# Properties

 Modulus 6026 Structure $$C_{1430}\times C_{2}$$ Order 2860

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(6026)

pari: g = idealstar(,6026,2)

## Character group

 sage: G.order()  pari: g.no Order = 2860 sage: H.invariants()  pari: g.cyc Structure = $$C_{1430}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6026}(5373,\cdot)$, $\chi_{6026}(3405,\cdot)$

## First 32 of 2860 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.

orbit label order primitive -1 1 3 5 7 9 11 13 15 17 19 21
$$\chi_{6026}(1,\cdot)$$ 6026.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6026}(3,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{367}{715}\right)$$ $$e\left(\frac{146}{715}\right)$$ $$e\left(\frac{706}{715}\right)$$ $$e\left(\frac{19}{715}\right)$$ $$e\left(\frac{401}{715}\right)$$ $$e\left(\frac{108}{715}\right)$$ $$e\left(\frac{513}{715}\right)$$ $$e\left(\frac{648}{715}\right)$$ $$e\left(\frac{42}{143}\right)$$ $$e\left(\frac{358}{715}\right)$$
$$\chi_{6026}(5,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{146}{715}\right)$$ $$e\left(\frac{461}{1430}\right)$$ $$e\left(\frac{1191}{1430}\right)$$ $$e\left(\frac{292}{715}\right)$$ $$e\left(\frac{321}{1430}\right)$$ $$e\left(\frac{4}{715}\right)$$ $$e\left(\frac{753}{1430}\right)$$ $$e\left(\frac{763}{1430}\right)$$ $$e\left(\frac{19}{286}\right)$$ $$e\left(\frac{53}{1430}\right)$$
$$\chi_{6026}(7,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{706}{715}\right)$$ $$e\left(\frac{1191}{1430}\right)$$ $$e\left(\frac{431}{1430}\right)$$ $$e\left(\frac{697}{715}\right)$$ $$e\left(\frac{181}{1430}\right)$$ $$e\left(\frac{274}{715}\right)$$ $$e\left(\frac{1173}{1430}\right)$$ $$e\left(\frac{1143}{1430}\right)$$ $$e\left(\frac{229}{286}\right)$$ $$e\left(\frac{413}{1430}\right)$$
$$\chi_{6026}(9,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{19}{715}\right)$$ $$e\left(\frac{292}{715}\right)$$ $$e\left(\frac{697}{715}\right)$$ $$e\left(\frac{38}{715}\right)$$ $$e\left(\frac{87}{715}\right)$$ $$e\left(\frac{216}{715}\right)$$ $$e\left(\frac{311}{715}\right)$$ $$e\left(\frac{581}{715}\right)$$ $$e\left(\frac{84}{143}\right)$$ $$e\left(\frac{1}{715}\right)$$
$$\chi_{6026}(11,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{401}{715}\right)$$ $$e\left(\frac{321}{1430}\right)$$ $$e\left(\frac{181}{1430}\right)$$ $$e\left(\frac{87}{715}\right)$$ $$e\left(\frac{1151}{1430}\right)$$ $$e\left(\frac{344}{715}\right)$$ $$e\left(\frac{1123}{1430}\right)$$ $$e\left(\frac{553}{1430}\right)$$ $$e\left(\frac{61}{286}\right)$$ $$e\left(\frac{983}{1430}\right)$$
$$\chi_{6026}(13,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{108}{715}\right)$$ $$e\left(\frac{4}{715}\right)$$ $$e\left(\frac{274}{715}\right)$$ $$e\left(\frac{216}{715}\right)$$ $$e\left(\frac{344}{715}\right)$$ $$e\left(\frac{287}{715}\right)$$ $$e\left(\frac{112}{715}\right)$$ $$e\left(\frac{292}{715}\right)$$ $$e\left(\frac{56}{143}\right)$$ $$e\left(\frac{382}{715}\right)$$
