# Properties

 Modulus $1805$ Structure $$C_{2}\times C_{684}$$ Order $1368$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1805)

pari: g = idealstar(,1805,2)

## Character group

 sage: G.order()  pari: g.no Order = 1368 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{684}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1805}(362,\cdot)$, $\chi_{1805}(1446,\cdot)$

## First 32 of 1368 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{1805}(1,\cdot)$$ 1805.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1805}(2,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{173}{684}\right)$$ $$e\left(\frac{107}{684}\right)$$ $$e\left(\frac{173}{342}\right)$$ $$e\left(\frac{70}{171}\right)$$ $$e\left(\frac{157}{228}\right)$$ $$e\left(\frac{173}{228}\right)$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{151}{228}\right)$$ $$e\left(\frac{487}{684}\right)$$
$$\chi_{1805}(3,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{107}{684}\right)$$ $$e\left(\frac{509}{684}\right)$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{154}{171}\right)$$ $$e\left(\frac{163}{228}\right)$$ $$e\left(\frac{107}{228}\right)$$ $$e\left(\frac{167}{342}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{13}{228}\right)$$ $$e\left(\frac{661}{684}\right)$$
$$\chi_{1805}(4,\cdot)$$ 1805.bf 342 yes $$1$$ $$1$$ $$e\left(\frac{173}{342}\right)$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{2}{171}\right)$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{107}{171}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{145}{342}\right)$$
$$\chi_{1805}(6,\cdot)$$ 1805.bc 171 no $$1$$ $$1$$ $$e\left(\frac{70}{171}\right)$$ $$e\left(\frac{154}{171}\right)$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{53}{171}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{116}{171}\right)$$
$$\chi_{1805}(7,\cdot)$$ 1805.bd 228 yes $$-1$$ $$1$$ $$e\left(\frac{157}{228}\right)$$ $$e\left(\frac{163}{228}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{5}{76}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{11}{228}\right)$$
$$\chi_{1805}(8,\cdot)$$ 1805.be 228 yes $$1$$ $$1$$ $$e\left(\frac{173}{228}\right)$$ $$e\left(\frac{107}{228}\right)$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{5}{76}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{75}{76}\right)$$ $$e\left(\frac{31}{228}\right)$$
$$\chi_{1805}(9,\cdot)$$ 1805.bf 342 yes $$1$$ $$1$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{167}{342}\right)$$ $$e\left(\frac{107}{171}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{167}{171}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{319}{342}\right)$$
$$\chi_{1805}(11,\cdot)$$ 1805.w 57 no $$1$$ $$1$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{57}\right)$$
$$\chi_{1805}(12,\cdot)$$ 1805.be 228 yes $$1$$ $$1$$ $$e\left(\frac{151}{228}\right)$$ $$e\left(\frac{13}{228}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{75}{76}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{89}{228}\right)$$
$$\chi_{1805}(13,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{487}{684}\right)$$ $$e\left(\frac{661}{684}\right)$$ $$e\left(\frac{145}{342}\right)$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{11}{228}\right)$$ $$e\left(\frac{31}{228}\right)$$ $$e\left(\frac{319}{342}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{89}{228}\right)$$ $$e\left(\frac{509}{684}\right)$$
$$\chi_{1805}(14,\cdot)$$ 1805.bg 342 yes $$-1$$ $$1$$ $$e\left(\frac{161}{171}\right)$$ $$e\left(\frac{149}{171}\right)$$ $$e\left(\frac{151}{171}\right)$$ $$e\left(\frac{139}{171}\right)$$ $$e\left(\frac{83}{114}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{127}{171}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{130}{171}\right)$$
$$\chi_{1805}(16,\cdot)$$ 1805.bc 171 no $$1$$ $$1$$ $$e\left(\frac{2}{171}\right)$$ $$e\left(\frac{107}{171}\right)$$ $$e\left(\frac{4}{171}\right)$$ $$e\left(\frac{109}{171}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{43}{171}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{145}{171}\right)$$
$$\chi_{1805}(17,\cdot)$$ 1805.bj 684 yes $$-1$$ $$1$$ $$e\left(\frac{623}{684}\right)$$ $$e\left(\frac{413}{684}\right)$$ $$e\left(\frac{281}{342}\right)$$ $$e\left(\frac{88}{171}\right)$$ $$e\left(\frac{85}{228}\right)$$ $$e\left(\frac{167}{228}\right)$$ $$e\left(\frac{71}{342}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{97}{228}\right)$$ $$e\left(\frac{109}{684}\right)$$
$$\chi_{1805}(18,\cdot)$$ 1805.x 76 yes $$1$$ $$1$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{49}{76}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{9}{76}\right)$$ $$e\left(\frac{53}{76}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{59}{76}\right)$$ $$e\left(\frac{49}{76}\right)$$
