# Properties

 Modulus $6034$ Structure $$C_{1290}\times C_{2}$$ Order $2580$

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(6034)

pari: g = idealstar(,6034,2)

## Character group

 sage: G.order()  pari: g.no Order = 2580 sage: H.invariants()  pari: g.cyc Structure = $$C_{1290}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6034}(4317,\cdot)$, $\chi_{6034}(1723,\cdot)$

## First 32 of 2580 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{6034}(1,\cdot)$$ 6034.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6034}(3,\cdot)$$ 6034.x 258 no $$-1$$ $$1$$ $$e\left(\frac{127}{258}\right)$$ $$e\left(\frac{137}{258}\right)$$ $$e\left(\frac{127}{129}\right)$$ $$e\left(\frac{110}{129}\right)$$ $$e\left(\frac{21}{86}\right)$$ $$e\left(\frac{1}{43}\right)$$ $$e\left(\frac{91}{258}\right)$$ $$e\left(\frac{35}{258}\right)$$ $$e\left(\frac{79}{129}\right)$$ $$e\left(\frac{8}{129}\right)$$
$$\chi_{6034}(5,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{137}{258}\right)$$ $$e\left(\frac{227}{1290}\right)$$ $$e\left(\frac{8}{129}\right)$$ $$e\left(\frac{509}{645}\right)$$ $$e\left(\frac{139}{430}\right)$$ $$e\left(\frac{152}{215}\right)$$ $$e\left(\frac{631}{1290}\right)$$ $$e\left(\frac{719}{1290}\right)$$ $$e\left(\frac{613}{645}\right)$$ $$e\left(\frac{227}{645}\right)$$
$$\chi_{6034}(9,\cdot)$$ 6034.u 129 no $$1$$ $$1$$ $$e\left(\frac{127}{129}\right)$$ $$e\left(\frac{8}{129}\right)$$ $$e\left(\frac{125}{129}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{21}{43}\right)$$ $$e\left(\frac{2}{43}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{35}{129}\right)$$ $$e\left(\frac{29}{129}\right)$$ $$e\left(\frac{16}{129}\right)$$
$$\chi_{6034}(11,\cdot)$$ 6034.bc 645 no $$1$$ $$1$$ $$e\left(\frac{110}{129}\right)$$ $$e\left(\frac{509}{645}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{1}{645}\right)$$ $$e\left(\frac{73}{215}\right)$$ $$e\left(\frac{138}{215}\right)$$ $$e\left(\frac{517}{645}\right)$$ $$e\left(\frac{308}{645}\right)$$ $$e\left(\frac{152}{645}\right)$$ $$e\left(\frac{373}{645}\right)$$
$$\chi_{6034}(13,\cdot)$$ 6034.bb 430 no $$1$$ $$1$$ $$e\left(\frac{21}{86}\right)$$ $$e\left(\frac{139}{430}\right)$$ $$e\left(\frac{21}{43}\right)$$ $$e\left(\frac{73}{215}\right)$$ $$e\left(\frac{77}{215}\right)$$ $$e\left(\frac{122}{215}\right)$$ $$e\left(\frac{116}{215}\right)$$ $$e\left(\frac{33}{430}\right)$$ $$e\left(\frac{131}{215}\right)$$ $$e\left(\frac{139}{215}\right)$$
