Properties

Modulus $637$
Structure \(C_{84}\times C_{6}\)
Order $504$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(637)
 
pari: g = idealstar(,637,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 504
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{637}(248,\cdot)$, $\chi_{637}(197,\cdot)$

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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{637}(1,\cdot)\) 637.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{637}(2,\cdot)\) 637.cg 84 yes \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{13}{42}\right)\)
\(\chi_{637}(3,\cdot)\) 637.bx 42 yes \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{42}\right)\)
\(\chi_{637}(4,\cdot)\) 637.bz 42 yes \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{637}(5,\cdot)\) 637.cc 84 yes \(1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{637}(6,\cdot)\) 637.cb 84 yes \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{637}(8,\cdot)\) 637.bm 28 yes \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{637}(9,\cdot)\) 637.bj 21 yes \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{637}(10,\cdot)\) 637.bu 42 yes \(-1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{17}{42}\right)\)
\(\chi_{637}(11,\cdot)\) 637.ca 84 yes \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{41}{42}\right)\)
\(\chi_{637}(12,\cdot)\) 637.br 42 yes \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{637}(15,\cdot)\) 637.cf 84 yes \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{637}(16,\cdot)\) 637.bi 21 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{637}(17,\cdot)\) 637.by 42 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{637}(18,\cdot)\) 637.ba 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{637}(19,\cdot)\) 637.x 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(1\) \(1\) \(i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{637}(20,\cdot)\) 637.cb 84 yes \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{637}(22,\cdot)\) 637.bk 21 yes \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{637}(23,\cdot)\) 637.bz 42 yes \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{637}(24,\cdot)\) 637.ch 84 yes \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{637}(25,\cdot)\) 637.bs 42 yes \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{637}(27,\cdot)\) 637.bf 14 no \(-1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{637}(29,\cdot)\) 637.bk 21 yes \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{637}(30,\cdot)\) 637.u 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{637}(31,\cdot)\) 637.bc 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{637}(32,\cdot)\) 637.cg 84 yes \(-1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{637}(33,\cdot)\) 637.ch 84 yes \(1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{637}(34,\cdot)\) 637.bn 28 yes \(1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{637}(36,\cdot)\) 637.bt 42 yes \(1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{637}(37,\cdot)\) 637.cg 84 yes \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{637}(38,\cdot)\) 637.br 42 yes \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{41}{42}\right)\)
\(\chi_{637}(40,\cdot)\) 637.bv 42 no \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{42}\right)\)