LMFDB - Group of Dirichlet characters of modulus 1805

Show commands: PariGP / 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	$-1$	$1$	$e\left(\frac{67}{684}\right)$	$e\left(\frac{421}{684}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{497}{684}\right)$

Click here to search among the remaining 1336 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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	\(-1\)	\(1\)	\(e\left(\frac{67}{684}\right)\)	\(e\left(\frac{421}{684}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{497}{684}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1368 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.