# Properties

 Modulus $1077$ Structure $$C_{358}\times C_{2}$$ Order $716$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1077)

pari: g = idealstar(,1077,2)

## Character group

 sage: G.order()  pari: g.no Order = 716 sage: H.invariants()  pari: g.cyc Structure = $$C_{358}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1077}(719,\cdot)$, $\chi_{1077}(7,\cdot)$

## First 32 of 716 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{1077}(1,\cdot)$$ 1077.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1077}(2,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{325}{358}\right)$$ $$e\left(\frac{146}{179}\right)$$ $$e\left(\frac{357}{358}\right)$$ $$e\left(\frac{157}{179}\right)$$ $$e\left(\frac{259}{358}\right)$$ $$e\left(\frac{162}{179}\right)$$ $$e\left(\frac{121}{358}\right)$$ $$e\left(\frac{144}{179}\right)$$ $$e\left(\frac{281}{358}\right)$$ $$e\left(\frac{113}{179}\right)$$
$$\chi_{1077}(4,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{146}{179}\right)$$ $$e\left(\frac{113}{179}\right)$$ $$e\left(\frac{178}{179}\right)$$ $$e\left(\frac{135}{179}\right)$$ $$e\left(\frac{80}{179}\right)$$ $$e\left(\frac{145}{179}\right)$$ $$e\left(\frac{121}{179}\right)$$ $$e\left(\frac{109}{179}\right)$$ $$e\left(\frac{102}{179}\right)$$ $$e\left(\frac{47}{179}\right)$$
$$\chi_{1077}(5,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{357}{358}\right)$$ $$e\left(\frac{178}{179}\right)$$ $$e\left(\frac{141}{358}\right)$$ $$e\left(\frac{59}{179}\right)$$ $$e\left(\frac{355}{358}\right)$$ $$e\left(\frac{70}{179}\right)$$ $$e\left(\frac{123}{358}\right)$$ $$e\left(\frac{102}{179}\right)$$ $$e\left(\frac{117}{358}\right)$$ $$e\left(\frac{177}{179}\right)$$
$$\chi_{1077}(7,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{157}{179}\right)$$ $$e\left(\frac{135}{179}\right)$$ $$e\left(\frac{59}{179}\right)$$ $$e\left(\frac{1}{358}\right)$$ $$e\left(\frac{113}{179}\right)$$ $$e\left(\frac{37}{179}\right)$$ $$e\left(\frac{21}{179}\right)$$ $$e\left(\frac{205}{358}\right)$$ $$e\left(\frac{315}{358}\right)$$ $$e\left(\frac{91}{179}\right)$$
$$\chi_{1077}(8,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{259}{358}\right)$$ $$e\left(\frac{80}{179}\right)$$ $$e\left(\frac{355}{358}\right)$$ $$e\left(\frac{113}{179}\right)$$ $$e\left(\frac{61}{358}\right)$$ $$e\left(\frac{128}{179}\right)$$ $$e\left(\frac{5}{358}\right)$$ $$e\left(\frac{74}{179}\right)$$ $$e\left(\frac{127}{358}\right)$$ $$e\left(\frac{160}{179}\right)$$
$$\chi_{1077}(10,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{162}{179}\right)$$ $$e\left(\frac{145}{179}\right)$$ $$e\left(\frac{70}{179}\right)$$ $$e\left(\frac{37}{179}\right)$$ $$e\left(\frac{128}{179}\right)$$ $$e\left(\frac{53}{179}\right)$$ $$e\left(\frac{122}{179}\right)$$ $$e\left(\frac{67}{179}\right)$$ $$e\left(\frac{20}{179}\right)$$ $$e\left(\frac{111}{179}\right)$$
$$\chi_{1077}(11,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{121}{358}\right)$$ $$e\left(\frac{121}{179}\right)$$ $$e\left(\frac{123}{358}\right)$$ $$e\left(\frac{21}{179}\right)$$ $$e\left(\frac{5}{358}\right)$$ $$e\left(\frac{122}{179}\right)$$ $$e\left(\frac{153}{358}\right)$$ $$e\left(\frac{9}{179}\right)$$ $$e\left(\frac{163}{358}\right)$$ $$e\left(\frac{63}{179}\right)$$
