# Properties

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

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 $$-1$$ $$1$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$