Properties

Modulus $1156$
Structure \(C_{2}\times C_{272}\)
Order $544$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1156)
 
pari: g = idealstar(,1156,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 544
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{272}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1156}(579,\cdot)$, $\chi_{1156}(581,\cdot)$

First 32 of 544 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(19\) \(21\) \(23\)
\(\chi_{1156}(1,\cdot)\) 1156.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1156}(3,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{137}{272}\right)\) \(e\left(\frac{229}{272}\right)\) \(e\left(\frac{19}{272}\right)\) \(e\left(\frac{1}{136}\right)\) \(e\left(\frac{159}{272}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{47}{136}\right)\) \(e\left(\frac{75}{136}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{87}{272}\right)\)
\(\chi_{1156}(5,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{229}{272}\right)\) \(e\left(\frac{217}{272}\right)\) \(e\left(\frac{135}{272}\right)\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{99}{272}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{87}{136}\right)\) \(e\left(\frac{107}{136}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{203}{272}\right)\)
\(\chi_{1156}(7,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{19}{272}\right)\) \(e\left(\frac{135}{272}\right)\) \(e\left(\frac{225}{272}\right)\) \(e\left(\frac{19}{136}\right)\) \(e\left(\frac{165}{272}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{77}{136}\right)\) \(e\left(\frac{65}{136}\right)\) \(e\left(\frac{61}{68}\right)\) \(e\left(\frac{157}{272}\right)\)
\(\chi_{1156}(9,\cdot)\) 1156.q 136 no \(1\) \(1\) \(e\left(\frac{1}{136}\right)\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{19}{136}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{23}{136}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{7}{68}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{87}{136}\right)\)
\(\chi_{1156}(11,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{159}{272}\right)\) \(e\left(\frac{99}{272}\right)\) \(e\left(\frac{165}{272}\right)\) \(e\left(\frac{23}{136}\right)\) \(e\left(\frac{121}{272}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{129}{136}\right)\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{97}{272}\right)\)
\(\chi_{1156}(13,\cdot)\) 1156.p 68 no \(1\) \(1\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{47}{68}\right)\)
\(\chi_{1156}(15,\cdot)\) 1156.r 136 yes \(-1\) \(1\) \(e\left(\frac{47}{136}\right)\) \(e\left(\frac{87}{136}\right)\) \(e\left(\frac{77}{136}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{129}{136}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{9}{136}\right)\)
\(\chi_{1156}(19,\cdot)\) 1156.r 136 yes \(-1\) \(1\) \(e\left(\frac{75}{136}\right)\) \(e\left(\frac{107}{136}\right)\) \(e\left(\frac{65}{136}\right)\) \(e\left(\frac{7}{68}\right)\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{15}{68}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{133}{136}\right)\)
\(\chi_{1156}(21,\cdot)\) 1156.p 68 no \(1\) \(1\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{61}{68}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{61}{68}\right)\)
\(\chi_{1156}(23,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{87}{272}\right)\) \(e\left(\frac{203}{272}\right)\) \(e\left(\frac{157}{272}\right)\) \(e\left(\frac{87}{136}\right)\) \(e\left(\frac{97}{272}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{9}{136}\right)\) \(e\left(\frac{133}{136}\right)\) \(e\left(\frac{61}{68}\right)\) \(e\left(\frac{89}{272}\right)\)
\(\chi_{1156}(25,\cdot)\) 1156.q 136 no \(1\) \(1\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{81}{136}\right)\) \(e\left(\frac{135}{136}\right)\) \(e\left(\frac{25}{68}\right)\) \(e\left(\frac{99}{136}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{19}{68}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{67}{136}\right)\)
\(\chi_{1156}(27,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{139}{272}\right)\) \(e\left(\frac{143}{272}\right)\) \(e\left(\frac{57}{272}\right)\) \(e\left(\frac{3}{136}\right)\) \(e\left(\frac{205}{272}\right)\) \(e\left(\frac{11}{68}\right)\) \(e\left(\frac{5}{136}\right)\) \(e\left(\frac{89}{136}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{261}{272}\right)\)
\(\chi_{1156}(29,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{125}{272}\right)\) \(e\left(\frac{65}{272}\right)\) \(e\left(\frac{63}{272}\right)\) \(e\left(\frac{125}{136}\right)\) \(e\left(\frac{155}{272}\right)\) \(e\left(\frac{5}{68}\right)\) \(e\left(\frac{95}{136}\right)\) \(e\left(\frac{59}{136}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{131}{272}\right)\)
\(\chi_{1156}(31,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{145}{272}\right)\) \(e\left(\frac{157}{272}\right)\) \(e\left(\frac{171}{272}\right)\) \(e\left(\frac{9}{136}\right)\) \(e\left(\frac{71}{272}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{15}{136}\right)\) \(e\left(\frac{131}{136}\right)\) \(e\left(\frac{11}{68}\right)\) \(e\left(\frac{239}{272}\right)\)