$$\chi_{1077}(13,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{144}{179}\right)$$ $$e\left(\frac{109}{179}\right)$$ $$e\left(\frac{102}{179}\right)$$ $$e\left(\frac{205}{358}\right)$$ $$e\left(\frac{74}{179}\right)$$ $$e\left(\frac{67}{179}\right)$$ $$e\left(\frac{9}{179}\right)$$ $$e\left(\frac{139}{358}\right)$$ $$e\left(\frac{135}{358}\right)$$ $$e\left(\frac{39}{179}\right)$$
$$\chi_{1077}(14,\cdot)$$ 1077.h 358 yes $$1$$ $$1$$ $$e\left(\frac{281}{358}\right)$$ $$e\left(\frac{102}{179}\right)$$ $$e\left(\frac{117}{358}\right)$$ $$e\left(\frac{315}{358}\right)$$ $$e\left(\frac{127}{358}\right)$$ $$e\left(\frac{20}{179}\right)$$ $$e\left(\frac{163}{358}\right)$$ $$e\left(\frac{135}{358}\right)$$ $$e\left(\frac{119}{179}\right)$$ $$e\left(\frac{25}{179}\right)$$
$$\chi_{1077}(16,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{113}{179}\right)$$ $$e\left(\frac{47}{179}\right)$$ $$e\left(\frac{177}{179}\right)$$ $$e\left(\frac{91}{179}\right)$$ $$e\left(\frac{160}{179}\right)$$ $$e\left(\frac{111}{179}\right)$$ $$e\left(\frac{63}{179}\right)$$ $$e\left(\frac{39}{179}\right)$$ $$e\left(\frac{25}{179}\right)$$ $$e\left(\frac{94}{179}\right)$$
$$\chi_{1077}(17,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{319}{358}\right)$$ $$e\left(\frac{140}{179}\right)$$ $$e\left(\frac{129}{358}\right)$$ $$e\left(\frac{153}{179}\right)$$ $$e\left(\frac{241}{358}\right)$$ $$e\left(\frac{45}{179}\right)$$ $$e\left(\frac{143}{358}\right)$$ $$e\left(\frac{40}{179}\right)$$ $$e\left(\frac{267}{358}\right)$$ $$e\left(\frac{101}{179}\right)$$
$$\chi_{1077}(19,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{126}{179}\right)$$ $$e\left(\frac{73}{179}\right)$$ $$e\left(\frac{134}{179}\right)$$ $$e\left(\frac{157}{358}\right)$$ $$e\left(\frac{20}{179}\right)$$ $$e\left(\frac{81}{179}\right)$$ $$e\left(\frac{75}{179}\right)$$ $$e\left(\frac{323}{358}\right)$$ $$e\left(\frac{51}{358}\right)$$ $$e\left(\frac{146}{179}\right)$$
$$\chi_{1077}(20,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{291}{358}\right)$$ $$e\left(\frac{112}{179}\right)$$ $$e\left(\frac{139}{358}\right)$$ $$e\left(\frac{15}{179}\right)$$ $$e\left(\frac{157}{358}\right)$$ $$e\left(\frac{36}{179}\right)$$ $$e\left(\frac{7}{358}\right)$$ $$e\left(\frac{32}{179}\right)$$ $$e\left(\frac{321}{358}\right)$$ $$e\left(\frac{45}{179}\right)$$
$$\chi_{1077}(22,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{44}{179}\right)$$ $$e\left(\frac{88}{179}\right)$$ $$e\left(\frac{61}{179}\right)$$ $$e\left(\frac{178}{179}\right)$$ $$e\left(\frac{132}{179}\right)$$ $$e\left(\frac{105}{179}\right)$$ $$e\left(\frac{137}{179}\right)$$ $$e\left(\frac{153}{179}\right)$$ $$e\left(\frac{43}{179}\right)$$ $$e\left(\frac{176}{179}\right)$$
$$\chi_{1077}(23,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{53}{358}\right)$$ $$e\left(\frac{53}{179}\right)$$ $$e\left(\frac{45}{358}\right)$$ $$e\left(\frac{95}{179}\right)$$ $$e\left(\frac{159}{358}\right)$$ $$e\left(\frac{49}{179}\right)$$ $$e\left(\frac{283}{358}\right)$$ $$e\left(\frac{143}{179}\right)$$ $$e\left(\frac{243}{358}\right)$$ $$e\left(\frac{106}{179}\right)$$
