Properties

Modulus $195$
Structure \(C_{2}\times C_{4}\times C_{12}\)
Order $96$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(195)
 
pari: g = idealstar(,195,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{4}\times C_{12}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{195}(131,\cdot)$, $\chi_{195}(157,\cdot)$, $\chi_{195}(106,\cdot)$

First 32 of 96 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(14\) \(16\) \(17\) \(19\) \(22\)
\(\chi_{195}(1,\cdot)\) 195.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{195}(2,\cdot)\) 195.bn 12 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(4,\cdot)\) 195.v 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(7,\cdot)\) 195.bm 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(8,\cdot)\) 195.j 4 yes \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(i\) \(1\) \(1\) \(-i\) \(-i\) \(-i\)
\(\chi_{195}(11,\cdot)\) 195.bg 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(14,\cdot)\) 195.f 2 no \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\)
\(\chi_{195}(16,\cdot)\) 195.i 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(17,\cdot)\) 195.bf 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(19,\cdot)\) 195.bi 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(22,\cdot)\) 195.be 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(23,\cdot)\) 195.bf 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{195}(28,\cdot)\) 195.bm 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{195}(29,\cdot)\) 195.x 6 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{195}(31,\cdot)\) 195.p 4 no \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(i\) \(1\) \(1\) \(-1\) \(-i\) \(1\)
\(\chi_{195}(32,\cdot)\) 195.bn 12 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(34,\cdot)\) 195.q 4 no \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(-i\) \(1\) \(1\) \(1\) \(i\) \(-1\)
\(\chi_{195}(37,\cdot)\) 195.bm 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(38,\cdot)\) 195.s 4 yes \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(1\) \(1\) \(i\) \(1\) \(-i\)
\(\chi_{195}(41,\cdot)\) 195.bg 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(43,\cdot)\) 195.bk 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{195}(44,\cdot)\) 195.n 4 yes \(1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\) \(1\) \(-1\) \(-i\) \(-1\)
\(\chi_{195}(46,\cdot)\) 195.bj 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(47,\cdot)\) 195.u 4 yes \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(i\) \(1\) \(1\) \(i\) \(-i\) \(i\)
\(\chi_{195}(49,\cdot)\) 195.v 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{195}(53,\cdot)\) 195.m 4 no \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(1\) \(1\) \(i\) \(-1\) \(-i\)
\(\chi_{195}(56,\cdot)\) 195.w 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(58,\cdot)\) 195.bm 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{195}(59,\cdot)\) 195.bh 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(61,\cdot)\) 195.i 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(62,\cdot)\) 195.bf 12 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(64,\cdot)\) 195.h 2 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\)
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