# Properties

 Modulus $2675$ Structure $$C_{2}\times C_{1060}$$ Order $2120$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2675)

pari: g = idealstar(,2675,2)

## Character group

 sage: G.order()  pari: g.no Order = 2120 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{1060}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2675}(1927,\cdot)$, $\chi_{2675}(751,\cdot)$

## First 32 of 2120 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{2675}(1,\cdot)$$ 2675.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2675}(2,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{63}{1060}\right)$$ $$e\left(\frac{11}{1060}\right)$$ $$e\left(\frac{63}{530}\right)$$ $$e\left(\frac{37}{530}\right)$$ $$e\left(\frac{139}{212}\right)$$ $$e\left(\frac{189}{1060}\right)$$ $$e\left(\frac{11}{530}\right)$$ $$e\left(\frac{2}{265}\right)$$ $$e\left(\frac{137}{1060}\right)$$ $$e\left(\frac{87}{1060}\right)$$
$$\chi_{2675}(3,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{11}{1060}\right)$$ $$e\left(\frac{717}{1060}\right)$$ $$e\left(\frac{11}{530}\right)$$ $$e\left(\frac{182}{265}\right)$$ $$e\left(\frac{31}{212}\right)$$ $$e\left(\frac{33}{1060}\right)$$ $$e\left(\frac{187}{530}\right)$$ $$e\left(\frac{34}{265}\right)$$ $$e\left(\frac{739}{1060}\right)$$ $$e\left(\frac{949}{1060}\right)$$
$$\chi_{2675}(4,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{63}{530}\right)$$ $$e\left(\frac{11}{530}\right)$$ $$e\left(\frac{63}{265}\right)$$ $$e\left(\frac{37}{265}\right)$$ $$e\left(\frac{33}{106}\right)$$ $$e\left(\frac{189}{530}\right)$$ $$e\left(\frac{11}{265}\right)$$ $$e\left(\frac{4}{265}\right)$$ $$e\left(\frac{137}{530}\right)$$ $$e\left(\frac{87}{530}\right)$$
$$\chi_{2675}(6,\cdot)$$ 2675.u 530 yes $$-1$$ $$1$$ $$e\left(\frac{37}{530}\right)$$ $$e\left(\frac{182}{265}\right)$$ $$e\left(\frac{37}{265}\right)$$ $$e\left(\frac{401}{530}\right)$$ $$e\left(\frac{85}{106}\right)$$ $$e\left(\frac{111}{530}\right)$$ $$e\left(\frac{99}{265}\right)$$ $$e\left(\frac{36}{265}\right)$$ $$e\left(\frac{219}{265}\right)$$ $$e\left(\frac{259}{265}\right)$$
$$\chi_{2675}(7,\cdot)$$ 2675.r 212 no $$1$$ $$1$$ $$e\left(\frac{139}{212}\right)$$ $$e\left(\frac{31}{212}\right)$$ $$e\left(\frac{33}{106}\right)$$ $$e\left(\frac{85}{106}\right)$$ $$e\left(\frac{147}{212}\right)$$ $$e\left(\frac{205}{212}\right)$$ $$e\left(\frac{31}{106}\right)$$ $$e\left(\frac{49}{53}\right)$$ $$e\left(\frac{97}{212}\right)$$ $$e\left(\frac{91}{212}\right)$$
$$\chi_{2675}(8,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{189}{1060}\right)$$ $$e\left(\frac{33}{1060}\right)$$ $$e\left(\frac{189}{530}\right)$$ $$e\left(\frac{111}{530}\right)$$ $$e\left(\frac{205}{212}\right)$$ $$e\left(\frac{567}{1060}\right)$$ $$e\left(\frac{33}{530}\right)$$ $$e\left(\frac{6}{265}\right)$$ $$e\left(\frac{411}{1060}\right)$$ $$e\left(\frac{261}{1060}\right)$$
$$\chi_{2675}(9,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{11}{530}\right)$$ $$e\left(\frac{187}{530}\right)$$ $$e\left(\frac{11}{265}\right)$$ $$e\left(\frac{99}{265}\right)$$ $$e\left(\frac{31}{106}\right)$$ $$e\left(\frac{33}{530}\right)$$ $$e\left(\frac{187}{265}\right)$$ $$e\left(\frac{68}{265}\right)$$ $$e\left(\frac{209}{530}\right)$$ $$e\left(\frac{419}{530}\right)$$
