LMFDB - Group of Dirichlet characters of modulus 783

sage:H = DirichletGroup(783)

pari:g = idealstar(,783,2)

Character group

sage:G.order() pari:g.no
Order	=	504
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{252}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{783}(407,\cdot)$, $\chi_{783}(379,\cdot)$

First 32 of 504 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{783}(1,\cdot)$	783.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{783}(2,\cdot)$	783.bj	252	yes	$1$	$1$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{103}{252}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{783}(4,\cdot)$	783.bf	126	yes	$1$	$1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{46}{63}\right)$
$\chi_{783}(5,\cdot)$	783.bh	126	yes	$-1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{783}(7,\cdot)$	783.bc	63	yes	$1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{17}{63}\right)$
$\chi_{783}(8,\cdot)$	783.be	84	no	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{783}(10,\cdot)$	783.bd	84	no	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{783}(11,\cdot)$	783.bj	252	yes	$1$	$1$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{783}(13,\cdot)$	783.bf	126	yes	$1$	$1$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{783}(14,\cdot)$	783.bj	252	yes	$1$	$1$	$e\left(\frac{103}{252}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{40}{63}\right)$
$\chi_{783}(16,\cdot)$	783.bc	63	yes	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{783}(17,\cdot)$	783.m	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{783}(19,\cdot)$	783.bd	84	no	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{783}(20,\cdot)$	783.bg	126	yes	$-1$	$1$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{783}(22,\cdot)$	783.bf	126	yes	$1$	$1$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{783}(23,\cdot)$	783.bg	126	yes	$-1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{19}{63}\right)$
$\chi_{783}(25,\cdot)$	783.bc	63	yes	$1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{783}(26,\cdot)$	783.v	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{783}(28,\cdot)$	783.c	2	no	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$1$
$\chi_{783}(31,\cdot)$	783.bi	252	yes	$-1$	$1$	$e\left(\frac{37}{252}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{37}{63}\right)$
$\chi_{783}(32,\cdot)$	783.bj	252	yes	$1$	$1$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{19}{252}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{11}{252}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{783}(34,\cdot)$	783.bf	126	yes	$1$	$1$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{783}(35,\cdot)$	783.bb	42	no	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{783}(37,\cdot)$	783.bd	84	no	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{783}(38,\cdot)$	783.bh	126	yes	$-1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{783}(40,\cdot)$	783.bi	252	yes	$-1$	$1$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{25}{252}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{783}(41,\cdot)$	783.x	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{783}(43,\cdot)$	783.bi	252	yes	$-1$	$1$	$e\left(\frac{173}{252}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{125}{252}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{783}(44,\cdot)$	783.be	84	no	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{783}(46,\cdot)$	783.n	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{783}(47,\cdot)$	783.bj	252	yes	$1$	$1$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{221}{252}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{181}{252}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{783}(49,\cdot)$	783.bc	63	yes	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{34}{63}\right)$

Click here to search among the remaining 472 characters.

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	$783$
Structure	\(C_{2}\times C_{252}\)
Order	$504$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{783}(1,\cdot)\)	783.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{783}(2,\cdot)\)	783.bj	252	yes	\(1\)	\(1\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{783}(4,\cdot)\)	783.bf	126	yes	\(1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)
\(\chi_{783}(5,\cdot)\)	783.bh	126	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{783}(7,\cdot)\)	783.bc	63	yes	\(1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)
\(\chi_{783}(8,\cdot)\)	783.be	84	no	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{783}(10,\cdot)\)	783.bd	84	no	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{783}(11,\cdot)\)	783.bj	252	yes	\(1\)	\(1\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{783}(13,\cdot)\)	783.bf	126	yes	\(1\)	\(1\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{783}(14,\cdot)\)	783.bj	252	yes	\(1\)	\(1\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{40}{63}\right)\)
\(\chi_{783}(16,\cdot)\)	783.bc	63	yes	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{783}(17,\cdot)\)	783.m	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{783}(19,\cdot)\)	783.bd	84	no	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{783}(20,\cdot)\)	783.bg	126	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{783}(22,\cdot)\)	783.bf	126	yes	\(1\)	\(1\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{783}(23,\cdot)\)	783.bg	126	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)
\(\chi_{783}(25,\cdot)\)	783.bc	63	yes	\(1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{783}(26,\cdot)\)	783.v	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{783}(28,\cdot)\)	783.c	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{783}(31,\cdot)\)	783.bi	252	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{252}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{37}{63}\right)\)
\(\chi_{783}(32,\cdot)\)	783.bj	252	yes	\(1\)	\(1\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{19}{252}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{11}{252}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{783}(34,\cdot)\)	783.bf	126	yes	\(1\)	\(1\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{783}(35,\cdot)\)	783.bb	42	no	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{783}(37,\cdot)\)	783.bd	84	no	\(-1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{783}(38,\cdot)\)	783.bh	126	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{783}(40,\cdot)\)	783.bi	252	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{25}{252}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{783}(41,\cdot)\)	783.x	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{783}(43,\cdot)\)	783.bi	252	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{252}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{125}{252}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{783}(44,\cdot)\)	783.be	84	no	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{783}(46,\cdot)\)	783.n	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{783}(47,\cdot)\)	783.bj	252	yes	\(1\)	\(1\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{221}{252}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{181}{252}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{783}(49,\cdot)\)	783.bc	63	yes	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)

Introduction

L-functions

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Character group

First 32 of 504 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.