# Properties

 Modulus $1859$ Structure $$C_{2}\times C_{780}$$ Order $1560$

# Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1859)

pari: g = idealstar(,1859,2)

## Character group

 sage: G.order()  pari: g.no Order = 1560 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{780}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1859}(508,\cdot)$, $\chi_{1859}(1354,\cdot)$

## First 32 of 1560 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{1859}(1,\cdot)$$ 1859.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1859}(2,\cdot)$$ 1859.bv 780 yes $$1$$ $$1$$ $$e\left(\frac{83}{780}\right)$$ $$e\left(\frac{116}{195}\right)$$ $$e\left(\frac{83}{390}\right)$$ $$e\left(\frac{119}{260}\right)$$ $$e\left(\frac{547}{780}\right)$$ $$e\left(\frac{301}{780}\right)$$ $$e\left(\frac{83}{260}\right)$$ $$e\left(\frac{37}{195}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$
$$\chi_{1859}(3,\cdot)$$ 1859.bo 195 yes $$1$$ $$1$$ $$e\left(\frac{116}{195}\right)$$ $$e\left(\frac{188}{195}\right)$$ $$e\left(\frac{37}{195}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{109}{195}\right)$$ $$e\left(\frac{127}{195}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{181}{195}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$
$$\chi_{1859}(4,\cdot)$$ 1859.bs 390 yes $$1$$ $$1$$ $$e\left(\frac{83}{390}\right)$$ $$e\left(\frac{37}{195}\right)$$ $$e\left(\frac{83}{195}\right)$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{157}{390}\right)$$ $$e\left(\frac{301}{390}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{74}{195}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{1859}(5,\cdot)$$ 1859.bq 260 yes $$-1$$ $$1$$ $$e\left(\frac{119}{260}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{31}{260}\right)$$ $$e\left(\frac{211}{260}\right)$$ $$e\left(\frac{253}{260}\right)$$ $$e\left(\frac{97}{260}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$
$$\chi_{1859}(6,\cdot)$$ 1859.bv 780 yes $$1$$ $$1$$ $$e\left(\frac{547}{780}\right)$$ $$e\left(\frac{109}{195}\right)$$ $$e\left(\frac{157}{390}\right)$$ $$e\left(\frac{211}{260}\right)$$ $$e\left(\frac{203}{780}\right)$$ $$e\left(\frac{29}{780}\right)$$ $$e\left(\frac{27}{260}\right)$$ $$e\left(\frac{23}{195}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{1859}(7,\cdot)$$ 1859.bv 780 yes $$1$$ $$1$$ $$e\left(\frac{301}{780}\right)$$ $$e\left(\frac{127}{195}\right)$$ $$e\left(\frac{301}{390}\right)$$ $$e\left(\frac{253}{260}\right)$$ $$e\left(\frac{29}{780}\right)$$ $$e\left(\frac{227}{780}\right)$$ $$e\left(\frac{41}{260}\right)$$ $$e\left(\frac{59}{195}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{1859}(8,\cdot)$$ 1859.bp 260 yes $$1$$ $$1$$ $$e\left(\frac{83}{260}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{97}{260}\right)$$ $$e\left(\frac{27}{260}\right)$$ $$e\left(\frac{41}{260}\right)$$ $$e\left(\frac{249}{260}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{1859}(9,\cdot)$$ 1859.bo 195 yes $$1$$ $$1$$ $$e\left(\frac{37}{195}\right)$$ $$e\left(\frac{181}{195}\right)$$ $$e\left(\frac{74}{195}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{23}{195}\right)$$ $$e\left(\frac{59}{195}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{167}{195}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{1859}(10,\cdot)$$ 1859.bi 78 yes $$-1$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{1859}(12,\cdot)$$ 1859.w 26 no $$1$$ $$1$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{1859}(14,\cdot)$$ 1859.bf 65 yes $$1$$ $$1$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{1859}(15,\cdot)$$ 1859.bu 780 yes $$-1$$ $$1$$ $$e\left(\frac{41}{780}\right)$$ $$e\left(\frac{62}{195}\right)$$ $$e\left(\frac{41}{390}\right)$$ $$e\left(\frac{123}{260}\right)$$ $$e\left(\frac{289}{780}\right)$$ $$e\left(\frac{487}{780}\right)$$ $$e\left(\frac{41}{260}\right)$$ $$e\left(\frac{124}{195}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{1859}(16,\cdot)$$ 1859.bo 195 yes $$1$$ $$1$$ $$e\left(\frac{83}{195}\right)$$ $$e\left(\frac{74}{195}\right)$$ $$e\left(\frac{166}{195}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{157}{195}\right)$$ $$e\left(\frac{106}{195}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{148}{195}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{1859}(17,\cdot)$$ 1859.br 390 yes $$-1$$ $$1$$ $$e\left(\frac{163}{195}\right)$$ $$e\left(\frac{49}{195}\right)$$ $$e\left(\frac{131}{195}\right)$$ $$e\left(\frac{3}{130}\right)$$ $$e\left(\frac{17}{195}\right)$$ $$e\left(\frac{86}{195}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{98}{195}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{1859}(18,\cdot)$$ 1859.bp 260 yes $$1$$ $$1$$ $$e\left(\frac{77}{260}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{77}{130}\right)$$ $$e\left(\frac{43}{260}\right)$$ $$e\left(\frac{213}{260}\right)$$ $$e\left(\frac{179}{260}\right)$$ $$e\left(\frac{231}{260}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$
