# Properties

 Modulus $953$ Structure $$C_{952}$$ Order $952$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(953)

pari: g = idealstar(,953,2)

## Character group

 sage: G.order()  pari: g.no Order = 952 sage: H.invariants()  pari: g.cyc Structure = $$C_{952}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{953}(3,\cdot)$

## First 32 of 952 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{953}(1,\cdot)$$ 953.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{953}(2,\cdot)$$ 953.k 68 yes $$1$$ $$1$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{9}{68}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{15}{68}\right)$$ $$e\left(\frac{55}{68}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{61}{68}\right)$$ $$e\left(\frac{11}{68}\right)$$
$$\chi_{953}(3,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{9}{68}\right)$$ $$e\left(\frac{1}{952}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{47}{952}\right)$$ $$e\left(\frac{127}{952}\right)$$ $$e\left(\frac{201}{238}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{1}{476}\right)$$ $$e\left(\frac{173}{952}\right)$$ $$e\left(\frac{311}{952}\right)$$
$$\chi_{953}(4,\cdot)$$ 953.i 34 yes $$1$$ $$1$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{11}{34}\right)$$
$$\chi_{953}(5,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{15}{68}\right)$$ $$e\left(\frac{47}{952}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{305}{952}\right)$$ $$e\left(\frac{257}{952}\right)$$ $$e\left(\frac{165}{238}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{47}{476}\right)$$ $$e\left(\frac{515}{952}\right)$$ $$e\left(\frac{337}{952}\right)$$
$$\chi_{953}(6,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{55}{68}\right)$$ $$e\left(\frac{127}{952}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{257}{952}\right)$$ $$e\left(\frac{897}{952}\right)$$ $$e\left(\frac{61}{238}\right)$$ $$e\left(\frac{29}{68}\right)$$ $$e\left(\frac{127}{476}\right)$$ $$e\left(\frac{75}{952}\right)$$ $$e\left(\frac{465}{952}\right)$$
$$\chi_{953}(7,\cdot)$$ 953.n 238 yes $$1$$ $$1$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{201}{238}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{165}{238}\right)$$ $$e\left(\frac{61}{238}\right)$$ $$e\left(\frac{1}{119}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{82}{119}\right)$$ $$e\left(\frac{25}{238}\right)$$ $$e\left(\frac{155}{238}\right)$$
$$\chi_{953}(8,\cdot)$$ 953.k 68 yes $$1$$ $$1$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{29}{68}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{47}{68}\right)$$ $$e\left(\frac{33}{68}\right)$$
$$\chi_{953}(9,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{1}{476}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{47}{476}\right)$$ $$e\left(\frac{127}{476}\right)$$ $$e\left(\frac{82}{119}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{1}{238}\right)$$ $$e\left(\frac{173}{476}\right)$$ $$e\left(\frac{311}{476}\right)$$
$$\chi_{953}(10,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{61}{68}\right)$$ $$e\left(\frac{173}{952}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{515}{952}\right)$$ $$e\left(\frac{75}{952}\right)$$ $$e\left(\frac{25}{238}\right)$$ $$e\left(\frac{47}{68}\right)$$ $$e\left(\frac{173}{476}\right)$$ $$e\left(\frac{417}{952}\right)$$ $$e\left(\frac{491}{952}\right)$$
$$\chi_{953}(11,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{11}{68}\right)$$ $$e\left(\frac{311}{952}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{337}{952}\right)$$ $$e\left(\frac{465}{952}\right)$$ $$e\left(\frac{155}{238}\right)$$ $$e\left(\frac{33}{68}\right)$$ $$e\left(\frac{311}{476}\right)$$ $$e\left(\frac{491}{952}\right)$$ $$e\left(\frac{569}{952}\right)$$