$$\chi_{2675}(11,\cdot)$$ 2675.s 265 yes $$1$$ $$1$$ $$e\left(\frac{2}{265}\right)$$ $$e\left(\frac{34}{265}\right)$$ $$e\left(\frac{4}{265}\right)$$ $$e\left(\frac{36}{265}\right)$$ $$e\left(\frac{49}{53}\right)$$ $$e\left(\frac{6}{265}\right)$$ $$e\left(\frac{68}{265}\right)$$ $$e\left(\frac{97}{265}\right)$$ $$e\left(\frac{38}{265}\right)$$ $$e\left(\frac{28}{265}\right)$$
$$\chi_{2675}(12,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{137}{1060}\right)$$ $$e\left(\frac{739}{1060}\right)$$ $$e\left(\frac{137}{530}\right)$$ $$e\left(\frac{219}{265}\right)$$ $$e\left(\frac{97}{212}\right)$$ $$e\left(\frac{411}{1060}\right)$$ $$e\left(\frac{209}{530}\right)$$ $$e\left(\frac{38}{265}\right)$$ $$e\left(\frac{1013}{1060}\right)$$ $$e\left(\frac{63}{1060}\right)$$
$$\chi_{2675}(13,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{87}{1060}\right)$$ $$e\left(\frac{949}{1060}\right)$$ $$e\left(\frac{87}{530}\right)$$ $$e\left(\frac{259}{265}\right)$$ $$e\left(\frac{91}{212}\right)$$ $$e\left(\frac{261}{1060}\right)$$ $$e\left(\frac{419}{530}\right)$$ $$e\left(\frac{28}{265}\right)$$ $$e\left(\frac{63}{1060}\right)$$ $$e\left(\frac{953}{1060}\right)$$
$$\chi_{2675}(14,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{379}{530}\right)$$ $$e\left(\frac{83}{530}\right)$$ $$e\left(\frac{114}{265}\right)$$ $$e\left(\frac{231}{265}\right)$$ $$e\left(\frac{37}{106}\right)$$ $$e\left(\frac{77}{530}\right)$$ $$e\left(\frac{83}{265}\right)$$ $$e\left(\frac{247}{265}\right)$$ $$e\left(\frac{311}{530}\right)$$ $$e\left(\frac{271}{530}\right)$$
$$\chi_{2675}(16,\cdot)$$ 2675.s 265 yes $$1$$ $$1$$ $$e\left(\frac{63}{265}\right)$$ $$e\left(\frac{11}{265}\right)$$ $$e\left(\frac{126}{265}\right)$$ $$e\left(\frac{74}{265}\right)$$ $$e\left(\frac{33}{53}\right)$$ $$e\left(\frac{189}{265}\right)$$ $$e\left(\frac{22}{265}\right)$$ $$e\left(\frac{8}{265}\right)$$ $$e\left(\frac{137}{265}\right)$$ $$e\left(\frac{87}{265}\right)$$
$$\chi_{2675}(17,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{979}{1060}\right)$$ $$e\left(\frac{743}{1060}\right)$$ $$e\left(\frac{449}{530}\right)$$ $$e\left(\frac{331}{530}\right)$$ $$e\left(\frac{3}{212}\right)$$ $$e\left(\frac{817}{1060}\right)$$ $$e\left(\frac{213}{530}\right)$$ $$e\left(\frac{111}{265}\right)$$ $$e\left(\frac{581}{1060}\right)$$ $$e\left(\frac{191}{1060}\right)$$
$$\chi_{2675}(18,\cdot)$$ 2675.r 212 no $$1$$ $$1$$ $$e\left(\frac{17}{212}\right)$$ $$e\left(\frac{77}{212}\right)$$ $$e\left(\frac{17}{106}\right)$$ $$e\left(\frac{47}{106}\right)$$ $$e\left(\frac{201}{212}\right)$$ $$e\left(\frac{51}{212}\right)$$ $$e\left(\frac{77}{106}\right)$$ $$e\left(\frac{14}{53}\right)$$ $$e\left(\frac{111}{212}\right)$$ $$e\left(\frac{185}{212}\right)$$
$$\chi_{2675}(19,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{337}{530}\right)$$ $$e\left(\frac{429}{530}\right)$$ $$e\left(\frac{72}{265}\right)$$ $$e\left(\frac{118}{265}\right)$$ $$e\left(\frac{15}{106}\right)$$ $$e\left(\frac{481}{530}\right)$$ $$e\left(\frac{164}{265}\right)$$ $$e\left(\frac{156}{265}\right)$$ $$e\left(\frac{43}{530}\right)$$ $$e\left(\frac{213}{530}\right)$$
