LMFDB - Group of Dirichlet characters of modulus 71

Show commands: PariGP / SageMath

sage: H = DirichletGroup(71)

pari: g = idealstar(,71,2)

Character group

sage: G.order() pari: g.no
Order	=	70
sage: H.invariants() pari: g.cyc
Structure	=	$C_{70}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{71}(7,\cdot)$

First 32 of 70 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{71}(1,\cdot)$	71.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{71}(2,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{71}(3,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{71}(4,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{71}(5,\cdot)$	71.c	5	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{71}(6,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{71}(7,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{71}(8,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{71}(9,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{71}(10,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{71}(11,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{71}(12,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{71}(13,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{71}(14,\cdot)$	71.e	10	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{71}(15,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{71}(16,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{71}(17,\cdot)$	71.e	10	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{71}(18,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{71}(19,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{71}(20,\cdot)$	71.d	7	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{71}(21,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{71}(22,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{71}(23,\cdot)$	71.f	14	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{71}(24,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{71}(25,\cdot)$	71.c	5	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{71}(26,\cdot)$	71.f	14	yes	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{71}(27,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{71}(28,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{71}(29,\cdot)$	71.g	35	yes	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{71}(30,\cdot)$	71.d	7	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{71}(31,\cdot)$	71.h	70	yes	$-1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{61}{70}\right)$
$\chi_{71}(32,\cdot)$	71.d	7	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$

Click here to search among the remaining 38 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	$71$
Structure	\(C_{70}\)
Order	$70$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{71}(1,\cdot)\)	71.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{71}(2,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{71}(3,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{71}(4,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{71}(5,\cdot)\)	71.c	5	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{71}(6,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{71}(7,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{71}(8,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{71}(9,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{71}(10,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{71}(11,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{71}(12,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{71}(13,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{71}(14,\cdot)\)	71.e	10	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{71}(15,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{71}(16,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{71}(17,\cdot)\)	71.e	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{71}(18,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{71}(19,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{71}(20,\cdot)\)	71.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{71}(21,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{71}(22,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{71}(23,\cdot)\)	71.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{71}(24,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{71}(25,\cdot)\)	71.c	5	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{71}(26,\cdot)\)	71.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{71}(27,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{71}(28,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)
\(\chi_{71}(29,\cdot)\)	71.g	35	yes	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{71}(30,\cdot)\)	71.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{71}(31,\cdot)\)	71.h	70	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)
\(\chi_{71}(32,\cdot)\)	71.d	7	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 70 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.