# Properties

 Modulus 4012 Structure $$C_{464}\times C_{2}\times C_{2}$$ Order 1856

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4012)

pari: g = idealstar(,4012,2)

## Character group

 sage: G.order()  pari: g.no Order = 1856 sage: H.invariants()  pari: g.cyc Structure = $$C_{464}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4012}(533,\cdot)$, $\chi_{4012}(2005,\cdot)$, $\chi_{4012}(2007,\cdot)$

## First 32 of 1856 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
$$\chi_{4012}(1,\cdot)$$ 4012.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4012}(3,\cdot)$$ 4012.bn 464 yes $$1$$ $$1$$ $$e\left(\frac{309}{464}\right)$$ $$e\left(\frac{225}{464}\right)$$ $$e\left(\frac{327}{464}\right)$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{227}{464}\right)$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{31}{232}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{171}{464}\right)$$
$$\chi_{4012}(5,\cdot)$$ 4012.bm 464 no $$-1$$ $$1$$ $$e\left(\frac{225}{464}\right)$$ $$e\left(\frac{85}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{359}{464}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{91}{116}\right)$$ $$e\left(\frac{111}{464}\right)$$
$$\chi_{4012}(7,\cdot)$$ 4012.bn 464 yes $$1$$ $$1$$ $$e\left(\frac{327}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{301}{464}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{33}{464}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{217}{464}\right)$$
$$\chi_{4012}(9,\cdot)$$ 4012.bi 232 no $$1$$ $$1$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{171}{232}\right)$$
$$\chi_{4012}(11,\cdot)$$ 4012.bl 464 yes $$-1$$ $$1$$ $$e\left(\frac{227}{464}\right)$$ $$e\left(\frac{359}{464}\right)$$ $$e\left(\frac{33}{464}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{157}{464}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{61}{232}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{65}{116}\right)$$ $$e\left(\frac{245}{464}\right)$$
$$\chi_{4012}(13,\cdot)$$ 4012.bf 116 no $$-1$$ $$1$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{45}{116}\right)$$
$$\chi_{4012}(15,\cdot)$$ 4012.bj 232 yes $$-1$$ $$1$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{61}{232}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{141}{232}\right)$$
$$\chi_{4012}(19,\cdot)$$ 4012.bj 232 yes $$-1$$ $$1$$ $$e\left(\frac{31}{232}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{105}{232}\right)$$
$$\chi_{4012}(21,\cdot)$$ 4012.bd 116 no $$1$$ $$1$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{91}{116}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{65}{116}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{97}{116}\right)$$
$$\chi_{4012}(23,\cdot)$$ 4012.bl 464 yes $$-1$$ $$1$$ $$e\left(\frac{171}{464}\right)$$ $$e\left(\frac{111}{464}\right)$$ $$e\left(\frac{217}{464}\right)$$ $$e\left(\frac{171}{232}\right)$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{97}{116}\right)$$ $$e\left(\frac{205}{464}\right)$$
$$\chi_{4012}(25,\cdot)$$ 4012.bi 232 no $$1$$ $$1$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{127}{232}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{39}{116}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{111}{232}\right)$$
$$\chi_{4012}(27,\cdot)$$ 4012.bn 464 yes $$1$$ $$1$$ $$e\left(\frac{463}{464}\right)$$ $$e\left(\frac{211}{464}\right)$$ $$e\left(\frac{53}{464}\right)$$ $$e\left(\frac{231}{232}\right)$$ $$e\left(\frac{217}{464}\right)$$ $$e\left(\frac{15}{116}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{93}{232}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{49}{464}\right)$$
$$\chi_{4012}(29,\cdot)$$ 4012.bm 464 no $$-1$$ $$1$$ $$e\left(\frac{441}{464}\right)$$ $$e\left(\frac{445}{464}\right)$$ $$e\left(\frac{291}{464}\right)$$ $$e\left(\frac{209}{232}\right)$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{211}{232}\right)$$ $$e\left(\frac{167}{232}\right)$$ $$e\left(\frac{67}{116}\right)$$ $$e\left(\frac{199}{464}\right)$$
$$\chi_{4012}(31,\cdot)$$ 4012.bl 464 yes $$-1$$ $$1$$ $$e\left(\frac{141}{464}\right)$$ $$e\left(\frac{409}{464}\right)$$ $$e\left(\frac{415}{464}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{259}{464}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{43}{232}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{283}{464}\right)$$
$$\chi_{4012}(33,\cdot)$$ 4012.ba 58 no $$-1$$ $$1$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$
$$\chi_{4012}(35,\cdot)$$ 4012.z 58 no $$-1$$ $$1$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{41}{58}\right)$$