$$\chi_{6034}(15,\cdot)$$ 6034.v 215 no $$1$$ $$1$$ $$e\left(\frac{1}{43}\right)$$ $$e\left(\frac{152}{215}\right)$$ $$e\left(\frac{2}{43}\right)$$ $$e\left(\frac{138}{215}\right)$$ $$e\left(\frac{122}{215}\right)$$ $$e\left(\frac{157}{215}\right)$$ $$e\left(\frac{181}{215}\right)$$ $$e\left(\frac{149}{215}\right)$$ $$e\left(\frac{121}{215}\right)$$ $$e\left(\frac{89}{215}\right)$$
$$\chi_{6034}(17,\cdot)$$ 6034.be 1290 no $$1$$ $$1$$ $$e\left(\frac{91}{258}\right)$$ $$e\left(\frac{631}{1290}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{517}{645}\right)$$ $$e\left(\frac{116}{215}\right)$$ $$e\left(\frac{181}{215}\right)$$ $$e\left(\frac{259}{645}\right)$$ $$e\left(\frac{487}{1290}\right)$$ $$e\left(\frac{539}{645}\right)$$ $$e\left(\frac{631}{645}\right)$$
$$\chi_{6034}(19,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{35}{258}\right)$$ $$e\left(\frac{719}{1290}\right)$$ $$e\left(\frac{35}{129}\right)$$ $$e\left(\frac{308}{645}\right)$$ $$e\left(\frac{33}{430}\right)$$ $$e\left(\frac{149}{215}\right)$$ $$e\left(\frac{487}{1290}\right)$$ $$e\left(\frac{743}{1290}\right)$$ $$e\left(\frac{376}{645}\right)$$ $$e\left(\frac{74}{645}\right)$$
$$\chi_{6034}(23,\cdot)$$ 6034.bc 645 no $$1$$ $$1$$ $$e\left(\frac{79}{129}\right)$$ $$e\left(\frac{613}{645}\right)$$ $$e\left(\frac{29}{129}\right)$$ $$e\left(\frac{152}{645}\right)$$ $$e\left(\frac{131}{215}\right)$$ $$e\left(\frac{121}{215}\right)$$ $$e\left(\frac{539}{645}\right)$$ $$e\left(\frac{376}{645}\right)$$ $$e\left(\frac{529}{645}\right)$$ $$e\left(\frac{581}{645}\right)$$
$$\chi_{6034}(25,\cdot)$$ 6034.bc 645 no $$1$$ $$1$$ $$e\left(\frac{8}{129}\right)$$ $$e\left(\frac{227}{645}\right)$$ $$e\left(\frac{16}{129}\right)$$ $$e\left(\frac{373}{645}\right)$$ $$e\left(\frac{139}{215}\right)$$ $$e\left(\frac{89}{215}\right)$$ $$e\left(\frac{631}{645}\right)$$ $$e\left(\frac{74}{645}\right)$$ $$e\left(\frac{581}{645}\right)$$ $$e\left(\frac{454}{645}\right)$$
$$\chi_{6034}(27,\cdot)$$ 6034.t 86 no $$-1$$ $$1$$ $$e\left(\frac{41}{86}\right)$$ $$e\left(\frac{51}{86}\right)$$ $$e\left(\frac{41}{43}\right)$$ $$e\left(\frac{24}{43}\right)$$ $$e\left(\frac{63}{86}\right)$$ $$e\left(\frac{3}{43}\right)$$ $$e\left(\frac{5}{86}\right)$$ $$e\left(\frac{35}{86}\right)$$ $$e\left(\frac{36}{43}\right)$$ $$e\left(\frac{8}{43}\right)$$
$$\chi_{6034}(29,\cdot)$$ 6034.v 215 no $$1$$ $$1$$ $$e\left(\frac{21}{43}\right)$$ $$e\left(\frac{53}{215}\right)$$ $$e\left(\frac{42}{43}\right)$$ $$e\left(\frac{17}{215}\right)$$ $$e\left(\frac{68}{215}\right)$$ $$e\left(\frac{158}{215}\right)$$ $$e\left(\frac{189}{215}\right)$$ $$e\left(\frac{76}{215}\right)$$ $$e\left(\frac{4}{215}\right)$$ $$e\left(\frac{106}{215}\right)$$
