# Properties

 Modulus 8024 Structure $$C_{464}\times C_{2}\times C_{2}\times C_{2}$$ Order 3712

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(8024)

pari: g = idealstar(,8024,2)

## Character group

 sage: G.order()  pari: g.no Order = 3712 sage: H.invariants()  pari: g.cyc Structure = $$C_{464}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8024}(4545,\cdot)$, $\chi_{8024}(6017,\cdot)$, $\chi_{8024}(2007,\cdot)$, $\chi_{8024}(4013,\cdot)$

## First 32 of 3712 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 19 21 23
$$\chi_{8024}(1,\cdot)$$ 8024.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8024}(3,\cdot)$$ 8024.cz 464 yes $$1$$ $$1$$ $$e\left(\frac{77}{464}\right)$$ $$e\left(\frac{457}{464}\right)$$ $$e\left(\frac{327}{464}\right)$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{459}{464}\right)$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{171}{464}\right)$$
$$\chi_{8024}(5,\cdot)$$ 8024.db 464 yes $$-1$$ $$1$$ $$e\left(\frac{457}{464}\right)$$ $$e\left(\frac{317}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{127}{464}\right)$$ $$e\left(\frac{47}{116}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{33}{116}\right)$$ $$e\left(\frac{111}{464}\right)$$
$$\chi_{8024}(7,\cdot)$$ 8024.da 464 no $$1$$ $$1$$ $$e\left(\frac{327}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{301}{464}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{33}{464}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{217}{464}\right)$$
$$\chi_{8024}(9,\cdot)$$ 8024.cs 232 no $$1$$ $$1$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{171}{232}\right)$$
$$\chi_{8024}(11,\cdot)$$ 8024.cu 464 yes $$-1$$ $$1$$ $$e\left(\frac{459}{464}\right)$$ $$e\left(\frac{127}{464}\right)$$ $$e\left(\frac{33}{464}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{389}{464}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{61}{232}\right)$$ $$e\left(\frac{117}{232}\right)$$ $$e\left(\frac{7}{116}\right)$$ $$e\left(\frac{245}{464}\right)$$
$$\chi_{8024}(13,\cdot)$$ 8024.cg 116 yes $$-1$$ $$1$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{47}{116}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{45}{116}\right)$$
$$\chi_{8024}(15,\cdot)$$ 8024.ct 232 no $$-1$$ $$1$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{61}{232}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{141}{232}\right)$$
$$\chi_{8024}(19,\cdot)$$ 8024.cm 232 yes $$-1$$ $$1$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{117}{232}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{105}{232}\right)$$
$$\chi_{8024}(21,\cdot)$$ 8024.ck 116 yes $$1$$ $$1$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{33}{116}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{7}{116}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{97}{116}\right)$$
$$\chi_{8024}(23,\cdot)$$ 8024.cx 464 no $$-1$$ $$1$$ $$e\left(\frac{171}{464}\right)$$ $$e\left(\frac{111}{464}\right)$$ $$e\left(\frac{217}{464}\right)$$ $$e\left(\frac{171}{232}\right)$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{97}{116}\right)$$ $$e\left(\frac{205}{464}\right)$$
$$\chi_{8024}(25,\cdot)$$ 8024.cs 232 no $$1$$ $$1$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{127}{232}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{39}{116}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{111}{232}\right)$$
$$\chi_{8024}(27,\cdot)$$ 8024.cz 464 yes $$1$$ $$1$$ $$e\left(\frac{231}{464}\right)$$ $$e\left(\frac{443}{464}\right)$$ $$e\left(\frac{53}{464}\right)$$ $$e\left(\frac{231}{232}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{209}{232}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{49}{464}\right)$$
$$\chi_{8024}(29,\cdot)$$ 8024.db 464 yes $$-1$$ $$1$$ $$e\left(\frac{209}{464}\right)$$ $$e\left(\frac{213}{464}\right)$$ $$e\left(\frac{291}{464}\right)$$ $$e\left(\frac{209}{232}\right)$$ $$e\left(\frac{119}{464}\right)$$ $$e\left(\frac{55}{116}\right)$$ $$e\left(\frac{211}{232}\right)$$ $$e\left(\frac{51}{232}\right)$$ $$e\left(\frac{9}{116}\right)$$ $$e\left(\frac{199}{464}\right)$$
$$\chi_{8024}(31,\cdot)$$ 8024.cx 464 no $$-1$$ $$1$$ $$e\left(\frac{141}{464}\right)$$ $$e\left(\frac{409}{464}\right)$$ $$e\left(\frac{415}{464}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{259}{464}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{43}{232}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{283}{464}\right)$$
$$\chi_{8024}(33,\cdot)$$ 8024.cc 58 no $$-1$$ $$1$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$
