Properties

Modulus $588$
Structure \(C_{2}\times C_{2}\times C_{42}\)
Order $168$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(588)
 
pari: g = idealstar(,588,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 168
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{42}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{588}(295,\cdot)$, $\chi_{588}(197,\cdot)$, $\chi_{588}(493,\cdot)$

First 32 of 168 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{588}(1,\cdot)\) 588.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{588}(5,\cdot)\) 588.be 42 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{588}(11,\cdot)\) 588.bb 42 yes \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{588}(13,\cdot)\) 588.v 14 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{588}(17,\cdot)\) 588.be 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{588}(19,\cdot)\) 588.o 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{588}(23,\cdot)\) 588.bb 42 yes \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{588}(25,\cdot)\) 588.y 21 no \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{588}(29,\cdot)\) 588.w 14 no \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{588}(31,\cdot)\) 588.o 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{588}(37,\cdot)\) 588.y 21 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{588}(41,\cdot)\) 588.t 14 no \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{588}(43,\cdot)\) 588.s 14 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{588}(47,\cdot)\) 588.bf 42 yes \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{588}(53,\cdot)\) 588.z 42 no \(-1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{588}(55,\cdot)\) 588.x 14 no \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{588}(59,\cdot)\) 588.bf 42 yes \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{588}(61,\cdot)\) 588.bc 42 no \(-1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{588}(65,\cdot)\) 588.z 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{588}(67,\cdot)\) 588.l 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{588}(71,\cdot)\) 588.u 14 yes \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{588}(73,\cdot)\) 588.bc 42 no \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{588}(79,\cdot)\) 588.l 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{588}(83,\cdot)\) 588.r 14 yes \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{588}(85,\cdot)\) 588.q 7 no \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{588}(89,\cdot)\) 588.be 42 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{588}(95,\cdot)\) 588.bb 42 yes \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{588}(97,\cdot)\) 588.d 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{588}(101,\cdot)\) 588.be 42 no \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{588}(103,\cdot)\) 588.ba 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{588}(107,\cdot)\) 588.bb 42 yes \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{588}(109,\cdot)\) 588.y 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{10}{21}\right)\)
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