\(\chi_{1156}(33,\cdot)\) 1156.n 34 no \(1\) \(1\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{23}{34}\right)\)
\(\chi_{1156}(35,\cdot)\) 1156.m 34 yes \(-1\) \(1\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{1156}(37,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{129}{272}\right)\) \(e\left(\frac{165}{272}\right)\) \(e\left(\frac{139}{272}\right)\) \(e\left(\frac{129}{136}\right)\) \(e\left(\frac{247}{272}\right)\) \(e\left(\frac{65}{68}\right)\) \(e\left(\frac{11}{136}\right)\) \(e\left(\frac{87}{136}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{207}{272}\right)\)
\(\chi_{1156}(39,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{61}{272}\right)\) \(e\left(\frac{233}{272}\right)\) \(e\left(\frac{207}{272}\right)\) \(e\left(\frac{61}{136}\right)\) \(e\left(\frac{43}{272}\right)\) \(e\left(\frac{65}{68}\right)\) \(e\left(\frac{11}{136}\right)\) \(e\left(\frac{87}{136}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{3}{272}\right)\)
\(\chi_{1156}(41,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{171}{272}\right)\) \(e\left(\frac{263}{272}\right)\) \(e\left(\frac{121}{272}\right)\) \(e\left(\frac{35}{136}\right)\) \(e\left(\frac{125}{272}\right)\) \(e\left(\frac{15}{68}\right)\) \(e\left(\frac{81}{136}\right)\) \(e\left(\frac{109}{136}\right)\) \(e\left(\frac{5}{68}\right)\) \(e\left(\frac{53}{272}\right)\)
\(\chi_{1156}(43,\cdot)\) 1156.r 136 yes \(-1\) \(1\) \(e\left(\frac{45}{136}\right)\) \(e\left(\frac{37}{136}\right)\) \(e\left(\frac{39}{136}\right)\) \(e\left(\frac{45}{68}\right)\) \(e\left(\frac{83}{136}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{41}{68}\right)\) \(e\left(\frac{9}{68}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{107}{136}\right)\)
\(\chi_{1156}(45,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{231}{272}\right)\) \(e\left(\frac{131}{272}\right)\) \(e\left(\frac{173}{272}\right)\) \(e\left(\frac{95}{136}\right)\) \(e\left(\frac{145}{272}\right)\) \(e\left(\frac{31}{68}\right)\) \(e\left(\frac{45}{136}\right)\) \(e\left(\frac{121}{136}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{105}{272}\right)\)
\(\chi_{1156}(47,\cdot)\) 1156.o 68 yes \(-1\) \(1\) \(e\left(\frac{59}{68}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{65}{68}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{33}{68}\right)\)
\(\chi_{1156}(49,\cdot)\) 1156.q 136 no \(1\) \(1\) \(e\left(\frac{19}{136}\right)\) \(e\left(\frac{135}{136}\right)\) \(e\left(\frac{89}{136}\right)\) \(e\left(\frac{19}{68}\right)\) \(e\left(\frac{29}{136}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{9}{68}\right)\) \(e\left(\frac{65}{68}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{21}{136}\right)\)
\(\chi_{1156}(53,\cdot)\) 1156.q 136 no \(1\) \(1\) \(e\left(\frac{103}{136}\right)\) \(e\left(\frac{59}{136}\right)\) \(e\left(\frac{53}{136}\right)\) \(e\left(\frac{35}{68}\right)\) \(e\left(\frac{57}{136}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{41}{68}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{121}{136}\right)\)
\(\chi_{1156}(55,\cdot)\) 1156.o 68 yes \(-1\) \(1\) \(e\left(\frac{29}{68}\right)\) \(e\left(\frac{11}{68}\right)\) \(e\left(\frac{7}{68}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{7}{68}\right)\)
\(\chi_{1156}(57,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{15}{272}\right)\) \(e\left(\frac{171}{272}\right)\) \(e\left(\frac{149}{272}\right)\) \(e\left(\frac{15}{136}\right)\) \(e\left(\frac{73}{272}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{93}{136}\right)\) \(e\left(\frac{105}{136}\right)\) \(e\left(\frac{41}{68}\right)\) \(e\left(\frac{81}{272}\right)\)
\(\chi_{1156}(59,\cdot)\) 1156.r 136 yes \(-1\) \(1\) \(e\left(\frac{49}{136}\right)\) \(e\left(\frac{1}{136}\right)\) \(e\left(\frac{115}{136}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{39}{136}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{25}{68}\right)\) \(e\left(\frac{37}{68}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{47}{136}\right)\)
\(\chi_{1156}(61,\cdot)\) 1156.s 272 no \(-1\) \(1\) \(e\left(\frac{259}{272}\right)\) \(e\left(\frac{15}{272}\right)\) \(e\left(\frac{161}{272}\right)\) \(e\left(\frac{123}{136}\right)\) \(e\left(\frac{245}{272}\right)\) \(e\left(\frac{43}{68}\right)\) \(e\left(\frac{1}{136}\right)\) \(e\left(\frac{45}{136}\right)\) \(e\left(\frac{37}{68}\right)\) \(e\left(\frac{93}{272}\right)\)
\(\chi_{1156}(63,\cdot)\) 1156.t 272 yes \(1\) \(1\) \(e\left(\frac{21}{272}\right)\) \(e\left(\frac{49}{272}\right)\) \(e\left(\frac{263}{272}\right)\) \(e\left(\frac{21}{136}\right)\) \(e\left(\frac{211}{272}\right)\) \(e\left(\frac{9}{68}\right)\) \(e\left(\frac{35}{136}\right)\) \(e\left(\frac{79}{136}\right)\) \(e\left(\frac{3}{68}\right)\) \(e\left(\frac{59}{272}\right)\)
\(\chi_{1156}(65,\cdot)\) 1156.j 16 no \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{1156}(67,\cdot)\) 1156.l 34 yes \(-1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
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