# Properties

 Modulus $799$ Structure $$C_{2}\times C_{368}$$ Order $736$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(799)

pari: g = idealstar(,799,2)

## Character group

 sage: G.order()  pari: g.no Order = 736 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{368}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{799}(377,\cdot)$, $\chi_{799}(52,\cdot)$

## First 32 of 736 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{799}(1,\cdot)$$ 799.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{799}(2,\cdot)$$ 799.r 184 yes $$1$$ $$1$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{129}{184}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{141}{184}\right)$$ $$e\left(\frac{183}{184}\right)$$ $$e\left(\frac{27}{184}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{11}{184}\right)$$ $$e\left(\frac{159}{184}\right)$$
$$\chi_{799}(3,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{129}{184}\right)$$ $$e\left(\frac{279}{368}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{275}{368}\right)$$ $$e\left(\frac{169}{368}\right)$$ $$e\left(\frac{221}{368}\right)$$ $$e\left(\frac{19}{184}\right)$$ $$e\left(\frac{95}{184}\right)$$ $$e\left(\frac{165}{368}\right)$$ $$e\left(\frac{177}{368}\right)$$
$$\chi_{799}(4,\cdot)$$ 799.o 92 yes $$1$$ $$1$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{11}{92}\right)$$ $$e\left(\frac{67}{92}\right)$$
$$\chi_{799}(5,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{141}{184}\right)$$ $$e\left(\frac{275}{368}\right)$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{215}{368}\right)$$ $$e\left(\frac{189}{368}\right)$$ $$e\left(\frac{49}{368}\right)$$ $$e\left(\frac{55}{184}\right)$$ $$e\left(\frac{91}{184}\right)$$ $$e\left(\frac{129}{368}\right)$$ $$e\left(\frac{125}{368}\right)$$
$$\chi_{799}(6,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{183}{184}\right)$$ $$e\left(\frac{169}{368}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{189}{368}\right)$$ $$e\left(\frac{167}{368}\right)$$ $$e\left(\frac{275}{368}\right)$$ $$e\left(\frac{181}{184}\right)$$ $$e\left(\frac{169}{184}\right)$$ $$e\left(\frac{187}{368}\right)$$ $$e\left(\frac{127}{368}\right)$$
$$\chi_{799}(7,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{27}{184}\right)$$ $$e\left(\frac{221}{368}\right)$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{49}{368}\right)$$ $$e\left(\frac{275}{368}\right)$$ $$e\left(\frac{303}{368}\right)$$ $$e\left(\frac{81}{184}\right)$$ $$e\left(\frac{37}{184}\right)$$ $$e\left(\frac{103}{368}\right)$$ $$e\left(\frac{251}{368}\right)$$
$$\chi_{799}(8,\cdot)$$ 799.r 184 yes $$1$$ $$1$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{19}{184}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{55}{184}\right)$$ $$e\left(\frac{181}{184}\right)$$ $$e\left(\frac{81}{184}\right)$$ $$e\left(\frac{59}{92}\right)$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{33}{184}\right)$$ $$e\left(\frac{109}{184}\right)$$
$$\chi_{799}(9,\cdot)$$ 799.r 184 yes $$1$$ $$1$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{95}{184}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{91}{184}\right)$$ $$e\left(\frac{169}{184}\right)$$ $$e\left(\frac{37}{184}\right)$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{165}{184}\right)$$ $$e\left(\frac{177}{184}\right)$$
$$\chi_{799}(10,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{11}{184}\right)$$ $$e\left(\frac{165}{368}\right)$$ $$e\left(\frac{11}{92}\right)$$ $$e\left(\frac{129}{368}\right)$$ $$e\left(\frac{187}{368}\right)$$ $$e\left(\frac{103}{368}\right)$$ $$e\left(\frac{33}{184}\right)$$ $$e\left(\frac{165}{184}\right)$$ $$e\left(\frac{151}{368}\right)$$ $$e\left(\frac{75}{368}\right)$$