$$\chi_{4012}(37,\cdot)$$ 4012.bk 464 no $$1$$ $$1$$ $$e\left(\frac{221}{464}\right)$$ $$e\left(\frac{1}{464}\right)$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{221}{232}\right)$$ $$e\left(\frac{67}{464}\right)$$ $$e\left(\frac{107}{116}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{211}{232}\right)$$ $$e\left(\frac{27}{116}\right)$$ $$e\left(\frac{75}{464}\right)$$
$$\chi_{4012}(39,\cdot)$$ 4012.bl 464 yes $$-1$$ $$1$$ $$e\left(\frac{329}{464}\right)$$ $$e\left(\frac{181}{464}\right)$$ $$e\left(\frac{195}{464}\right)$$ $$e\left(\frac{97}{232}\right)$$ $$e\left(\frac{295}{464}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{27}{232}\right)$$ $$e\left(\frac{15}{116}\right)$$ $$e\left(\frac{351}{464}\right)$$
$$\chi_{4012}(41,\cdot)$$ 4012.bm 464 no $$-1$$ $$1$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{411}{464}\right)$$ $$e\left(\frac{421}{464}\right)$$ $$e\left(\frac{119}{232}\right)$$ $$e\left(\frac{393}{464}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{149}{232}\right)$$ $$e\left(\frac{185}{232}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{433}{464}\right)$$
$$\chi_{4012}(43,\cdot)$$ 4012.bh 232 yes $$1$$ $$1$$ $$e\left(\frac{17}{232}\right)$$ $$e\left(\frac{9}{232}\right)$$ $$e\left(\frac{27}{232}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{211}{232}\right)$$
$$\chi_{4012}(45,\cdot)$$ 4012.bm 464 no $$-1$$ $$1$$ $$e\left(\frac{379}{464}\right)$$ $$e\left(\frac{71}{464}\right)$$ $$e\left(\frac{329}{464}\right)$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{349}{464}\right)$$ $$e\left(\frac{115}{116}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{133}{232}\right)$$ $$e\left(\frac{61}{116}\right)$$ $$e\left(\frac{453}{464}\right)$$
$$\chi_{4012}(47,\cdot)$$ 4012.be 116 yes $$1$$ $$1$$ $$e\left(\frac{67}{116}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{19}{116}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{23}{116}\right)$$
$$\chi_{4012}(49,\cdot)$$ 4012.bi 232 no $$1$$ $$1$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{69}{232}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{33}{232}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{97}{116}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{217}{232}\right)$$
$$\chi_{4012}(53,\cdot)$$ 4012.bi 232 no $$1$$ $$1$$ $$e\left(\frac{195}{232}\right)$$ $$e\left(\frac{151}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{79}{116}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{189}{232}\right)$$
$$\chi_{4012}(55,\cdot)$$ 4012.be 116 yes $$1$$ $$1$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{89}{116}\right)$$
$$\chi_{4012}(57,\cdot)$$ 4012.bm 464 no $$-1$$ $$1$$ $$e\left(\frac{371}{464}\right)$$ $$e\left(\frac{367}{464}\right)$$ $$e\left(\frac{289}{464}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{229}{464}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{137}{232}\right)$$ $$e\left(\frac{181}{232}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{381}{464}\right)$$
$$\chi_{4012}(61,\cdot)$$ 4012.bk 464 no $$1$$ $$1$$ $$e\left(\frac{23}{464}\right)$$ $$e\left(\frac{19}{464}\right)$$ $$e\left(\frac{173}{464}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{345}{464}\right)$$ $$e\left(\frac{61}{116}\right)$$ $$e\left(\frac{21}{232}\right)$$ $$e\left(\frac{65}{232}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{33}{464}\right)$$
$$\chi_{4012}(63,\cdot)$$ 4012.bn 464 yes $$1$$ $$1$$ $$e\left(\frac{17}{464}\right)$$ $$e\left(\frac{125}{464}\right)$$ $$e\left(\frac{27}{464}\right)$$ $$e\left(\frac{17}{232}\right)$$ $$e\left(\frac{23}{464}\right)$$ $$e\left(\frac{93}{116}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{43}{232}\right)$$ $$e\left(\frac{11}{116}\right)$$ $$e\left(\frac{95}{464}\right)$$
$$\chi_{4012}(65,\cdot)$$ 4012.bk 464 no $$1$$ $$1$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{41}{464}\right)$$ $$e\left(\frac{7}{464}\right)$$ $$e\left(\frac{13}{232}\right)$$ $$e\left(\frac{427}{464}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{143}{232}\right)$$ $$e\left(\frac{67}{232}\right)$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{291}{464}\right)$$
$$\chi_{4012}(67,\cdot)$$ 4012.x 58 yes $$1$$ $$1$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{19}{58}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{27}{58}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{45}{58}\right)$$
$$\chi_{4012}(69,\cdot)$$ 4012.v 58 no $$-1$$ $$1$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$