$$\chi_{8024}(35,\cdot)$$ 8024.bu 58 no $$-1$$ $$1$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{41}{58}\right)$$
$$\chi_{8024}(37,\cdot)$$ 8024.cw 464 yes $$1$$ $$1$$ $$e\left(\frac{453}{464}\right)$$ $$e\left(\frac{233}{464}\right)$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{221}{232}\right)$$ $$e\left(\frac{299}{464}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{85}{116}\right)$$ $$e\left(\frac{75}{464}\right)$$
$$\chi_{8024}(39,\cdot)$$ 8024.cx 464 no $$-1$$ $$1$$ $$e\left(\frac{329}{464}\right)$$ $$e\left(\frac{181}{464}\right)$$ $$e\left(\frac{195}{464}\right)$$ $$e\left(\frac{97}{232}\right)$$ $$e\left(\frac{295}{464}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{27}{232}\right)$$ $$e\left(\frac{15}{116}\right)$$ $$e\left(\frac{351}{464}\right)$$
$$\chi_{8024}(41,\cdot)$$ 8024.cy 464 no $$-1$$ $$1$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{411}{464}\right)$$ $$e\left(\frac{421}{464}\right)$$ $$e\left(\frac{119}{232}\right)$$ $$e\left(\frac{393}{464}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{149}{232}\right)$$ $$e\left(\frac{185}{232}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{433}{464}\right)$$
$$\chi_{8024}(43,\cdot)$$ 8024.cq 232 yes $$1$$ $$1$$ $$e\left(\frac{133}{232}\right)$$ $$e\left(\frac{125}{232}\right)$$ $$e\left(\frac{27}{232}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{211}{232}\right)$$
$$\chi_{8024}(45,\cdot)$$ 8024.db 464 yes $$-1$$ $$1$$ $$e\left(\frac{147}{464}\right)$$ $$e\left(\frac{303}{464}\right)$$ $$e\left(\frac{329}{464}\right)$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{117}{464}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{17}{232}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{453}{464}\right)$$
$$\chi_{8024}(47,\cdot)$$ 8024.ci 116 no $$1$$ $$1$$ $$e\left(\frac{67}{116}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{19}{116}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{23}{116}\right)$$
$$\chi_{8024}(49,\cdot)$$ 8024.cs 232 no $$1$$ $$1$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{69}{232}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{33}{232}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{97}{116}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{217}{232}\right)$$
$$\chi_{8024}(53,\cdot)$$ 8024.cn 232 yes $$1$$ $$1$$ $$e\left(\frac{79}{232}\right)$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{79}{116}\right)$$ $$e\left(\frac{25}{232}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{19}{116}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{189}{232}\right)$$
$$\chi_{8024}(55,\cdot)$$ 8024.ci 116 no $$1$$ $$1$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{89}{116}\right)$$
$$\chi_{8024}(57,\cdot)$$ 8024.cy 464 no $$-1$$ $$1$$ $$e\left(\frac{371}{464}\right)$$ $$e\left(\frac{367}{464}\right)$$ $$e\left(\frac{289}{464}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{229}{464}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{137}{232}\right)$$ $$e\left(\frac{181}{232}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{381}{464}\right)$$
$$\chi_{8024}(61,\cdot)$$ 8024.cw 464 yes $$1$$ $$1$$ $$e\left(\frac{255}{464}\right)$$ $$e\left(\frac{251}{464}\right)$$ $$e\left(\frac{173}{464}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{113}{464}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{21}{232}\right)$$ $$e\left(\frac{181}{232}\right)$$ $$e\left(\frac{107}{116}\right)$$ $$e\left(\frac{33}{464}\right)$$
$$\chi_{8024}(63,\cdot)$$ 8024.da 464 no $$1$$ $$1$$ $$e\left(\frac{17}{464}\right)$$ $$e\left(\frac{125}{464}\right)$$ $$e\left(\frac{27}{464}\right)$$ $$e\left(\frac{17}{232}\right)$$ $$e\left(\frac{23}{464}\right)$$ $$e\left(\frac{93}{116}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{43}{232}\right)$$ $$e\left(\frac{11}{116}\right)$$ $$e\left(\frac{95}{464}\right)$$
$$\chi_{8024}(65,\cdot)$$ 8024.cv 464 no $$1$$ $$1$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{41}{464}\right)$$ $$e\left(\frac{7}{464}\right)$$ $$e\left(\frac{13}{232}\right)$$ $$e\left(\frac{427}{464}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{143}{232}\right)$$ $$e\left(\frac{67}{232}\right)$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{291}{464}\right)$$
$$\chi_{8024}(67,\cdot)$$ 8024.bw 58 yes $$1$$ $$1$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{45}{58}\right)$$
$$\chi_{8024}(69,\cdot)$$ 8024.ca 58 no $$-1$$ $$1$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{47}{58}\right)$$