LMFDB - Group of Dirichlet characters of modulus 245

Show commands: PariGP / SageMath

sage: H = DirichletGroup(245)

pari: g = idealstar(,245,2)

Character group

sage: G.order() pari: g.no
Order	=	168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{245}(197,\cdot)$, $\chi_{245}(101,\cdot)$

First 32 of 168 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{245}(1,\cdot)$	245.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{245}(2,\cdot)$	245.w	84	yes	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{245}(3,\cdot)$	245.x	84	yes	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{245}(4,\cdot)$	245.t	42	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{245}(6,\cdot)$	245.n	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{245}(8,\cdot)$	245.r	28	yes	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{245}(9,\cdot)$	245.t	42	yes	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{245}(11,\cdot)$	245.q	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{245}(12,\cdot)$	245.x	84	yes	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{245}(13,\cdot)$	245.s	28	yes	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{245}(16,\cdot)$	245.q	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{245}(17,\cdot)$	245.x	84	yes	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{245}(18,\cdot)$	245.m	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{245}(19,\cdot)$	245.i	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{245}(22,\cdot)$	245.r	28	yes	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{245}(23,\cdot)$	245.w	84	yes	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{245}(24,\cdot)$	245.u	42	yes	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{245}(26,\cdot)$	245.v	42	no	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{245}(27,\cdot)$	245.s	28	yes	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{245}(29,\cdot)$	245.p	14	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{245}(31,\cdot)$	245.h	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{245}(32,\cdot)$	245.w	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{245}(33,\cdot)$	245.x	84	yes	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{245}(34,\cdot)$	245.o	14	yes	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{245}(36,\cdot)$	245.k	7	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{245}(37,\cdot)$	245.w	84	yes	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{245}(38,\cdot)$	245.x	84	yes	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{245}(39,\cdot)$	245.t	42	yes	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{245}(41,\cdot)$	245.n	14	no	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{245}(43,\cdot)$	245.r	28	yes	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{245}(44,\cdot)$	245.t	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{245}(46,\cdot)$	245.q	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$

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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	$245$
Structure	\(C_{2}\times C_{84}\)
Order	$168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{245}(1,\cdot)\)	245.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{245}(2,\cdot)\)	245.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{245}(3,\cdot)\)	245.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{245}(4,\cdot)\)	245.t	42	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{245}(6,\cdot)\)	245.n	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{245}(8,\cdot)\)	245.r	28	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{245}(9,\cdot)\)	245.t	42	yes	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{245}(11,\cdot)\)	245.q	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{245}(12,\cdot)\)	245.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{245}(13,\cdot)\)	245.s	28	yes	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{245}(16,\cdot)\)	245.q	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{245}(17,\cdot)\)	245.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{245}(18,\cdot)\)	245.m	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{245}(19,\cdot)\)	245.i	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{245}(22,\cdot)\)	245.r	28	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{245}(23,\cdot)\)	245.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{245}(24,\cdot)\)	245.u	42	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{245}(26,\cdot)\)	245.v	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{245}(27,\cdot)\)	245.s	28	yes	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{245}(29,\cdot)\)	245.p	14	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{245}(31,\cdot)\)	245.h	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{245}(32,\cdot)\)	245.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{245}(33,\cdot)\)	245.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{245}(34,\cdot)\)	245.o	14	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{245}(36,\cdot)\)	245.k	7	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{245}(37,\cdot)\)	245.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{245}(38,\cdot)\)	245.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{245}(39,\cdot)\)	245.t	42	yes	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{245}(41,\cdot)\)	245.n	14	no	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{245}(43,\cdot)\)	245.r	28	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{245}(44,\cdot)\)	245.t	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{245}(46,\cdot)\)	245.q	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)

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L-functions

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First 32 of 168 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.