$$\chi_{1077}(25,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{178}{179}\right)$$ $$e\left(\frac{177}{179}\right)$$ $$e\left(\frac{141}{179}\right)$$ $$e\left(\frac{118}{179}\right)$$ $$e\left(\frac{176}{179}\right)$$ $$e\left(\frac{140}{179}\right)$$ $$e\left(\frac{123}{179}\right)$$ $$e\left(\frac{25}{179}\right)$$ $$e\left(\frac{117}{179}\right)$$ $$e\left(\frac{175}{179}\right)$$
$$\chi_{1077}(26,\cdot)$$ 1077.h 358 yes $$1$$ $$1$$ $$e\left(\frac{255}{358}\right)$$ $$e\left(\frac{76}{179}\right)$$ $$e\left(\frac{203}{358}\right)$$ $$e\left(\frac{161}{358}\right)$$ $$e\left(\frac{49}{358}\right)$$ $$e\left(\frac{50}{179}\right)$$ $$e\left(\frac{139}{358}\right)$$ $$e\left(\frac{69}{358}\right)$$ $$e\left(\frac{29}{179}\right)$$ $$e\left(\frac{152}{179}\right)$$
$$\chi_{1077}(28,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{124}{179}\right)$$ $$e\left(\frac{69}{179}\right)$$ $$e\left(\frac{58}{179}\right)$$ $$e\left(\frac{271}{358}\right)$$ $$e\left(\frac{14}{179}\right)$$ $$e\left(\frac{3}{179}\right)$$ $$e\left(\frac{142}{179}\right)$$ $$e\left(\frac{65}{358}\right)$$ $$e\left(\frac{161}{358}\right)$$ $$e\left(\frac{138}{179}\right)$$
$$\chi_{1077}(29,\cdot)$$ 1077.h 358 yes $$1$$ $$1$$ $$e\left(\frac{137}{358}\right)$$ $$e\left(\frac{137}{179}\right)$$ $$e\left(\frac{15}{358}\right)$$ $$e\left(\frac{123}{358}\right)$$ $$e\left(\frac{53}{358}\right)$$ $$e\left(\frac{76}{179}\right)$$ $$e\left(\frac{333}{358}\right)$$ $$e\left(\frac{155}{358}\right)$$ $$e\left(\frac{130}{179}\right)$$ $$e\left(\frac{95}{179}\right)$$
$$\chi_{1077}(31,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{152}{179}\right)$$ $$e\left(\frac{125}{179}\right)$$ $$e\left(\frac{48}{179}\right)$$ $$e\left(\frac{107}{358}\right)$$ $$e\left(\frac{98}{179}\right)$$ $$e\left(\frac{21}{179}\right)$$ $$e\left(\frac{99}{179}\right)$$ $$e\left(\frac{97}{358}\right)$$ $$e\left(\frac{53}{358}\right)$$ $$e\left(\frac{71}{179}\right)$$
$$\chi_{1077}(32,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{193}{358}\right)$$ $$e\left(\frac{14}{179}\right)$$ $$e\left(\frac{353}{358}\right)$$ $$e\left(\frac{69}{179}\right)$$ $$e\left(\frac{221}{358}\right)$$ $$e\left(\frac{94}{179}\right)$$ $$e\left(\frac{247}{358}\right)$$ $$e\left(\frac{4}{179}\right)$$ $$e\left(\frac{331}{358}\right)$$ $$e\left(\frac{28}{179}\right)$$
$$\chi_{1077}(34,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{143}{179}\right)$$ $$e\left(\frac{107}{179}\right)$$ $$e\left(\frac{64}{179}\right)$$ $$e\left(\frac{131}{179}\right)$$ $$e\left(\frac{71}{179}\right)$$ $$e\left(\frac{28}{179}\right)$$ $$e\left(\frac{132}{179}\right)$$ $$e\left(\frac{5}{179}\right)$$ $$e\left(\frac{95}{179}\right)$$ $$e\left(\frac{35}{179}\right)$$
$$\chi_{1077}(35,\cdot)$$ 1077.h 358 yes $$1$$ $$1$$ $$e\left(\frac{313}{358}\right)$$ $$e\left(\frac{134}{179}\right)$$ $$e\left(\frac{259}{358}\right)$$ $$e\left(\frac{119}{358}\right)$$ $$e\left(\frac{223}{358}\right)$$ $$e\left(\frac{107}{179}\right)$$ $$e\left(\frac{165}{358}\right)$$ $$e\left(\frac{51}{358}\right)$$ $$e\left(\frac{37}{179}\right)$$ $$e\left(\frac{89}{179}\right)$$