$$\chi_{6034}(31,\cdot)$$ 6034.be 1290 no $$1$$ $$1$$ $$e\left(\frac{151}{258}\right)$$ $$e\left(\frac{979}{1290}\right)$$ $$e\left(\frac{22}{129}\right)$$ $$e\left(\frac{13}{645}\right)$$ $$e\left(\frac{89}{215}\right)$$ $$e\left(\frac{74}{215}\right)$$ $$e\left(\frac{271}{645}\right)$$ $$e\left(\frac{913}{1290}\right)$$ $$e\left(\frac{41}{645}\right)$$ $$e\left(\frac{334}{645}\right)$$
$$\chi_{6034}(33,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{89}{258}\right)$$ $$e\left(\frac{413}{1290}\right)$$ $$e\left(\frac{89}{129}\right)$$ $$e\left(\frac{551}{645}\right)$$ $$e\left(\frac{251}{430}\right)$$ $$e\left(\frac{143}{215}\right)$$ $$e\left(\frac{199}{1290}\right)$$ $$e\left(\frac{791}{1290}\right)$$ $$e\left(\frac{547}{645}\right)$$ $$e\left(\frac{413}{645}\right)$$
$$\chi_{6034}(37,\cdot)$$ 6034.bf 1290 no $$-1$$ $$1$$ $$e\left(\frac{31}{129}\right)$$ $$e\left(\frac{541}{645}\right)$$ $$e\left(\frac{62}{129}\right)$$ $$e\left(\frac{494}{645}\right)$$ $$e\left(\frac{99}{430}\right)$$ $$e\left(\frac{17}{215}\right)$$ $$e\left(\frac{601}{1290}\right)$$ $$e\left(\frac{577}{645}\right)$$ $$e\left(\frac{268}{645}\right)$$ $$e\left(\frac{437}{645}\right)$$
$$\chi_{6034}(39,\cdot)$$ 6034.bf 1290 no $$-1$$ $$1$$ $$e\left(\frac{95}{129}\right)$$ $$e\left(\frac{551}{645}\right)$$ $$e\left(\frac{61}{129}\right)$$ $$e\left(\frac{124}{645}\right)$$ $$e\left(\frac{259}{430}\right)$$ $$e\left(\frac{127}{215}\right)$$ $$e\left(\frac{1151}{1290}\right)$$ $$e\left(\frac{137}{645}\right)$$ $$e\left(\frac{143}{645}\right)$$ $$e\left(\frac{457}{645}\right)$$
$$\chi_{6034}(41,\cdot)$$ 6034.ba 430 no $$-1$$ $$1$$ $$e\left(\frac{45}{86}\right)$$ $$e\left(\frac{3}{430}\right)$$ $$e\left(\frac{2}{43}\right)$$ $$e\left(\frac{181}{215}\right)$$ $$e\left(\frac{373}{430}\right)$$ $$e\left(\frac{114}{215}\right)$$ $$e\left(\frac{319}{430}\right)$$ $$e\left(\frac{341}{430}\right)$$ $$e\left(\frac{207}{215}\right)$$ $$e\left(\frac{3}{215}\right)$$
$$\chi_{6034}(43,\cdot)$$ 6034.z 430 no $$-1$$ $$1$$ $$e\left(\frac{2}{43}\right)$$ $$e\left(\frac{3}{215}\right)$$ $$e\left(\frac{4}{43}\right)$$ $$e\left(\frac{147}{215}\right)$$ $$e\left(\frac{101}{430}\right)$$ $$e\left(\frac{13}{215}\right)$$ $$e\left(\frac{423}{430}\right)$$ $$e\left(\frac{126}{215}\right)$$ $$e\left(\frac{199}{215}\right)$$ $$e\left(\frac{6}{215}\right)$$
