290}(53,\cdot)$	290.q	28	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{28}\right)$	$-i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{290}(57,\cdot)$	290.g	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$-i$	$-i$	$1$	$-1$	$-i$	$-i$
$\chi_{290}(59,\cdot)$	290.b	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{290}(61,\cdot)$	290.p	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$-i$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{290}(63,\cdot)$	290.r	28	no	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{28}\right)$	$i$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{290}(67,\cdot)$	290.r	28	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{28}\right)$	$-i$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{290}(69,\cdot)$	290.s	28	no	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{4}{7}\right)$	$i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{290}(71,\cdot)$	290.m	14	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{290}(73,\cdot)$	290.t	28	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{290}(77,\cdot)$	290.t	28	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{15}{28}\right)$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{290}(79,\cdot)$	290.s	28	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{290}(81,\cdot)$	290.k	7	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$290$
Structure	\(C_{4}\times C_{28}\)
Order	$112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{290}(1,\cdot)\)	290.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{290}(3,\cdot)\)	290.o	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{290}(7,\cdot)\)	290.q	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{290}(9,\cdot)\)	290.l	14	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{290}(11,\cdot)\)	290.p	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{290}(13,\cdot)\)	290.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{290}(17,\cdot)\)	290.e	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{290}(19,\cdot)\)	290.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(i\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{290}(21,\cdot)\)	290.p	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{290}(23,\cdot)\)	290.q	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{290}(27,\cdot)\)	290.o	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{290}(31,\cdot)\)	290.p	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{290}(33,\cdot)\)	290.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{290}(37,\cdot)\)	290.o	28	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{290}(39,\cdot)\)	290.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{290}(41,\cdot)\)	290.i	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-i\)
\(\chi_{290}(43,\cdot)\)	290.o	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{290}(47,\cdot)\)	290.o	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{290}(49,\cdot)\)	290.n	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{290}(51,\cdot)\)	290.m	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{290}(53,\cdot)\)	290.q	28	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{290}(57,\cdot)\)	290.g	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{290}(59,\cdot)\)	290.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{290}(61,\cdot)\)	290.p	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-i\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{290}(63,\cdot)\)	290.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(i\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{290}(67,\cdot)\)	290.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{290}(69,\cdot)\)	290.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{290}(71,\cdot)\)	290.m	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{290}(73,\cdot)\)	290.t	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{290}(77,\cdot)\)	290.t	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{290}(79,\cdot)\)	290.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{290}(81,\cdot)\)	290.k	7	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)

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L-functions

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Character group

First 32 of 112 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.