Properties

Modulus 71
Structure \(C_{70}\)
Order 70

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(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.

orbit label 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 \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{7}\right)\)