LMFDB - Group of Dirichlet characters of modulus 1270

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1270)

pari: g = idealstar(,1270,2)

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	=	$\chi_{1270}(1017,\cdot)$, $\chi_{1270}(511,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1270}(1,\cdot)$	1270.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1270}(3,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{167}{252}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{251}{252}\right)$	$e\left(\frac{13}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{1270}(7,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{167}{252}\right)$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{47}{252}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{1270}(9,\cdot)$	1270.bf	126	no	$1$	$1$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{1270}(11,\cdot)$	1270.bc	63	no	$1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1270}(13,\cdot)$	1270.bj	252	no	$-1$	$1$	$e\left(\frac{251}{252}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{25}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{131}{252}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{1270}(17,\cdot)$	1270.bj	252	no	$-1$	$1$	$e\left(\frac{13}{252}\right)$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{25}{252}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{1270}(19,\cdot)$	1270.j	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{1270}(21,\cdot)$	1270.bc	63	no	$1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1270}(23,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{47}{252}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{131}{252}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{113}{252}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{1270}(27,\cdot)$	1270.be	84	no	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{84}\right)$	$-1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1270}(29,\cdot)$	1270.bh	126	no	$-1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{1270}(31,\cdot)$	1270.bc	63	no	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1270}(33,\cdot)$	1270.be	84	no	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{47}{84}\right)$	$-1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{1270}(37,\cdot)$	1270.x	36	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1270}(39,\cdot)$	1270.bh	126	no	$-1$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1270}(41,\cdot)$	1270.bc	63	no	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1270}(43,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{109}{252}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{1270}(47,\cdot)$	1270.bd	84	no	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{29}{84}\right)$	$-1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{1270}(49,\cdot)$	1270.bf	126	no	$1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{1270}(51,\cdot)$	1270.ba	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{1270}(53,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{25}{252}\right)$	$e\left(\frac{103}{252}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{252}\right)$	$e\left(\frac{5}{252}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{252}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{1270}(57,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{107}{252}\right)$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{1270}(59,\cdot)$	1270.r	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1270}(61,\cdot)$	1270.u	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1270}(63,\cdot)$	1270.v	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{28}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1270}(67,\cdot)$	1270.bi	252	no	$1$	$1$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{125}{252}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{11}{252}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{1270}(69,\cdot)$	1270.bf	126	no	$1$	$1$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{1270}(71,\cdot)$	1270.bc	63	no	$1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1270}(73,\cdot)$	1270.bd	84	no	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{31}{84}\right)$	$-1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{1270}(77,\cdot)$	1270.be	84	no	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{37}{84}\right)$	$-1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{1270}(79,\cdot)$	1270.bf	126	no	$1$	$1$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{37}{42}\right)$

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 $\F_{q}$

Modulus	$1270$
Structure	\(C_{2}\times C_{252}\)
Order	$504$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1270}(1,\cdot)\)	1270.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1270}(3,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{167}{252}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{251}{252}\right)\)	\(e\left(\frac{13}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{1270}(7,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{167}{252}\right)\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{47}{252}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{1270}(9,\cdot)\)	1270.bf	126	no	\(1\)	\(1\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{1270}(11,\cdot)\)	1270.bc	63	no	\(1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1270}(13,\cdot)\)	1270.bj	252	no	\(-1\)	\(1\)	\(e\left(\frac{251}{252}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{25}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{131}{252}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{1270}(17,\cdot)\)	1270.bj	252	no	\(-1\)	\(1\)	\(e\left(\frac{13}{252}\right)\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{25}{252}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{1270}(19,\cdot)\)	1270.j	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{1270}(21,\cdot)\)	1270.bc	63	no	\(1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1270}(23,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{47}{252}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{131}{252}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{113}{252}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{1270}(27,\cdot)\)	1270.be	84	no	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(-1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1270}(29,\cdot)\)	1270.bh	126	no	\(-1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{1270}(31,\cdot)\)	1270.bc	63	no	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1270}(33,\cdot)\)	1270.be	84	no	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(-1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1270}(37,\cdot)\)	1270.x	36	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1270}(39,\cdot)\)	1270.bh	126	no	\(-1\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1270}(41,\cdot)\)	1270.bc	63	no	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1270}(43,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{109}{252}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{1270}(47,\cdot)\)	1270.bd	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(-1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1270}(49,\cdot)\)	1270.bf	126	no	\(1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{1270}(51,\cdot)\)	1270.ba	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{1270}(53,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{25}{252}\right)\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{252}\right)\)	\(e\left(\frac{5}{252}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{252}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{1270}(57,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{107}{252}\right)\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{1270}(59,\cdot)\)	1270.r	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1270}(61,\cdot)\)	1270.u	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1270}(63,\cdot)\)	1270.v	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1270}(67,\cdot)\)	1270.bi	252	no	\(1\)	\(1\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{125}{252}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{11}{252}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{1270}(69,\cdot)\)	1270.bf	126	no	\(1\)	\(1\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{1270}(71,\cdot)\)	1270.bc	63	no	\(1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1270}(73,\cdot)\)	1270.bd	84	no	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(-1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1270}(77,\cdot)\)	1270.be	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(-1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1270}(79,\cdot)\)	1270.bf	126	no	\(1\)	\(1\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{37}{42}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

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.