LMFDB - Group of Dirichlet characters of modulus 113

Show commands: PariGP / SageMath

sage: H = DirichletGroup(113)

pari: g = idealstar(,113,2)

Character group

sage: G.order() pari: g.no
Order	=	112
sage: H.invariants() pari: g.cyc
Structure	=	$C_{112}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{113}(3,\cdot)$

First 32 of 112 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{113}(1,\cdot)$	113.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{113}(2,\cdot)$	113.h	28	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{113}(3,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{113}(4,\cdot)$	113.f	14	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{113}(5,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{113}(6,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{113}(7,\cdot)$	113.f	14	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{113}(8,\cdot)$	113.h	28	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{113}(9,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{113}(10,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{113}(11,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{113}(12,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{113}(13,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{113}(14,\cdot)$	113.h	28	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{113}(15,\cdot)$	113.c	4	yes	$1$	$1$	$1$	$-i$	$1$	$i$	$-i$	$1$	$1$	$-1$	$i$	$-1$
$\chi_{113}(16,\cdot)$	113.d	7	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{113}(17,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{113}(18,\cdot)$	113.e	8	yes	$1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$	$i$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{113}(19,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{113}(20,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{113}(21,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{113}(22,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{113}(23,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{113}(24,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{113}(25,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{113}(26,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{113}(27,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{55}{56}\right)$
$\chi_{113}(28,\cdot)$	113.d	7	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{113}(29,\cdot)$	113.j	112	yes	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{113}(30,\cdot)$	113.d	7	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{113}(31,\cdot)$	113.i	56	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{113}(32,\cdot)$	113.h	28	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{14}\right)$

Click here to search among the remaining 80 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	$113$
Structure	\(C_{112}\)
Order	$112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{113}(1,\cdot)\)	113.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{113}(2,\cdot)\)	113.h	28	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{113}(3,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{113}(4,\cdot)\)	113.f	14	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{113}(5,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{113}(6,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{113}(7,\cdot)\)	113.f	14	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{113}(8,\cdot)\)	113.h	28	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{113}(9,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{113}(10,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{113}(11,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{113}(12,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{113}(13,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{113}(14,\cdot)\)	113.h	28	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{113}(15,\cdot)\)	113.c	4	yes	\(1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{113}(16,\cdot)\)	113.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{113}(17,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{113}(18,\cdot)\)	113.e	8	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{113}(19,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{113}(20,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{113}(21,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{113}(22,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{113}(23,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{113}(24,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{113}(25,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{113}(26,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{113}(27,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)
\(\chi_{113}(28,\cdot)\)	113.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{113}(29,\cdot)\)	113.j	112	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{113}(30,\cdot)\)	113.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{113}(31,\cdot)\)	113.i	56	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{113}(32,\cdot)\)	113.h	28	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 112 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.