$$\chi_{6034}(45,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{133}{258}\right)$$ $$e\left(\frac{307}{1290}\right)$$ $$e\left(\frac{4}{129}\right)$$ $$e\left(\frac{319}{645}\right)$$ $$e\left(\frac{349}{430}\right)$$ $$e\left(\frac{162}{215}\right)$$ $$e\left(\frac{251}{1290}\right)$$ $$e\left(\frac{1069}{1290}\right)$$ $$e\left(\frac{113}{645}\right)$$ $$e\left(\frac{307}{645}\right)$$
$$\chi_{6034}(47,\cdot)$$ 6034.w 258 no $$1$$ $$1$$ $$e\left(\frac{245}{258}\right)$$ $$e\left(\frac{181}{258}\right)$$ $$e\left(\frac{116}{129}\right)$$ $$e\left(\frac{70}{129}\right)$$ $$e\left(\frac{36}{43}\right)$$ $$e\left(\frac{28}{43}\right)$$ $$e\left(\frac{70}{129}\right)$$ $$e\left(\frac{163}{258}\right)$$ $$e\left(\frac{62}{129}\right)$$ $$e\left(\frac{52}{129}\right)$$
$$\chi_{6034}(51,\cdot)$$ 6034.bf 1290 no $$-1$$ $$1$$ $$e\left(\frac{109}{129}\right)$$ $$e\left(\frac{13}{645}\right)$$ $$e\left(\frac{89}{129}\right)$$ $$e\left(\frac{422}{645}\right)$$ $$e\left(\frac{337}{430}\right)$$ $$e\left(\frac{186}{215}\right)$$ $$e\left(\frac{973}{1290}\right)$$ $$e\left(\frac{331}{645}\right)$$ $$e\left(\frac{289}{645}\right)$$ $$e\left(\frac{26}{645}\right)$$
$$\chi_{6034}(53,\cdot)$$ 6034.bc 645 no $$1$$ $$1$$ $$e\left(\frac{71}{129}\right)$$ $$e\left(\frac{128}{645}\right)$$ $$e\left(\frac{13}{129}\right)$$ $$e\left(\frac{37}{645}\right)$$ $$e\left(\frac{121}{215}\right)$$ $$e\left(\frac{161}{215}\right)$$ $$e\left(\frac{424}{645}\right)$$ $$e\left(\frac{431}{645}\right)$$ $$e\left(\frac{464}{645}\right)$$ $$e\left(\frac{256}{645}\right)$$
$$\chi_{6034}(55,\cdot)$$ 6034.t 86 no $$-1$$ $$1$$ $$e\left(\frac{33}{86}\right)$$ $$e\left(\frac{83}{86}\right)$$ $$e\left(\frac{33}{43}\right)$$ $$e\left(\frac{34}{43}\right)$$ $$e\left(\frac{57}{86}\right)$$ $$e\left(\frac{15}{43}\right)$$ $$e\left(\frac{25}{86}\right)$$ $$e\left(\frac{3}{86}\right)$$ $$e\left(\frac{8}{43}\right)$$ $$e\left(\frac{40}{43}\right)$$
$$\chi_{6034}(57,\cdot)$$ 6034.v 215 no $$1$$ $$1$$ $$e\left(\frac{27}{43}\right)$$ $$e\left(\frac{19}{215}\right)$$ $$e\left(\frac{11}{43}\right)$$ $$e\left(\frac{71}{215}\right)$$ $$e\left(\frac{69}{215}\right)$$ $$e\left(\frac{154}{215}\right)$$ $$e\left(\frac{157}{215}\right)$$ $$e\left(\frac{153}{215}\right)$$ $$e\left(\frac{42}{215}\right)$$ $$e\left(\frac{38}{215}\right)$$
$$\chi_{6034}(59,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{109}{258}\right)$$ $$e\left(\frac{529}{1290}\right)$$ $$e\left(\frac{109}{129}\right)$$ $$e\left(\frac{598}{645}\right)$$ $$e\left(\frac{233}{430}\right)$$ $$e\left(\frac{179}{215}\right)$$ $$e\left(\frac{1067}{1290}\right)$$ $$e\left(\frac{73}{1290}\right)$$ $$e\left(\frac{596}{645}\right)$$ $$e\left(\frac{529}{645}\right)$$