$$\chi_{799}(11,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{159}{184}\right)$$ $$e\left(\frac{177}{368}\right)$$ $$e\left(\frac{67}{92}\right)$$ $$e\left(\frac{125}{368}\right)$$ $$e\left(\frac{127}{368}\right)$$ $$e\left(\frac{251}{368}\right)$$ $$e\left(\frac{109}{184}\right)$$ $$e\left(\frac{177}{184}\right)$$ $$e\left(\frac{75}{368}\right)$$ $$e\left(\frac{47}{368}\right)$$
$$\chi_{799}(12,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{53}{184}\right)$$ $$e\left(\frac{59}{368}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{103}{368}\right)$$ $$e\left(\frac{165}{368}\right)$$ $$e\left(\frac{329}{368}\right)$$ $$e\left(\frac{159}{184}\right)$$ $$e\left(\frac{59}{184}\right)$$ $$e\left(\frac{209}{368}\right)$$ $$e\left(\frac{77}{368}\right)$$
$$\chi_{799}(13,\cdot)$$ 799.p 92 yes $$-1$$ $$1$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{45}{92}\right)$$ $$e\left(\frac{77}{92}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{39}{92}\right)$$
$$\chi_{799}(14,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{81}{184}\right)$$ $$e\left(\frac{111}{368}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{331}{368}\right)$$ $$e\left(\frac{273}{368}\right)$$ $$e\left(\frac{357}{368}\right)$$ $$e\left(\frac{59}{184}\right)$$ $$e\left(\frac{111}{184}\right)$$ $$e\left(\frac{125}{368}\right)$$ $$e\left(\frac{201}{368}\right)$$
$$\chi_{799}(15,\cdot)$$ 799.q 184 yes $$-1$$ $$1$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{93}{184}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{61}{184}\right)$$ $$e\left(\frac{179}{184}\right)$$ $$e\left(\frac{135}{184}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{147}{184}\right)$$ $$e\left(\frac{151}{184}\right)$$
$$\chi_{799}(16,\cdot)$$ 799.n 46 yes $$1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{21}{46}\right)$$
$$\chi_{799}(18,\cdot)$$ 799.k 23 no $$1$$ $$1$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$
$$\chi_{799}(19,\cdot)$$ 799.q 184 yes $$-1$$ $$1$$ $$e\left(\frac{79}{92}\right)$$ $$e\left(\frac{81}{184}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{65}{184}\right)$$ $$e\left(\frac{55}{184}\right)$$ $$e\left(\frac{171}{184}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{39}{184}\right)$$ $$e\left(\frac{179}{184}\right)$$
$$\chi_{799}(20,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{65}{184}\right)$$ $$e\left(\frac{55}{368}\right)$$ $$e\left(\frac{65}{92}\right)$$ $$e\left(\frac{43}{368}\right)$$ $$e\left(\frac{185}{368}\right)$$ $$e\left(\frac{157}{368}\right)$$ $$e\left(\frac{11}{184}\right)$$ $$e\left(\frac{55}{184}\right)$$ $$e\left(\frac{173}{368}\right)$$ $$e\left(\frac{25}{368}\right)$$
$$\chi_{799}(21,\cdot)$$ 799.o 92 yes $$1$$ $$1$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{33}{92}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{39}{92}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{67}{92}\right)$$ $$e\left(\frac{15}{92}\right)$$
$$\chi_{799}(22,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{29}{184}\right)$$ $$e\left(\frac{67}{368}\right)$$ $$e\left(\frac{29}{92}\right)$$ $$e\left(\frac{39}{368}\right)$$ $$e\left(\frac{125}{368}\right)$$ $$e\left(\frac{305}{368}\right)$$ $$e\left(\frac{87}{184}\right)$$ $$e\left(\frac{67}{184}\right)$$ $$e\left(\frac{97}{368}\right)$$ $$e\left(\frac{365}{368}\right)$$