$$\chi_{6026}(15,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{513}{715}\right)$$ $$e\left(\frac{753}{1430}\right)$$ $$e\left(\frac{1173}{1430}\right)$$ $$e\left(\frac{311}{715}\right)$$ $$e\left(\frac{1123}{1430}\right)$$ $$e\left(\frac{112}{715}\right)$$ $$e\left(\frac{349}{1430}\right)$$ $$e\left(\frac{629}{1430}\right)$$ $$e\left(\frac{103}{286}\right)$$ $$e\left(\frac{769}{1430}\right)$$
$$\chi_{6026}(17,\cdot)$$ 6026.be 1430 no $$1$$ $$1$$ $$e\left(\frac{648}{715}\right)$$ $$e\left(\frac{763}{1430}\right)$$ $$e\left(\frac{1143}{1430}\right)$$ $$e\left(\frac{581}{715}\right)$$ $$e\left(\frac{553}{1430}\right)$$ $$e\left(\frac{292}{715}\right)$$ $$e\left(\frac{629}{1430}\right)$$ $$e\left(\frac{322}{715}\right)$$ $$e\left(\frac{50}{143}\right)$$ $$e\left(\frac{1009}{1430}\right)$$
$$\chi_{6026}(19,\cdot)$$ 6026.ba 286 no $$1$$ $$1$$ $$e\left(\frac{42}{143}\right)$$ $$e\left(\frac{19}{286}\right)$$ $$e\left(\frac{229}{286}\right)$$ $$e\left(\frac{84}{143}\right)$$ $$e\left(\frac{61}{286}\right)$$ $$e\left(\frac{56}{143}\right)$$ $$e\left(\frac{103}{286}\right)$$ $$e\left(\frac{50}{143}\right)$$ $$e\left(\frac{93}{143}\right)$$ $$e\left(\frac{27}{286}\right)$$
$$\chi_{6026}(21,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{358}{715}\right)$$ $$e\left(\frac{53}{1430}\right)$$ $$e\left(\frac{413}{1430}\right)$$ $$e\left(\frac{1}{715}\right)$$ $$e\left(\frac{983}{1430}\right)$$ $$e\left(\frac{382}{715}\right)$$ $$e\left(\frac{769}{1430}\right)$$ $$e\left(\frac{1009}{1430}\right)$$ $$e\left(\frac{27}{286}\right)$$ $$e\left(\frac{1129}{1430}\right)$$
$$\chi_{6026}(25,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{292}{715}\right)$$ $$e\left(\frac{461}{715}\right)$$ $$e\left(\frac{476}{715}\right)$$ $$e\left(\frac{584}{715}\right)$$ $$e\left(\frac{321}{715}\right)$$ $$e\left(\frac{8}{715}\right)$$ $$e\left(\frac{38}{715}\right)$$ $$e\left(\frac{48}{715}\right)$$ $$e\left(\frac{19}{143}\right)$$ $$e\left(\frac{53}{715}\right)$$
$$\chi_{6026}(27,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{386}{715}\right)$$ $$e\left(\frac{438}{715}\right)$$ $$e\left(\frac{688}{715}\right)$$ $$e\left(\frac{57}{715}\right)$$ $$e\left(\frac{488}{715}\right)$$ $$e\left(\frac{324}{715}\right)$$ $$e\left(\frac{109}{715}\right)$$ $$e\left(\frac{514}{715}\right)$$ $$e\left(\frac{126}{143}\right)$$ $$e\left(\frac{359}{715}\right)$$
$$\chi_{6026}(29,\cdot)$$ 6026.bd 1430 no $$-1$$ $$1$$ $$e\left(\frac{241}{715}\right)$$ $$e\left(\frac{618}{715}\right)$$ $$e\left(\frac{148}{715}\right)$$ $$e\left(\frac{482}{715}\right)$$ $$e\left(\frac{238}{715}\right)$$ $$e\left(\frac{369}{715}\right)$$ $$e\left(\frac{144}{715}\right)$$ $$e\left(\frac{853}{1430}\right)$$ $$e\left(\frac{1}{286}\right)$$ $$e\left(\frac{389}{715}\right)$$
$$\chi_{6026}(31,\cdot)$$ 6026.bd 1430 no $$-1$$ $$1$$ $$e\left(\frac{304}{715}\right)$$ $$e\left(\frac{382}{715}\right)$$ $$e\left(\frac{427}{715}\right)$$ $$e\left(\frac{608}{715}\right)$$ $$e\left(\frac{677}{715}\right)$$ $$e\left(\frac{596}{715}\right)$$ $$e\left(\frac{686}{715}\right)$$ $$e\left(\frac{717}{1430}\right)$$ $$e\left(\frac{257}{286}\right)$$ $$e\left(\frac{16}{715}\right)$$
