LMFDB - Group of Dirichlet characters of modulus 262

Show commands: PariGP / SageMath

sage: H = DirichletGroup(262)

pari: g = idealstar(,262,2)

Character group

sage: G.order() pari: g.no
Order	=	130
sage: H.invariants() pari: g.cyc
Structure	=	$C_{130}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{262}(133,\cdot)$

First 32 of 130 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{262}(1,\cdot)$	262.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{262}(3,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{262}(5,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{65}\right)$
$\chi_{262}(7,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{65}\right)$
$\chi_{262}(9,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{6}{65}\right)$
$\chi_{262}(11,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{262}(13,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{17}{65}\right)$
$\chi_{262}(15,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{262}(17,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{37}{65}\right)$
$\chi_{262}(19,\cdot)$	262.f	26	no	$-1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{262}(21,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{262}(23,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{47}{65}\right)$
$\chi_{262}(25,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{58}{65}\right)$
$\chi_{262}(27,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{9}{65}\right)$
$\chi_{262}(29,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{59}{65}\right)$
$\chi_{262}(31,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{31}{65}\right)$
$\chi_{262}(33,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{262}(35,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{262}(37,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{64}{65}\right)$
$\chi_{262}(39,\cdot)$	262.e	13	no	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{262}(41,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{54}{65}\right)$
$\chi_{262}(43,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{16}{65}\right)$
$\chi_{262}(45,\cdot)$	262.e	13	no	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{262}(47,\cdot)$	262.f	26	no	$-1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{262}(49,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{8}{65}\right)$
$\chi_{262}(51,\cdot)$	262.f	26	no	$-1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{262}(53,\cdot)$	262.c	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$
$\chi_{262}(55,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{53}{65}\right)$
$\chi_{262}(57,\cdot)$	262.h	130	no	$-1$	$1$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{18}{65}\right)$
$\chi_{262}(59,\cdot)$	262.g	65	no	$1$	$1$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{262}(61,\cdot)$	262.c	5	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$
$\chi_{262}(63,\cdot)$	262.e	13	no	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{13}\right)$

Click here to search among the remaining 98 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 $\F_{q}$

Modulus	$262$
Structure	\(C_{130}\)
Order	$130$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{262}(1,\cdot)\)	262.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{262}(3,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{262}(5,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{65}\right)\)
\(\chi_{262}(7,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{65}\right)\)
\(\chi_{262}(9,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{6}{65}\right)\)
\(\chi_{262}(11,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{262}(13,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{17}{65}\right)\)
\(\chi_{262}(15,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{262}(17,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{37}{65}\right)\)
\(\chi_{262}(19,\cdot)\)	262.f	26	no	\(-1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{262}(21,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{262}(23,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{47}{65}\right)\)
\(\chi_{262}(25,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{58}{65}\right)\)
\(\chi_{262}(27,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{9}{65}\right)\)
\(\chi_{262}(29,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{59}{65}\right)\)
\(\chi_{262}(31,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{65}\right)\)
\(\chi_{262}(33,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{262}(35,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{262}(37,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{64}{65}\right)\)
\(\chi_{262}(39,\cdot)\)	262.e	13	no	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{262}(41,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{54}{65}\right)\)
\(\chi_{262}(43,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{16}{65}\right)\)
\(\chi_{262}(45,\cdot)\)	262.e	13	no	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{262}(47,\cdot)\)	262.f	26	no	\(-1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{262}(49,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{8}{65}\right)\)
\(\chi_{262}(51,\cdot)\)	262.f	26	no	\(-1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{262}(53,\cdot)\)	262.c	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{262}(55,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{53}{65}\right)\)
\(\chi_{262}(57,\cdot)\)	262.h	130	no	\(-1\)	\(1\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{18}{65}\right)\)
\(\chi_{262}(59,\cdot)\)	262.g	65	no	\(1\)	\(1\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{262}(61,\cdot)\)	262.c	5	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{262}(63,\cdot)\)	262.e	13	no	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 130 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.