$$\chi_{1077}(37,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{167}{179}\right)$$ $$e\left(\frac{155}{179}\right)$$ $$e\left(\frac{81}{179}\right)$$ $$e\left(\frac{163}{179}\right)$$ $$e\left(\frac{143}{179}\right)$$ $$e\left(\frac{69}{179}\right)$$ $$e\left(\frac{44}{179}\right)$$ $$e\left(\frac{121}{179}\right)$$ $$e\left(\frac{151}{179}\right)$$ $$e\left(\frac{131}{179}\right)$$
$$\chi_{1077}(38,\cdot)$$ 1077.h 358 yes $$1$$ $$1$$ $$e\left(\frac{219}{358}\right)$$ $$e\left(\frac{40}{179}\right)$$ $$e\left(\frac{267}{358}\right)$$ $$e\left(\frac{113}{358}\right)$$ $$e\left(\frac{299}{358}\right)$$ $$e\left(\frac{64}{179}\right)$$ $$e\left(\frac{271}{358}\right)$$ $$e\left(\frac{253}{358}\right)$$ $$e\left(\frac{166}{179}\right)$$ $$e\left(\frac{80}{179}\right)$$
$$\chi_{1077}(40,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{129}{179}\right)$$ $$e\left(\frac{79}{179}\right)$$ $$e\left(\frac{69}{179}\right)$$ $$e\left(\frac{172}{179}\right)$$ $$e\left(\frac{29}{179}\right)$$ $$e\left(\frac{19}{179}\right)$$ $$e\left(\frac{64}{179}\right)$$ $$e\left(\frac{176}{179}\right)$$ $$e\left(\frac{122}{179}\right)$$ $$e\left(\frac{158}{179}\right)$$
$$\chi_{1077}(41,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{45}{358}\right)$$ $$e\left(\frac{45}{179}\right)$$ $$e\left(\frac{99}{358}\right)$$ $$e\left(\frac{30}{179}\right)$$ $$e\left(\frac{135}{358}\right)$$ $$e\left(\frac{72}{179}\right)$$ $$e\left(\frac{193}{358}\right)$$ $$e\left(\frac{64}{179}\right)$$ $$e\left(\frac{105}{358}\right)$$ $$e\left(\frac{90}{179}\right)$$
$$\chi_{1077}(43,\cdot)$$ 1077.f 358 no $$-1$$ $$1$$ $$e\left(\frac{74}{179}\right)$$ $$e\left(\frac{148}{179}\right)$$ $$e\left(\frac{127}{179}\right)$$ $$e\left(\frac{257}{358}\right)$$ $$e\left(\frac{43}{179}\right)$$ $$e\left(\frac{22}{179}\right)$$ $$e\left(\frac{27}{179}\right)$$ $$e\left(\frac{59}{358}\right)$$ $$e\left(\frac{47}{358}\right)$$ $$e\left(\frac{117}{179}\right)$$
$$\chi_{1077}(44,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{55}{358}\right)$$ $$e\left(\frac{55}{179}\right)$$ $$e\left(\frac{121}{358}\right)$$ $$e\left(\frac{156}{179}\right)$$ $$e\left(\frac{165}{358}\right)$$ $$e\left(\frac{88}{179}\right)$$ $$e\left(\frac{37}{358}\right)$$ $$e\left(\frac{118}{179}\right)$$ $$e\left(\frac{9}{358}\right)$$ $$e\left(\frac{110}{179}\right)$$
$$\chi_{1077}(46,\cdot)$$ 1077.e 179 no $$1$$ $$1$$ $$e\left(\frac{10}{179}\right)$$ $$e\left(\frac{20}{179}\right)$$ $$e\left(\frac{22}{179}\right)$$ $$e\left(\frac{73}{179}\right)$$ $$e\left(\frac{30}{179}\right)$$ $$e\left(\frac{32}{179}\right)$$ $$e\left(\frac{23}{179}\right)$$ $$e\left(\frac{108}{179}\right)$$ $$e\left(\frac{83}{179}\right)$$ $$e\left(\frac{40}{179}\right)$$
$$\chi_{1077}(47,\cdot)$$ 1077.g 358 yes $$-1$$ $$1$$ $$e\left(\frac{239}{358}\right)$$ $$e\left(\frac{60}{179}\right)$$ $$e\left(\frac{311}{358}\right)$$ $$e\left(\frac{40}{179}\right)$$ $$e\left(\frac{1}{358}\right)$$ $$e\left(\frac{96}{179}\right)$$ $$e\left(\frac{317}{358}\right)$$ $$e\left(\frac{145}{179}\right)$$ $$e\left(\frac{319}{358}\right)$$ $$e\left(\frac{120}{179}\right)$$