Properties

Modulus $294$
Structure \(C_{2}\times C_{42}\)
Order $84$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(294)
 
pari: g = idealstar(,294,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 84
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{42}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{294}(197,\cdot)$, $\chi_{294}(199,\cdot)$

First 32 of 84 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{294}(1,\cdot)\) 294.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{294}(5,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{294}(11,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{294}(13,\cdot)\) 294.k 14 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{294}(17,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{294}(19,\cdot)\) 294.g 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{294}(23,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{294}(25,\cdot)\) 294.m 21 no \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{294}(29,\cdot)\) 294.l 14 no \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{294}(31,\cdot)\) 294.g 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{294}(37,\cdot)\) 294.m 21 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{294}(41,\cdot)\) 294.j 14 no \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{294}(43,\cdot)\) 294.i 7 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{294}(47,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{294}(53,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{294}(55,\cdot)\) 294.k 14 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{294}(59,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{294}(61,\cdot)\) 294.o 42 no \(-1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{294}(65,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{294}(67,\cdot)\) 294.e 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{294}(71,\cdot)\) 294.l 14 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{294}(73,\cdot)\) 294.o 42 no \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{294}(79,\cdot)\) 294.e 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{294}(83,\cdot)\) 294.j 14 no \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{294}(85,\cdot)\) 294.i 7 no \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{294}(89,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{294}(95,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{294}(97,\cdot)\) 294.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{294}(101,\cdot)\) 294.p 42 no \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{294}(103,\cdot)\) 294.o 42 no \(-1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{294}(107,\cdot)\) 294.n 42 no \(-1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{294}(109,\cdot)\) 294.m 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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