$$\chi_{953}(12,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{33}{68}\right)$$ $$e\left(\frac{253}{952}\right)$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{467}{952}\right)$$ $$e\left(\frac{715}{952}\right)$$ $$e\left(\frac{159}{238}\right)$$ $$e\left(\frac{31}{68}\right)$$ $$e\left(\frac{253}{476}\right)$$ $$e\left(\frac{929}{952}\right)$$ $$e\left(\frac{619}{952}\right)$$
$$\chi_{953}(13,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{171}{476}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{421}{476}\right)$$ $$e\left(\frac{297}{476}\right)$$ $$e\left(\frac{99}{119}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{171}{238}\right)$$ $$e\left(\frac{71}{476}\right)$$ $$e\left(\frac{345}{476}\right)$$
$$\chi_{953}(14,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{465}{476}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{435}{476}\right)$$ $$e\left(\frac{31}{476}\right)$$ $$e\left(\frac{50}{119}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{227}{238}\right)$$ $$e\left(\frac{1}{476}\right)$$ $$e\left(\frac{387}{476}\right)$$
$$\chi_{953}(15,\cdot)$$ 953.l 119 yes $$1$$ $$1$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{6}{119}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{44}{119}\right)$$ $$e\left(\frac{48}{119}\right)$$ $$e\left(\frac{64}{119}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{12}{119}\right)$$ $$e\left(\frac{86}{119}\right)$$ $$e\left(\frac{81}{119}\right)$$
$$\chi_{953}(16,\cdot)$$ 953.g 17 yes $$1$$ $$1$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$
$$\chi_{953}(17,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{123}{476}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{69}{476}\right)$$ $$e\left(\frac{389}{476}\right)$$ $$e\left(\frac{90}{119}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{123}{238}\right)$$ $$e\left(\frac{335}{476}\right)$$ $$e\left(\frac{173}{476}\right)$$
$$\chi_{953}(18,\cdot)$$ 953.l 119 yes $$1$$ $$1$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{16}{119}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{38}{119}\right)$$ $$e\left(\frac{9}{119}\right)$$ $$e\left(\frac{12}{119}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{32}{119}\right)$$ $$e\left(\frac{31}{119}\right)$$ $$e\left(\frac{97}{119}\right)$$
$$\chi_{953}(19,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{1}{68}\right)$$ $$e\left(\frac{257}{952}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{655}{952}\right)$$ $$e\left(\frac{271}{952}\right)$$ $$e\left(\frac{11}{238}\right)$$ $$e\left(\frac{3}{68}\right)$$ $$e\left(\frac{257}{476}\right)$$ $$e\left(\frac{669}{952}\right)$$ $$e\left(\frac{911}{952}\right)$$
$$\chi_{953}(20,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{39}{68}\right)$$ $$e\left(\frac{299}{952}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{725}{952}\right)$$ $$e\left(\frac{845}{952}\right)$$ $$e\left(\frac{123}{238}\right)$$ $$e\left(\frac{49}{68}\right)$$ $$e\left(\frac{299}{476}\right)$$ $$e\left(\frac{319}{952}\right)$$ $$e\left(\frac{645}{952}\right)$$
$$\chi_{953}(21,\cdot)$$ 953.m 136 yes $$-1$$ $$1$$ $$e\left(\frac{37}{68}\right)$$ $$e\left(\frac{115}{136}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{101}{136}\right)$$ $$e\left(\frac{53}{136}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{43}{68}\right)$$ $$e\left(\frac{47}{68}\right)$$ $$e\left(\frac{39}{136}\right)$$ $$e\left(\frac{133}{136}\right)$$
$$\chi_{953}(22,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{57}{68}\right)$$ $$e\left(\frac{437}{952}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{547}{952}\right)$$ $$e\left(\frac{283}{952}\right)$$ $$e\left(\frac{15}{238}\right)$$ $$e\left(\frac{35}{68}\right)$$ $$e\left(\frac{437}{476}\right)$$ $$e\left(\frac{393}{952}\right)$$ $$e\left(\frac{723}{952}\right)$$