$$\chi_{799}(23,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{15}{184}\right)$$ $$e\left(\frac{41}{368}\right)$$ $$e\left(\frac{15}{92}\right)$$ $$e\left(\frac{293}{368}\right)$$ $$e\left(\frac{71}{368}\right)$$ $$e\left(\frac{291}{368}\right)$$ $$e\left(\frac{45}{184}\right)$$ $$e\left(\frac{41}{184}\right)$$ $$e\left(\frac{323}{368}\right)$$ $$e\left(\frac{119}{368}\right)$$
$$\chi_{799}(24,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{107}{184}\right)$$ $$e\left(\frac{317}{368}\right)$$ $$e\left(\frac{15}{92}\right)$$ $$e\left(\frac{17}{368}\right)$$ $$e\left(\frac{163}{368}\right)$$ $$e\left(\frac{15}{368}\right)$$ $$e\left(\frac{137}{184}\right)$$ $$e\left(\frac{133}{184}\right)$$ $$e\left(\frac{231}{368}\right)$$ $$e\left(\frac{27}{368}\right)$$
$$\chi_{799}(25,\cdot)$$ 799.r 184 yes $$1$$ $$1$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{91}{184}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{31}{184}\right)$$ $$e\left(\frac{5}{184}\right)$$ $$e\left(\frac{49}{184}\right)$$ $$e\left(\frac{55}{92}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{129}{184}\right)$$ $$e\left(\frac{125}{184}\right)$$
$$\chi_{799}(26,\cdot)$$ 799.q 184 yes $$-1$$ $$1$$ $$e\left(\frac{9}{92}\right)$$ $$e\left(\frac{135}{184}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{47}{184}\right)$$ $$e\left(\frac{153}{184}\right)$$ $$e\left(\frac{101}{184}\right)$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{65}{184}\right)$$ $$e\left(\frac{53}{184}\right)$$
$$\chi_{799}(27,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{19}{184}\right)$$ $$e\left(\frac{101}{368}\right)$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{89}{368}\right)$$ $$e\left(\frac{139}{368}\right)$$ $$e\left(\frac{295}{368}\right)$$ $$e\left(\frac{57}{184}\right)$$ $$e\left(\frac{101}{184}\right)$$ $$e\left(\frac{127}{368}\right)$$ $$e\left(\frac{163}{368}\right)$$
$$\chi_{799}(28,\cdot)$$ 799.t 368 yes $$-1$$ $$1$$ $$e\left(\frac{135}{184}\right)$$ $$e\left(\frac{1}{368}\right)$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{245}{368}\right)$$ $$e\left(\frac{271}{368}\right)$$ $$e\left(\frac{43}{368}\right)$$ $$e\left(\frac{37}{184}\right)$$ $$e\left(\frac{1}{184}\right)$$ $$e\left(\frac{147}{368}\right)$$ $$e\left(\frac{151}{368}\right)$$
$$\chi_{799}(29,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{13}{184}\right)$$ $$e\left(\frac{11}{368}\right)$$ $$e\left(\frac{13}{92}\right)$$ $$e\left(\frac{303}{368}\right)$$ $$e\left(\frac{37}{368}\right)$$ $$e\left(\frac{105}{368}\right)$$ $$e\left(\frac{39}{184}\right)$$ $$e\left(\frac{11}{184}\right)$$ $$e\left(\frac{329}{368}\right)$$ $$e\left(\frac{5}{368}\right)$$
$$\chi_{799}(30,\cdot)$$ 799.p 92 yes $$-1$$ $$1$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{9}{92}\right)$$ $$e\left(\frac{89}{92}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{79}{92}\right)$$ $$e\left(\frac{63}{92}\right)$$
$$\chi_{799}(31,\cdot)$$ 799.s 368 yes $$1$$ $$1$$ $$e\left(\frac{9}{184}\right)$$ $$e\left(\frac{319}{368}\right)$$ $$e\left(\frac{9}{92}\right)$$ $$e\left(\frac{323}{368}\right)$$ $$e\left(\frac{337}{368}\right)$$ $$e\left(\frac{101}{368}\right)$$ $$e\left(\frac{27}{184}\right)$$ $$e\left(\frac{135}{184}\right)$$ $$e\left(\frac{341}{368}\right)$$ $$e\left(\frac{145}{368}\right)$$
$$\chi_{799}(32,\cdot)$$ 799.r 184 yes $$1$$ $$1$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{93}{184}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{153}{184}\right)$$ $$e\left(\frac{179}{184}\right)$$ $$e\left(\frac{135}{184}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{55}{184}\right)$$ $$e\left(\frac{59}{184}\right)$$
$$\chi_{799}(33,\cdot)$$ 799.m 46 yes $$-1$$ $$1$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$