$$\chi_{6034}(61,\cdot)$$ 6034.bd 1290 no $$-1$$ $$1$$ $$e\left(\frac{179}{258}\right)$$ $$e\left(\frac{419}{1290}\right)$$ $$e\left(\frac{50}{129}\right)$$ $$e\left(\frac{53}{645}\right)$$ $$e\left(\frac{213}{430}\right)$$ $$e\left(\frac{4}{215}\right)$$ $$e\left(\frac{1267}{1290}\right)$$ $$e\left(\frac{1043}{1290}\right)$$ $$e\left(\frac{316}{645}\right)$$ $$e\left(\frac{419}{645}\right)$$
$$\chi_{6034}(65,\cdot)$$ 6034.bf 1290 no $$-1$$ $$1$$ $$e\left(\frac{100}{129}\right)$$ $$e\left(\frac{322}{645}\right)$$ $$e\left(\frac{71}{129}\right)$$ $$e\left(\frac{83}{645}\right)$$ $$e\left(\frac{293}{430}\right)$$ $$e\left(\frac{59}{215}\right)$$ $$e\left(\frac{37}{1290}\right)$$ $$e\left(\frac{409}{645}\right)$$ $$e\left(\frac{361}{645}\right)$$ $$e\left(\frac{644}{645}\right)$$
$$\chi_{6034}(67,\cdot)$$ 6034.bf 1290 no $$-1$$ $$1$$ $$e\left(\frac{74}{129}\right)$$ $$e\left(\frac{584}{645}\right)$$ $$e\left(\frac{19}{129}\right)$$ $$e\left(\frac{451}{645}\right)$$ $$e\left(\frac{271}{430}\right)$$ $$e\left(\frac{103}{215}\right)$$ $$e\left(\frac{1289}{1290}\right)$$ $$e\left(\frac{233}{645}\right)$$ $$e\left(\frac{182}{645}\right)$$ $$e\left(\frac{523}{645}\right)$$
$$\chi_{6034}(69,\cdot)$$ 6034.ba 430 no $$-1$$ $$1$$ $$e\left(\frac{9}{86}\right)$$ $$e\left(\frac{207}{430}\right)$$ $$e\left(\frac{9}{43}\right)$$ $$e\left(\frac{19}{215}\right)$$ $$e\left(\frac{367}{430}\right)$$ $$e\left(\frac{126}{215}\right)$$ $$e\left(\frac{81}{430}\right)$$ $$e\left(\frac{309}{430}\right)$$ $$e\left(\frac{93}{215}\right)$$ $$e\left(\frac{207}{215}\right)$$
$$\chi_{6034}(71,\cdot)$$ 6034.z 430 no $$-1$$ $$1$$ $$e\left(\frac{5}{43}\right)$$ $$e\left(\frac{72}{215}\right)$$ $$e\left(\frac{10}{43}\right)$$ $$e\left(\frac{88}{215}\right)$$ $$e\left(\frac{59}{430}\right)$$ $$e\left(\frac{97}{215}\right)$$ $$e\left(\frac{47}{430}\right)$$ $$e\left(\frac{14}{215}\right)$$ $$e\left(\frac{46}{215}\right)$$ $$e\left(\frac{144}{215}\right)$$
$$\chi_{6034}(73,\cdot)$$ 6034.be 1290 no $$1$$ $$1$$ $$e\left(\frac{61}{258}\right)$$ $$e\left(\frac{1231}{1290}\right)$$ $$e\left(\frac{61}{129}\right)$$ $$e\left(\frac{382}{645}\right)$$ $$e\left(\frac{151}{215}\right)$$ $$e\left(\frac{41}{215}\right)$$ $$e\left(\frac{124}{645}\right)$$ $$e\left(\frac{1177}{1290}\right)$$ $$e\left(\frac{14}{645}\right)$$ $$e\left(\frac{586}{645}\right)$$