$$\chi_{1805}(21,\cdot)$$ 1805.bh 342 no $$-1$$ $$1$$ $$e\left(\frac{289}{342}\right)$$ $$e\left(\frac{157}{342}\right)$$ $$e\left(\frac{118}{171}\right)$$ $$e\left(\frac{52}{171}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{61}{114}\right)$$ $$e\left(\frac{157}{171}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{17}{114}\right)$$ $$e\left(\frac{5}{342}\right)$$
$$\chi_{1805}(22,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{377}{684}\right)$$ $$e\left(\frac{419}{684}\right)$$ $$e\left(\frac{35}{342}\right)$$ $$e\left(\frac{28}{171}\right)$$ $$e\left(\frac{97}{228}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{77}{342}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{163}{228}\right)$$ $$e\left(\frac{571}{684}\right)$$
$$\chi_{1805}(23,\cdot)$$ 1805.bj 684 yes $$-1$$ $$1$$ $$e\left(\frac{121}{684}\right)$$ $$e\left(\frac{403}{684}\right)$$ $$e\left(\frac{121}{342}\right)$$ $$e\left(\frac{131}{171}\right)$$ $$e\left(\frac{179}{228}\right)$$ $$e\left(\frac{121}{228}\right)$$ $$e\left(\frac{61}{342}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{215}{228}\right)$$ $$e\left(\frac{479}{684}\right)$$
$$\chi_{1805}(24,\cdot)$$ 1805.bf 342 yes $$1$$ $$1$$ $$e\left(\frac{313}{342}\right)$$ $$e\left(\frac{73}{342}\right)$$ $$e\left(\frac{142}{171}\right)$$ $$e\left(\frac{22}{171}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{85}{114}\right)$$ $$e\left(\frac{73}{171}\right)$$ $$e\left(\frac{20}{57}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{35}{342}\right)$$
$$\chi_{1805}(26,\cdot)$$ 1805.w 57 no $$1$$ $$1$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{26}{57}\right)$$
$$\chi_{1805}(27,\cdot)$$ 1805.be 228 yes $$1$$ $$1$$ $$e\left(\frac{107}{228}\right)$$ $$e\left(\frac{53}{228}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{11}{76}\right)$$ $$e\left(\frac{31}{76}\right)$$ $$e\left(\frac{53}{114}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{13}{76}\right)$$ $$e\left(\frac{205}{228}\right)$$
$$\chi_{1805}(28,\cdot)$$ 1805.r 36 no $$-1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$
$$\chi_{1805}(29,\cdot)$$ 1805.bg 342 yes $$-1$$ $$1$$ $$e\left(\frac{94}{171}\right)$$ $$e\left(\frac{70}{171}\right)$$ $$e\left(\frac{17}{171}\right)$$ $$e\left(\frac{164}{171}\right)$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{146}{171}\right)$$
$$\chi_{1805}(31,\cdot)$$ 1805.z 114 no $$-1$$ $$1$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{17}{114}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{55}{114}\right)$$
$$\chi_{1805}(32,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{181}{684}\right)$$ $$e\left(\frac{535}{684}\right)$$ $$e\left(\frac{181}{342}\right)$$ $$e\left(\frac{8}{171}\right)$$ $$e\left(\frac{101}{228}\right)$$ $$e\left(\frac{181}{228}\right)$$ $$e\left(\frac{193}{342}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{71}{228}\right)$$ $$e\left(\frac{383}{684}\right)$$
$$\chi_{1805}(33,\cdot)$$ 1805.bi 684 yes $$1$$ $$1$$ $$e\left(\frac{311}{684}\right)$$ $$e\left(\frac{137}{684}\right)$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{112}{171}\right)$$ $$e\left(\frac{103}{228}\right)$$ $$e\left(\frac{83}{228}\right)$$ $$e\left(\frac{137}{342}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{25}{228}\right)$$ $$e\left(\frac{61}{684}\right)$$
$$\chi_{1805}(34,\cdot)$$ 1805.bg 342 yes $$-1$$ $$1$$ $$e\left(\frac{28}{171}\right)$$ $$e\left(\frac{130}{171}\right)$$ $$e\left(\frac{56}{171}\right)$$ $$e\left(\frac{158}{171}\right)$$ $$e\left(\frac{7}{114}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{89}{171}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{149}{171}\right)$$
$$\chi_{1805}(36,\cdot)$$ 1805.bc 171 no $$1$$ $$1$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{109}{171}\right)$$ $$e\left(\frac{106}{171}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{61}{171}\right)$$
$$\chi_{1805}(37,\cdot)$$ 1805.x 76 yes $$1$$ $$1$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{75}{76}\right)$$ $$e\left(\frac{11}{76}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{3}{76}\right)$$
$$\chi_{1805}(39,\cdot)$$ 1805.v 38 yes $$1$$ $$1$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{27}{38}\right)$$
$$\chi_{1805}(41,\cdot)$$ 1805.bh 342 no $$-1$$ $$1$$ $$e\left(\frac{67}{342}\right)$$ $$e\left(\frac{79}{342}\right)$$ $$e\left(\frac{67}{171}\right)$$ $$e\left(\frac{73}{171}\right)$$ $$e\left(\frac{22}{57}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{79}{171}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{155}{342}\right)$$
$$\chi_{1805}(42,\cdot)$$ 1805.bj 684 yes $$-1$$ $$1$$ $$e\left(\frac{67}{684}\right)$$ $$e\left(\frac{421}{684}\right)$$ $$e\left(\frac{67}{342}\right)$$ $$e\left(\frac{122}{171}\right)$$ $$e\left(\frac{101}{228}\right)$$ $$e\left(\frac{67}{228}\right)$$ $$e\left(\frac{79}{342}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{185}{228}\right)$$ $$e\left(\frac{497}{684}\right)$$
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