$$\chi_{1859}(19,\cdot)$$ 1859.bd 60 no $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{1859}(20,\cdot)$$ 1859.bu 780 yes $$-1$$ $$1$$ $$e\left(\frac{523}{780}\right)$$ $$e\left(\frac{106}{195}\right)$$ $$e\left(\frac{133}{390}\right)$$ $$e\left(\frac{9}{260}\right)$$ $$e\left(\frac{167}{780}\right)$$ $$e\left(\frac{581}{780}\right)$$ $$e\left(\frac{3}{260}\right)$$ $$e\left(\frac{17}{195}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{1859}(21,\cdot)$$ 1859.bb 52 yes $$1$$ $$1$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{1859}(23,\cdot)$$ 1859.j 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{1859}(24,\cdot)$$ 1859.bv 780 yes $$1$$ $$1$$ $$e\left(\frac{713}{780}\right)$$ $$e\left(\frac{146}{195}\right)$$ $$e\left(\frac{323}{390}\right)$$ $$e\left(\frac{189}{260}\right)$$ $$e\left(\frac{517}{780}\right)$$ $$e\left(\frac{631}{780}\right)$$ $$e\left(\frac{193}{260}\right)$$ $$e\left(\frac{97}{195}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{1859}(25,\cdot)$$ 1859.bj 130 yes $$1$$ $$1$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{31}{130}\right)$$ $$e\left(\frac{81}{130}\right)$$ $$e\left(\frac{123}{130}\right)$$ $$e\left(\frac{97}{130}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{1859}(27,\cdot)$$ 1859.bf 65 yes $$1$$ $$1$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$
$$\chi_{1859}(28,\cdot)$$ 1859.bv 780 yes $$1$$ $$1$$ $$e\left(\frac{467}{780}\right)$$ $$e\left(\frac{164}{195}\right)$$ $$e\left(\frac{77}{390}\right)$$ $$e\left(\frac{231}{260}\right)$$ $$e\left(\frac{343}{780}\right)$$ $$e\left(\frac{49}{780}\right)$$ $$e\left(\frac{207}{260}\right)$$ $$e\left(\frac{133}{195}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{1}{26}\right)$$
$$\chi_{1859}(29,\cdot)$$ 1859.bt 390 yes $$-1$$ $$1$$ $$e\left(\frac{373}{390}\right)$$ $$e\left(\frac{77}{195}\right)$$ $$e\left(\frac{178}{195}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{137}{390}\right)$$ $$e\left(\frac{131}{390}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{154}{195}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{1859}(30,\cdot)$$ 1859.br 390 yes $$-1$$ $$1$$ $$e\left(\frac{31}{195}\right)$$ $$e\left(\frac{178}{195}\right)$$ $$e\left(\frac{62}{195}\right)$$ $$e\left(\frac{121}{130}\right)$$ $$e\left(\frac{14}{195}\right)$$ $$e\left(\frac{2}{195}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{161}{195}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{1859}(31,\cdot)$$ 1859.bq 260 yes $$-1$$ $$1$$ $$e\left(\frac{191}{260}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{159}{260}\right)$$ $$e\left(\frac{59}{260}\right)$$ $$e\left(\frac{157}{260}\right)$$ $$e\left(\frac{53}{260}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{1859}(32,\cdot)$$ 1859.bn 156 yes $$1$$ $$1$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{1}{26}\right)$$
$$\chi_{1859}(34,\cdot)$$ 1859.bc 52 no $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{1859}(35,\cdot)$$ 1859.bt 390 yes $$-1$$ $$1$$ $$e\left(\frac{329}{390}\right)$$ $$e\left(\frac{1}{195}\right)$$ $$e\left(\frac{134}{195}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{331}{390}\right)$$ $$e\left(\frac{103}{390}\right)$$ $$e\left(\frac{69}{130}\right)$$ $$e\left(\frac{2}{195}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{1859}(36,\cdot)$$ 1859.bs 390 yes $$1$$ $$1$$ $$e\left(\frac{157}{390}\right)$$ $$e\left(\frac{23}{195}\right)$$ $$e\left(\frac{157}{195}\right)$$ $$e\left(\frac{81}{130}\right)$$ $$e\left(\frac{203}{390}\right)$$ $$e\left(\frac{29}{390}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{46}{195}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{1859}(37,\cdot)$$ 1859.bu 780 yes $$-1$$ $$1$$ $$e\left(\frac{131}{780}\right)$$ $$e\left(\frac{122}{195}\right)$$ $$e\left(\frac{131}{390}\right)$$ $$e\left(\frac{133}{260}\right)$$ $$e\left(\frac{619}{780}\right)$$ $$e\left(\frac{757}{780}\right)$$ $$e\left(\frac{131}{260}\right)$$ $$e\left(\frac{49}{195}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{25}{26}\right)$$
Click here to search among the remaining 1528 characters.