LMFDB - Group of Dirichlet characters of modulus 212

Show commands: PariGP / SageMath

sage: H = DirichletGroup(212)

pari: g = idealstar(,212,2)

Character group

sage: G.order() pari: g.no
Order	=	104
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{52}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{212}(107,\cdot)$, $\chi_{212}(161,\cdot)$

First 32 of 104 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{212}(1,\cdot)$	212.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{212}(3,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{212}(5,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{212}(7,\cdot)$	212.h	26	yes	$-1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{212}(9,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{212}(11,\cdot)$	212.h	26	yes	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{212}(13,\cdot)$	212.g	13	no	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{212}(15,\cdot)$	212.i	26	yes	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{212}(17,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{212}(19,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{212}(21,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{25}{52}\right)$
$\chi_{212}(23,\cdot)$	212.f	4	yes	$1$	$1$	$i$	$i$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$i$	$i$
$\chi_{212}(25,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{212}(27,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{21}{52}\right)$
$\chi_{212}(29,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{212}(31,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$
$\chi_{212}(33,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{212}(35,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{212}(37,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{212}(39,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{212}(41,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{212}(43,\cdot)$	212.h	26	yes	$-1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{212}(45,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{212}(47,\cdot)$	212.i	26	yes	$-1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{212}(49,\cdot)$	212.g	13	no	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{212}(51,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{212}(55,\cdot)$	212.k	52	yes	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{212}(57,\cdot)$	212.j	26	no	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{212}(59,\cdot)$	212.h	26	yes	$-1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{212}(61,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{41}{52}\right)$
$\chi_{212}(63,\cdot)$	212.i	26	yes	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{212}(65,\cdot)$	212.l	52	no	$-1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{17}{52}\right)$

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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	$212$
Structure	\(C_{2}\times C_{52}\)
Order	$104$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{212}(1,\cdot)\)	212.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{212}(3,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{212}(5,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{212}(7,\cdot)\)	212.h	26	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{212}(9,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{212}(11,\cdot)\)	212.h	26	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{212}(13,\cdot)\)	212.g	13	no	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{212}(15,\cdot)\)	212.i	26	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{212}(17,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{212}(19,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{212}(21,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)
\(\chi_{212}(23,\cdot)\)	212.f	4	yes	\(1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{212}(25,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{212}(27,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)
\(\chi_{212}(29,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{212}(31,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)
\(\chi_{212}(33,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{212}(35,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{212}(37,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{212}(39,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{212}(41,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{212}(43,\cdot)\)	212.h	26	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{212}(45,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{212}(47,\cdot)\)	212.i	26	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{212}(49,\cdot)\)	212.g	13	no	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{212}(51,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{212}(55,\cdot)\)	212.k	52	yes	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{212}(57,\cdot)\)	212.j	26	no	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{212}(59,\cdot)\)	212.h	26	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{212}(61,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)
\(\chi_{212}(63,\cdot)\)	212.i	26	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{212}(65,\cdot)\)	212.l	52	no	\(-1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)

Introduction

L-functions

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Character group

First 32 of 104 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.