# Properties

 Modulus 8007 Structure $$C_{624}\times C_{4}\times C_{2}$$ Order 4992

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(8007)

pari: g = idealstar(,8007,2)

## Character group

 sage: G.order()  pari: g.no Order = 4992 sage: H.invariants()  pari: g.cyc Structure = $$C_{624}\times C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8007}(7384,\cdot)$, $\chi_{8007}(7564,\cdot)$, $\chi_{8007}(5339,\cdot)$

## First 32 of 4992 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 2 4 5 7 8 10 11 13 14 16
$$\chi_{8007}(1,\cdot)$$ 8007.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8007}(2,\cdot)$$ 8007.ed 104 yes $$1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{81}{104}\right)$$ $$e\left(\frac{51}{104}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{101}{104}\right)$$ $$e\left(\frac{97}{104}\right)$$ $$1$$ $$e\left(\frac{71}{104}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{8007}(4,\cdot)$$ 8007.dd 52 no $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$1$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{8007}(5,\cdot)$$ 8007.fj 624 yes $$-1$$ $$1$$ $$e\left(\frac{81}{104}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{43}{624}\right)$$ $$e\left(\frac{79}{208}\right)$$ $$e\left(\frac{35}{104}\right)$$ $$e\left(\frac{529}{624}\right)$$ $$e\left(\frac{541}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{33}{208}\right)$$ $$e\left(\frac{3}{26}\right)$$
$$\chi_{8007}(7,\cdot)$$ 8007.et 208 no $$1$$ $$1$$ $$e\left(\frac{51}{104}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{79}{208}\right)$$ $$e\left(\frac{17}{208}\right)$$ $$e\left(\frac{49}{104}\right)$$ $$e\left(\frac{181}{208}\right)$$ $$e\left(\frac{41}{208}\right)$$ $$i$$ $$e\left(\frac{119}{208}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{8007}(8,\cdot)$$ 8007.ed 104 yes $$1$$ $$1$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{35}{104}\right)$$ $$e\left(\frac{49}{104}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{95}{104}\right)$$ $$e\left(\frac{83}{104}\right)$$ $$1$$ $$e\left(\frac{5}{104}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{8007}(10,\cdot)$$ 8007.fl 624 no $$-1$$ $$1$$ $$e\left(\frac{101}{104}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{529}{624}\right)$$ $$e\left(\frac{181}{208}\right)$$ $$e\left(\frac{95}{104}\right)$$ $$e\left(\frac{511}{624}\right)$$ $$e\left(\frac{499}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{175}{208}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{8007}(11,\cdot)$$ 8007.fh 624 yes $$1$$ $$1$$ $$e\left(\frac{97}{104}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{541}{624}\right)$$ $$e\left(\frac{41}{208}\right)$$ $$e\left(\frac{83}{104}\right)$$ $$e\left(\frac{499}{624}\right)$$ $$e\left(\frac{367}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{27}{208}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{8007}(13,\cdot)$$ 8007.bu 12 no $$1$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$1$$
$$\chi_{8007}(14,\cdot)$$ 8007.ew 208 yes $$1$$ $$1$$ $$e\left(\frac{71}{104}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{33}{208}\right)$$ $$e\left(\frac{119}{208}\right)$$ $$e\left(\frac{5}{104}\right)$$ $$e\left(\frac{175}{208}\right)$$ $$e\left(\frac{27}{208}\right)$$ $$i$$ $$e\left(\frac{53}{208}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{8007}(16,\cdot)$$ 8007.cp 26 no $$1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$1$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{8007}(19,\cdot)$$ 8007.fc 312 no $$1$$ $$1$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{53}{312}\right)$$ $$e\left(\frac{49}{104}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{155}{312}\right)$$ $$e\left(\frac{119}{312}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{83}{104}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{8007}(20,\cdot)$$ 8007.fg 624 yes $$-1$$ $$1$$ $$e\left(\frac{17}{104}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{391}{624}\right)$$ $$e\left(\frac{75}{208}\right)$$ $$e\left(\frac{51}{104}\right)$$ $$e\left(\frac{493}{624}\right)$$ $$e\left(\frac{457}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{109}{208}\right)$$ $$e\left(\frac{17}{26}\right)$$
$$\chi_{8007}(22,\cdot)$$ 8007.cy 48 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$
