Properties

Modulus $1110$
Structure \(C_{36}\times C_{4}\times C_{2}\)
Order $288$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1110)
 
pari: g = idealstar(,1110,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 288
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1110}(371,\cdot)$, $\chi_{1110}(667,\cdot)$, $\chi_{1110}(631,\cdot)$

First 32 of 288 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(41\) \(43\)
\(\chi_{1110}(1,\cdot)\) 1110.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1110}(7,\cdot)\) 1110.ca 36 no \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{7}{9}\right)\) \(-i\)
\(\chi_{1110}(11,\cdot)\) 1110.w 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)
\(\chi_{1110}(13,\cdot)\) 1110.ch 36 no \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{11}{18}\right)\) \(-1\)
\(\chi_{1110}(17,\cdot)\) 1110.cb 36 no \(-1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{8}{9}\right)\) \(1\)
\(\chi_{1110}(19,\cdot)\) 1110.cf 36 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{17}{18}\right)\) \(-i\)
\(\chi_{1110}(23,\cdot)\) 1110.bm 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(-i\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{1110}(29,\cdot)\) 1110.bo 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(-i\) \(i\) \(e\left(\frac{2}{3}\right)\) \(i\)
\(\chi_{1110}(31,\cdot)\) 1110.t 4 no \(-1\) \(1\) \(1\) \(-1\) \(-i\) \(-i\) \(-i\) \(-i\) \(i\) \(i\) \(-1\) \(-i\)
\(\chi_{1110}(41,\cdot)\) 1110.bs 18 no \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(-1\)
\(\chi_{1110}(43,\cdot)\) 1110.l 4 no \(1\) \(1\) \(-i\) \(-1\) \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\) \(-1\)
\(\chi_{1110}(47,\cdot)\) 1110.bh 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\)
\(\chi_{1110}(49,\cdot)\) 1110.bq 18 no \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{9}\right)\) \(-1\)
\(\chi_{1110}(53,\cdot)\) 1110.cd 36 no \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{13}{18}\right)\) \(i\)
\(\chi_{1110}(59,\cdot)\) 1110.by 36 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{2}{9}\right)\) \(-i\)
\(\chi_{1110}(61,\cdot)\) 1110.ce 36 no \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{11}{18}\right)\) \(-i\)
\(\chi_{1110}(67,\cdot)\) 1110.bx 36 no \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{9}\right)\) \(i\)
\(\chi_{1110}(71,\cdot)\) 1110.bv 18 no \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{17}{18}\right)\) \(1\)
\(\chi_{1110}(73,\cdot)\) 1110.r 4 no \(-1\) \(1\) \(-i\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(1\) \(-1\) \(1\) \(-i\)
\(\chi_{1110}(77,\cdot)\) 1110.cg 36 no \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{17}{18}\right)\) \(i\)
\(\chi_{1110}(79,\cdot)\) 1110.cf 36 no \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{5}{18}\right)\) \(-i\)
\(\chi_{1110}(83,\cdot)\) 1110.cd 36 no \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{18}\right)\) \(i\)
\(\chi_{1110}(89,\cdot)\) 1110.by 36 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{2}{9}\right)\) \(i\)
\(\chi_{1110}(91,\cdot)\) 1110.ce 36 no \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{7}{18}\right)\) \(i\)
\(\chi_{1110}(97,\cdot)\) 1110.bf 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(i\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{1110}(101,\cdot)\) 1110.w 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)
\(\chi_{1110}(103,\cdot)\) 1110.bf 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-i\) \(i\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{1110}(107,\cdot)\) 1110.cd 36 no \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{11}{18}\right)\) \(-i\)
\(\chi_{1110}(109,\cdot)\) 1110.cf 36 no \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{18}\right)\) \(-i\)
\(\chi_{1110}(113,\cdot)\) 1110.cb 36 no \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{9}\right)\) \(1\)
\(\chi_{1110}(119,\cdot)\) 1110.bo 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(i\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(-i\)
\(\chi_{1110}(121,\cdot)\) 1110.i 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)