$$\chi_{2675}(21,\cdot)$$ 2675.u 530 yes $$-1$$ $$1$$ $$e\left(\frac{353}{530}\right)$$ $$e\left(\frac{218}{265}\right)$$ $$e\left(\frac{88}{265}\right)$$ $$e\left(\frac{259}{530}\right)$$ $$e\left(\frac{89}{106}\right)$$ $$e\left(\frac{529}{530}\right)$$ $$e\left(\frac{171}{265}\right)$$ $$e\left(\frac{14}{265}\right)$$ $$e\left(\frac{41}{265}\right)$$ $$e\left(\frac{86}{265}\right)$$
$$\chi_{2675}(22,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{71}{1060}\right)$$ $$e\left(\frac{147}{1060}\right)$$ $$e\left(\frac{71}{530}\right)$$ $$e\left(\frac{109}{530}\right)$$ $$e\left(\frac{123}{212}\right)$$ $$e\left(\frac{213}{1060}\right)$$ $$e\left(\frac{147}{530}\right)$$ $$e\left(\frac{99}{265}\right)$$ $$e\left(\frac{289}{1060}\right)$$ $$e\left(\frac{199}{1060}\right)$$
$$\chi_{2675}(23,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{143}{1060}\right)$$ $$e\left(\frac{841}{1060}\right)$$ $$e\left(\frac{143}{530}\right)$$ $$e\left(\frac{246}{265}\right)$$ $$e\left(\frac{191}{212}\right)$$ $$e\left(\frac{429}{1060}\right)$$ $$e\left(\frac{311}{530}\right)$$ $$e\left(\frac{177}{265}\right)$$ $$e\left(\frac{67}{1060}\right)$$ $$e\left(\frac{677}{1060}\right)$$
$$\chi_{2675}(24,\cdot)$$ 2675.n 106 no $$-1$$ $$1$$ $$e\left(\frac{10}{53}\right)$$ $$e\left(\frac{75}{106}\right)$$ $$e\left(\frac{20}{53}\right)$$ $$e\left(\frac{95}{106}\right)$$ $$e\left(\frac{6}{53}\right)$$ $$e\left(\frac{30}{53}\right)$$ $$e\left(\frac{22}{53}\right)$$ $$e\left(\frac{8}{53}\right)$$ $$e\left(\frac{9}{106}\right)$$ $$e\left(\frac{15}{106}\right)$$
$$\chi_{2675}(26,\cdot)$$ 2675.o 106 no $$-1$$ $$1$$ $$e\left(\frac{15}{106}\right)$$ $$e\left(\frac{48}{53}\right)$$ $$e\left(\frac{15}{53}\right)$$ $$e\left(\frac{5}{106}\right)$$ $$e\left(\frac{9}{106}\right)$$ $$e\left(\frac{45}{106}\right)$$ $$e\left(\frac{43}{53}\right)$$ $$e\left(\frac{6}{53}\right)$$ $$e\left(\frac{10}{53}\right)$$ $$e\left(\frac{52}{53}\right)$$
$$\chi_{2675}(27,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{33}{1060}\right)$$ $$e\left(\frac{31}{1060}\right)$$ $$e\left(\frac{33}{530}\right)$$ $$e\left(\frac{16}{265}\right)$$ $$e\left(\frac{93}{212}\right)$$ $$e\left(\frac{99}{1060}\right)$$ $$e\left(\frac{31}{530}\right)$$ $$e\left(\frac{102}{265}\right)$$ $$e\left(\frac{97}{1060}\right)$$ $$e\left(\frac{727}{1060}\right)$$
$$\chi_{2675}(28,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{821}{1060}\right)$$ $$e\left(\frac{177}{1060}\right)$$ $$e\left(\frac{291}{530}\right)$$ $$e\left(\frac{499}{530}\right)$$ $$e\left(\frac{1}{212}\right)$$ $$e\left(\frac{343}{1060}\right)$$ $$e\left(\frac{177}{530}\right)$$ $$e\left(\frac{249}{265}\right)$$ $$e\left(\frac{759}{1060}\right)$$ $$e\left(\frac{629}{1060}\right)$$
$$\chi_{2675}(29,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{213}{530}\right)$$ $$e\left(\frac{441}{530}\right)$$ $$e\left(\frac{213}{265}\right)$$ $$e\left(\frac{62}{265}\right)$$ $$e\left(\frac{51}{106}\right)$$ $$e\left(\frac{109}{530}\right)$$ $$e\left(\frac{176}{265}\right)$$ $$e\left(\frac{64}{265}\right)$$ $$e\left(\frac{337}{530}\right)$$ $$e\left(\frac{67}{530}\right)$$