$$\chi_{8007}(23,\cdot)$$ 8007.eu 208 yes $$-1$$ $$1$$ $$e\left(\frac{67}{104}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{11}{208}\right)$$ $$e\left(\frac{109}{208}\right)$$ $$e\left(\frac{97}{104}\right)$$ $$e\left(\frac{145}{208}\right)$$ $$e\left(\frac{61}{208}\right)$$ $$i$$ $$e\left(\frac{35}{208}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{8007}(25,\cdot)$$ 8007.fd 312 no $$1$$ $$1$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{43}{312}\right)$$ $$e\left(\frac{79}{104}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{217}{312}\right)$$ $$e\left(\frac{229}{312}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{33}{104}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{8007}(26,\cdot)$$ 8007.fe 312 yes $$1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{61}{312}\right)$$ $$e\left(\frac{77}{104}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{121}{312}\right)$$ $$e\left(\frac{109}{312}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{97}{104}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{8007}(28,\cdot)$$ 8007.ce 16 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$
$$\chi_{8007}(29,\cdot)$$ 8007.eu 208 yes $$-1$$ $$1$$ $$e\left(\frac{49}{104}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{81}{208}\right)$$ $$e\left(\frac{103}{208}\right)$$ $$e\left(\frac{43}{104}\right)$$ $$e\left(\frac{179}{208}\right)$$ $$e\left(\frac{71}{208}\right)$$ $$-i$$ $$e\left(\frac{201}{208}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{8007}(31,\cdot)$$ 8007.fl 624 no $$-1$$ $$1$$ $$e\left(\frac{95}{104}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{131}{624}\right)$$ $$e\left(\frac{127}{208}\right)$$ $$e\left(\frac{77}{104}\right)$$ $$e\left(\frac{77}{624}\right)$$ $$e\left(\frac{41}{624}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{109}{208}\right)$$ $$e\left(\frac{17}{26}\right)$$
$$\chi_{8007}(32,\cdot)$$ 8007.ed 104 yes $$1$$ $$1$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{93}{104}\right)$$ $$e\left(\frac{47}{104}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{89}{104}\right)$$ $$e\left(\frac{69}{104}\right)$$ $$1$$ $$e\left(\frac{43}{104}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{8007}(35,\cdot)$$ 8007.ds 78 no $$-1$$ $$1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{8007}(37,\cdot)$$ 8007.fm 624 no $$-1$$ $$1$$ $$e\left(\frac{75}{104}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{35}{624}\right)$$ $$e\left(\frac{207}{208}\right)$$ $$e\left(\frac{17}{104}\right)$$ $$e\left(\frac{485}{624}\right)$$ $$e\left(\frac{161}{624}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{149}{208}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{8007}(38,\cdot)$$ 8007.en 156 yes $$1$$ $$1$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{8007}(40,\cdot)$$ 8007.fm 624 no $$-1$$ $$1$$ $$e\left(\frac{37}{104}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{253}{624}\right)$$ $$e\left(\frac{177}{208}\right)$$ $$e\left(\frac{7}{104}\right)$$ $$e\left(\frac{475}{624}\right)$$ $$e\left(\frac{415}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{43}{208}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{8007}(41,\cdot)$$ 8007.ex 208 yes $$-1$$ $$1$$ $$e\left(\frac{11}{104}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{15}{208}\right)$$ $$e\left(\frac{73}{208}\right)$$ $$e\left(\frac{33}{104}\right)$$ $$e\left(\frac{37}{208}\right)$$ $$e\left(\frac{17}{208}\right)$$ $$i$$ $$e\left(\frac{95}{208}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{8007}(43,\cdot)$$ 8007.ff 312 no $$-1$$ $$1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{109}{312}\right)$$ $$e\left(\frac{89}{104}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{73}{312}\right)$$ $$e\left(\frac{49}{312}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{77}{104}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{8007}(44,\cdot)$$ 8007.fi 624 yes $$1$$ $$1$$ $$e\left(\frac{33}{104}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{265}{624}\right)$$ $$e\left(\frac{37}{208}\right)$$ $$e\left(\frac{99}{104}\right)$$ $$e\left(\frac{463}{624}\right)$$ $$e\left(\frac{283}{624}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{103}{208}\right)$$ $$e\left(\frac{7}{26}\right)$$
$$\chi_{8007}(46,\cdot)$$ 8007.er 208 no $$-1$$ $$1$$ $$e\left(\frac{87}{104}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{173}{208}\right)$$ $$e\left(\frac{3}{208}\right)$$ $$e\left(\frac{53}{104}\right)$$ $$e\left(\frac{139}{208}\right)$$ $$e\left(\frac{47}{208}\right)$$ $$i$$ $$e\left(\frac{177}{208}\right)$$ $$e\left(\frac{9}{26}\right)$$
$$\chi_{8007}(47,\cdot)$$ 8007.ee 156 yes $$-1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{77}{156}\right)$$ $$e\left(\frac{119}{156}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{8007}(49,\cdot)$$ 8007.dy 104 no $$1$$ $$1$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{79}{104}\right)$$ $$e\left(\frac{17}{104}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{77}{104}\right)$$ $$e\left(\frac{41}{104}\right)$$ $$-1$$ $$e\left(\frac{15}{104}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{8007}(50,\cdot)$$ 8007.bo 12 yes $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$