$$\chi_{6026}(33,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{53}{715}\right)$$ $$e\left(\frac{613}{1430}\right)$$ $$e\left(\frac{163}{1430}\right)$$ $$e\left(\frac{106}{715}\right)$$ $$e\left(\frac{523}{1430}\right)$$ $$e\left(\frac{452}{715}\right)$$ $$e\left(\frac{719}{1430}\right)$$ $$e\left(\frac{419}{1430}\right)$$ $$e\left(\frac{145}{286}\right)$$ $$e\left(\frac{269}{1430}\right)$$
$$\chi_{6026}(35,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{137}{715}\right)$$ $$e\left(\frac{111}{715}\right)$$ $$e\left(\frac{96}{715}\right)$$ $$e\left(\frac{274}{715}\right)$$ $$e\left(\frac{251}{715}\right)$$ $$e\left(\frac{278}{715}\right)$$ $$e\left(\frac{248}{715}\right)$$ $$e\left(\frac{238}{715}\right)$$ $$e\left(\frac{124}{143}\right)$$ $$e\left(\frac{233}{715}\right)$$
$$\chi_{6026}(37,\cdot)$$ 6026.be 1430 no $$1$$ $$1$$ $$e\left(\frac{701}{715}\right)$$ $$e\left(\frac{661}{1430}\right)$$ $$e\left(\frac{591}{1430}\right)$$ $$e\left(\frac{687}{715}\right)$$ $$e\left(\frac{361}{1430}\right)$$ $$e\left(\frac{29}{715}\right)$$ $$e\left(\frac{633}{1430}\right)$$ $$e\left(\frac{174}{715}\right)$$ $$e\left(\frac{51}{143}\right)$$ $$e\left(\frac{563}{1430}\right)$$
$$\chi_{6026}(39,\cdot)$$ 6026.y 143 no $$1$$ $$1$$ $$e\left(\frac{95}{143}\right)$$ $$e\left(\frac{30}{143}\right)$$ $$e\left(\frac{53}{143}\right)$$ $$e\left(\frac{47}{143}\right)$$ $$e\left(\frac{6}{143}\right)$$ $$e\left(\frac{79}{143}\right)$$ $$e\left(\frac{125}{143}\right)$$ $$e\left(\frac{45}{143}\right)$$ $$e\left(\frac{98}{143}\right)$$ $$e\left(\frac{5}{143}\right)$$
$$\chi_{6026}(41,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{366}{715}\right)$$ $$e\left(\frac{93}{715}\right)$$ $$e\left(\frac{293}{715}\right)$$ $$e\left(\frac{17}{715}\right)$$ $$e\left(\frac{133}{715}\right)$$ $$e\left(\frac{59}{715}\right)$$ $$e\left(\frac{459}{715}\right)$$ $$e\left(\frac{354}{715}\right)$$ $$e\left(\frac{15}{143}\right)$$ $$e\left(\frac{659}{715}\right)$$
$$\chi_{6026}(43,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{224}{715}\right)$$ $$e\left(\frac{149}{1430}\right)$$ $$e\left(\frac{1269}{1430}\right)$$ $$e\left(\frac{448}{715}\right)$$ $$e\left(\frac{659}{1430}\right)$$ $$e\left(\frac{251}{715}\right)$$ $$e\left(\frac{597}{1430}\right)$$ $$e\left(\frac{867}{1430}\right)$$ $$e\left(\frac{227}{286}\right)$$ $$e\left(\frac{287}{1430}\right)$$
$$\chi_{6026}(45,\cdot)$$ 6026.p 26 no $$-1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$
$$\chi_{6026}(47,\cdot)$$ 6026.n 26 no $$-1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{6026}(49,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{697}{715}\right)$$ $$e\left(\frac{476}{715}\right)$$ $$e\left(\frac{431}{715}\right)$$ $$e\left(\frac{679}{715}\right)$$ $$e\left(\frac{181}{715}\right)$$ $$e\left(\frac{548}{715}\right)$$ $$e\left(\frac{458}{715}\right)$$ $$e\left(\frac{428}{715}\right)$$ $$e\left(\frac{86}{143}\right)$$ $$e\left(\frac{413}{715}\right)$$