$$\chi_{2675}(31,\cdot)$$ 2675.u 530 yes $$-1$$ $$1$$ $$e\left(\frac{347}{530}\right)$$ $$e\left(\frac{167}{265}\right)$$ $$e\left(\frac{82}{265}\right)$$ $$e\left(\frac{151}{530}\right)$$ $$e\left(\frac{101}{106}\right)$$ $$e\left(\frac{511}{530}\right)$$ $$e\left(\frac{69}{265}\right)$$ $$e\left(\frac{1}{265}\right)$$ $$e\left(\frac{249}{265}\right)$$ $$e\left(\frac{44}{265}\right)$$
$$\chi_{2675}(32,\cdot)$$ 2675.r 212 no $$1$$ $$1$$ $$e\left(\frac{63}{212}\right)$$ $$e\left(\frac{11}{212}\right)$$ $$e\left(\frac{63}{106}\right)$$ $$e\left(\frac{37}{106}\right)$$ $$e\left(\frac{59}{212}\right)$$ $$e\left(\frac{189}{212}\right)$$ $$e\left(\frac{11}{106}\right)$$ $$e\left(\frac{2}{53}\right)$$ $$e\left(\frac{137}{212}\right)$$ $$e\left(\frac{87}{212}\right)$$
$$\chi_{2675}(33,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{19}{1060}\right)$$ $$e\left(\frac{853}{1060}\right)$$ $$e\left(\frac{19}{530}\right)$$ $$e\left(\frac{218}{265}\right)$$ $$e\left(\frac{15}{212}\right)$$ $$e\left(\frac{57}{1060}\right)$$ $$e\left(\frac{323}{530}\right)$$ $$e\left(\frac{131}{265}\right)$$ $$e\left(\frac{891}{1060}\right)$$ $$e\left(\frac{1}{1060}\right)$$
$$\chi_{2675}(34,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{521}{530}\right)$$ $$e\left(\frac{377}{530}\right)$$ $$e\left(\frac{256}{265}\right)$$ $$e\left(\frac{184}{265}\right)$$ $$e\left(\frac{71}{106}\right)$$ $$e\left(\frac{503}{530}\right)$$ $$e\left(\frac{112}{265}\right)$$ $$e\left(\frac{113}{265}\right)$$ $$e\left(\frac{359}{530}\right)$$ $$e\left(\frac{139}{530}\right)$$
$$\chi_{2675}(36,\cdot)$$ 2675.s 265 yes $$1$$ $$1$$ $$e\left(\frac{37}{265}\right)$$ $$e\left(\frac{99}{265}\right)$$ $$e\left(\frac{74}{265}\right)$$ $$e\left(\frac{136}{265}\right)$$ $$e\left(\frac{32}{53}\right)$$ $$e\left(\frac{111}{265}\right)$$ $$e\left(\frac{198}{265}\right)$$ $$e\left(\frac{72}{265}\right)$$ $$e\left(\frac{173}{265}\right)$$ $$e\left(\frac{253}{265}\right)$$
$$\chi_{2675}(37,\cdot)$$ 2675.x 1060 yes $$-1$$ $$1$$ $$e\left(\frac{857}{1060}\right)$$ $$e\left(\frac{259}{1060}\right)$$ $$e\left(\frac{327}{530}\right)$$ $$e\left(\frac{14}{265}\right)$$ $$e\left(\frac{141}{212}\right)$$ $$e\left(\frac{451}{1060}\right)$$ $$e\left(\frac{259}{530}\right)$$ $$e\left(\frac{23}{265}\right)$$ $$e\left(\frac{913}{1060}\right)$$ $$e\left(\frac{603}{1060}\right)$$
$$\chi_{2675}(38,\cdot)$$ 2675.w 1060 yes $$1$$ $$1$$ $$e\left(\frac{737}{1060}\right)$$ $$e\left(\frac{869}{1060}\right)$$ $$e\left(\frac{207}{530}\right)$$ $$e\left(\frac{273}{530}\right)$$ $$e\left(\frac{169}{212}\right)$$ $$e\left(\frac{91}{1060}\right)$$ $$e\left(\frac{339}{530}\right)$$ $$e\left(\frac{158}{265}\right)$$ $$e\left(\frac{223}{1060}\right)$$ $$e\left(\frac{513}{1060}\right)$$
$$\chi_{2675}(39,\cdot)$$ 2675.t 530 yes $$1$$ $$1$$ $$e\left(\frac{49}{530}\right)$$ $$e\left(\frac{303}{530}\right)$$ $$e\left(\frac{49}{265}\right)$$ $$e\left(\frac{176}{265}\right)$$ $$e\left(\frac{61}{106}\right)$$ $$e\left(\frac{147}{530}\right)$$ $$e\left(\frac{38}{265}\right)$$ $$e\left(\frac{62}{265}\right)$$ $$e\left(\frac{401}{530}\right)$$ $$e\left(\frac{421}{530}\right)$$