$$\chi_{953}(23,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{3}{68}\right)$$ $$e\left(\frac{363}{952}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{877}{952}\right)$$ $$e\left(\frac{405}{952}\right)$$ $$e\left(\frac{135}{238}\right)$$ $$e\left(\frac{9}{68}\right)$$ $$e\left(\frac{363}{476}\right)$$ $$e\left(\frac{919}{952}\right)$$ $$e\left(\frac{557}{952}\right)$$
$$\chi_{953}(24,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{11}{68}\right)$$ $$e\left(\frac{379}{952}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{677}{952}\right)$$ $$e\left(\frac{533}{952}\right)$$ $$e\left(\frac{19}{238}\right)$$ $$e\left(\frac{33}{68}\right)$$ $$e\left(\frac{379}{476}\right)$$ $$e\left(\frac{831}{952}\right)$$ $$e\left(\frac{773}{952}\right)$$
$$\chi_{953}(25,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{47}{476}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{305}{476}\right)$$ $$e\left(\frac{257}{476}\right)$$ $$e\left(\frac{46}{119}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{47}{238}\right)$$ $$e\left(\frac{39}{476}\right)$$ $$e\left(\frac{337}{476}\right)$$
$$\chi_{953}(26,\cdot)$$ 953.n 238 yes $$1$$ $$1$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{117}{238}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{25}{238}\right)$$ $$e\left(\frac{103}{238}\right)$$ $$e\left(\frac{29}{119}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{117}{119}\right)$$ $$e\left(\frac{11}{238}\right)$$ $$e\left(\frac{211}{238}\right)$$
$$\chi_{953}(27,\cdot)$$ 953.p 952 yes $$-1$$ $$1$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{3}{952}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{141}{952}\right)$$ $$e\left(\frac{381}{952}\right)$$ $$e\left(\frac{127}{238}\right)$$ $$e\left(\frac{13}{68}\right)$$ $$e\left(\frac{3}{476}\right)$$ $$e\left(\frac{519}{952}\right)$$ $$e\left(\frac{933}{952}\right)$$
$$\chi_{953}(28,\cdot)$$ 953.l 119 yes $$1$$ $$1$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{13}{119}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{16}{119}\right)$$ $$e\left(\frac{104}{119}\right)$$ $$e\left(\frac{99}{119}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{26}{119}\right)$$ $$e\left(\frac{107}{119}\right)$$ $$e\left(\frac{116}{119}\right)$$
$$\chi_{953}(29,\cdot)$$ 953.n 238 yes $$1$$ $$1$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{223}{238}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{9}{238}\right)$$ $$e\left(\frac{237}{238}\right)$$ $$e\left(\frac{39}{119}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{104}{119}\right)$$ $$e\left(\frac{23}{238}\right)$$ $$e\left(\frac{95}{238}\right)$$
$$\chi_{953}(30,\cdot)$$ 953.o 476 yes $$1$$ $$1$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{87}{476}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{281}{476}\right)$$ $$e\left(\frac{101}{476}\right)$$ $$e\left(\frac{113}{119}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{87}{238}\right)$$ $$e\left(\frac{295}{476}\right)$$ $$e\left(\frac{401}{476}\right)$$
$$\chi_{953}(31,\cdot)$$ 953.m 136 yes $$-1$$ $$1$$ $$e\left(\frac{1}{68}\right)$$ $$e\left(\frac{95}{136}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{113}{136}\right)$$ $$e\left(\frac{97}{136}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{3}{68}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{115}{136}\right)$$ $$e\left(\frac{33}{136}\right)$$
$$\chi_{953}(32,\cdot)$$ 953.k 68 yes $$1$$ $$1$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{7}{68}\right)$$ $$e\left(\frac{3}{68}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{33}{68}\right)$$ $$e\left(\frac{55}{68}\right)$$