$$\chi_{6026}(51,\cdot)$$ 6026.ba 286 no $$1$$ $$1$$ $$e\left(\frac{60}{143}\right)$$ $$e\left(\frac{211}{286}\right)$$ $$e\left(\frac{225}{286}\right)$$ $$e\left(\frac{120}{143}\right)$$ $$e\left(\frac{271}{286}\right)$$ $$e\left(\frac{80}{143}\right)$$ $$e\left(\frac{45}{286}\right)$$ $$e\left(\frac{51}{143}\right)$$ $$e\left(\frac{92}{143}\right)$$ $$e\left(\frac{59}{286}\right)$$
$$\chi_{6026}(53,\cdot)$$ 6026.s 110 no $$-1$$ $$1$$ $$e\left(\frac{12}{55}\right)$$ $$e\left(\frac{7}{110}\right)$$ $$e\left(\frac{67}{110}\right)$$ $$e\left(\frac{24}{55}\right)$$ $$e\left(\frac{107}{110}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{71}{110}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{91}{110}\right)$$
$$\chi_{6026}(55,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{547}{715}\right)$$ $$e\left(\frac{391}{715}\right)$$ $$e\left(\frac{686}{715}\right)$$ $$e\left(\frac{379}{715}\right)$$ $$e\left(\frac{21}{715}\right)$$ $$e\left(\frac{348}{715}\right)$$ $$e\left(\frac{223}{715}\right)$$ $$e\left(\frac{658}{715}\right)$$ $$e\left(\frac{40}{143}\right)$$ $$e\left(\frac{518}{715}\right)$$
$$\chi_{6026}(57,\cdot)$$ 6026.be 1430 no $$1$$ $$1$$ $$e\left(\frac{577}{715}\right)$$ $$e\left(\frac{387}{1430}\right)$$ $$e\left(\frac{1127}{1430}\right)$$ $$e\left(\frac{439}{715}\right)$$ $$e\left(\frac{1107}{1430}\right)$$ $$e\left(\frac{388}{715}\right)$$ $$e\left(\frac{111}{1430}\right)$$ $$e\left(\frac{183}{715}\right)$$ $$e\left(\frac{135}{143}\right)$$ $$e\left(\frac{851}{1430}\right)$$
$$\chi_{6026}(59,\cdot)$$ 6026.bc 715 no $$1$$ $$1$$ $$e\left(\frac{427}{715}\right)$$ $$e\left(\frac{466}{715}\right)$$ $$e\left(\frac{461}{715}\right)$$ $$e\left(\frac{139}{715}\right)$$ $$e\left(\frac{36}{715}\right)$$ $$e\left(\frac{188}{715}\right)$$ $$e\left(\frac{178}{715}\right)$$ $$e\left(\frac{413}{715}\right)$$ $$e\left(\frac{89}{143}\right)$$ $$e\left(\frac{173}{715}\right)$$
$$\chi_{6026}(61,\cdot)$$ 6026.s 110 no $$-1$$ $$1$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{7}{55}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{34}{55}\right)$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{93}{110}\right)$$
$$\chi_{6026}(63,\cdot)$$ 6026.z 286 no $$-1$$ $$1$$ $$e\left(\frac{2}{143}\right)$$ $$e\left(\frac{69}{286}\right)$$ $$e\left(\frac{79}{286}\right)$$ $$e\left(\frac{4}{143}\right)$$ $$e\left(\frac{71}{286}\right)$$ $$e\left(\frac{98}{143}\right)$$ $$e\left(\frac{73}{286}\right)$$ $$e\left(\frac{175}{286}\right)$$ $$e\left(\frac{111}{286}\right)$$ $$e\left(\frac{83}{286}\right)$$
$$\chi_{6026}(65,\cdot)$$ 6026.bf 1430 no $$-1$$ $$1$$ $$e\left(\frac{254}{715}\right)$$ $$e\left(\frac{469}{1430}\right)$$ $$e\left(\frac{309}{1430}\right)$$ $$e\left(\frac{508}{715}\right)$$ $$e\left(\frac{1009}{1430}\right)$$ $$e\left(\frac{291}{715}\right)$$ $$e\left(\frac{977}{1430}\right)$$ $$e\left(\frac{1347}{1430}\right)$$ $$e\left(\frac{131}{286}\right)$$ $$e\left(\frac{817}{1430}\right)$$