LMFDB - Group of Dirichlet characters of modulus 1690

sage:H = DirichletGroup(1690)

pari:g = idealstar(,1690,2)

Character group

sage:G.order() pari:g.no
Order	=	624
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{156}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1690}(677,\cdot)$, $\chi_{1690}(171,\cdot)$

First 32 of 624 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{1690}(1,\cdot)$	1690.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1690}(3,\cdot)$	1690.bl	156	no	$-1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{1690}(7,\cdot)$	1690.bm	156	no	$1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{1690}(9,\cdot)$	1690.bf	78	no	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{1690}(11,\cdot)$	1690.bn	156	no	$-1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{1690}(17,\cdot)$	1690.bk	156	no	$-1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{1690}(19,\cdot)$	1690.t	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1690}(21,\cdot)$	1690.z	52	no	$-1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{26}\right)$	$i$	$e\left(\frac{3}{52}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{1690}(23,\cdot)$	1690.r	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{1690}(27,\cdot)$	1690.bb	52	no	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{21}{52}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$-i$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{1690}(29,\cdot)$	1690.bf	78	no	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{1690}(31,\cdot)$	1690.z	52	no	$-1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{26}\right)$	$-i$	$e\left(\frac{5}{52}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{1690}(33,\cdot)$	1690.bj	156	no	$1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{1690}(37,\cdot)$	1690.bm	156	no	$1$	$1$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{1690}(41,\cdot)$	1690.bn	156	no	$-1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{1690}(43,\cdot)$	1690.bk	156	no	$-1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{1690}(47,\cdot)$	1690.ba	52	no	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{52}\right)$	$-i$	$e\left(\frac{15}{52}\right)$	$i$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{1690}(49,\cdot)$	1690.bg	78	no	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{1690}(51,\cdot)$	1690.v	26	no	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$-1$	$e\left(\frac{21}{26}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{1690}(53,\cdot)$	1690.bb	52	no	$-1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{52}\right)$	$-1$	$e\left(\frac{9}{13}\right)$	$i$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{1690}(57,\cdot)$	1690.bd	52	no	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$	$i$	$e\left(\frac{45}{52}\right)$	$i$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{1690}(59,\cdot)$	1690.bi	156	no	$-1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{1690}(61,\cdot)$	1690.y	39	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{1690}(63,\cdot)$	1690.bj	156	no	$1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{1690}(67,\cdot)$	1690.bj	156	no	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{1690}(69,\cdot)$	1690.bg	78	no	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{1690}(71,\cdot)$	1690.bn	156	no	$-1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{1690}(73,\cdot)$	1690.bd	52	no	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{25}{52}\right)$	$-i$	$e\left(\frac{27}{52}\right)$	$-i$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{1690}(77,\cdot)$	1690.bc	52	no	$-1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{52}\right)$	$1$	$e\left(\frac{25}{26}\right)$	$-i$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{1690}(79,\cdot)$	1690.x	26	no	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{26}\right)$	$1$	$e\left(\frac{7}{13}\right)$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{1690}(81,\cdot)$	1690.y	39	no	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{1690}(83,\cdot)$	1690.ba	52	no	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{45}{52}\right)$	$i$	$e\left(\frac{33}{52}\right)$	$-i$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{26}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1690$
Structure	\(C_{4}\times C_{156}\)
Order	$624$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1690}(1,\cdot)\)	1690.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1690}(3,\cdot)\)	1690.bl	156	no	\(-1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{1690}(7,\cdot)\)	1690.bm	156	no	\(1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{1690}(9,\cdot)\)	1690.bf	78	no	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{1690}(11,\cdot)\)	1690.bn	156	no	\(-1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{1690}(17,\cdot)\)	1690.bk	156	no	\(-1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{1690}(19,\cdot)\)	1690.t	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1690}(21,\cdot)\)	1690.z	52	no	\(-1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(i\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{1690}(23,\cdot)\)	1690.r	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1690}(27,\cdot)\)	1690.bb	52	no	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{1690}(29,\cdot)\)	1690.bf	78	no	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{1690}(31,\cdot)\)	1690.z	52	no	\(-1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-i\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{1690}(33,\cdot)\)	1690.bj	156	no	\(1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{1690}(37,\cdot)\)	1690.bm	156	no	\(1\)	\(1\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{1690}(41,\cdot)\)	1690.bn	156	no	\(-1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{1690}(43,\cdot)\)	1690.bk	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{1690}(47,\cdot)\)	1690.ba	52	no	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(-i\)	\(e\left(\frac{15}{52}\right)\)	\(i\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{1690}(49,\cdot)\)	1690.bg	78	no	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{1690}(51,\cdot)\)	1690.v	26	no	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{1690}(53,\cdot)\)	1690.bb	52	no	\(-1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{1690}(57,\cdot)\)	1690.bd	52	no	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(i\)	\(e\left(\frac{45}{52}\right)\)	\(i\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{1690}(59,\cdot)\)	1690.bi	156	no	\(-1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{1690}(61,\cdot)\)	1690.y	39	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{1690}(63,\cdot)\)	1690.bj	156	no	\(1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{1690}(67,\cdot)\)	1690.bj	156	no	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{1690}(69,\cdot)\)	1690.bg	78	no	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{1690}(71,\cdot)\)	1690.bn	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{1690}(73,\cdot)\)	1690.bd	52	no	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(-i\)	\(e\left(\frac{27}{52}\right)\)	\(-i\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{1690}(77,\cdot)\)	1690.bc	52	no	\(-1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(-i\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{1690}(79,\cdot)\)	1690.x	26	no	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{1690}(81,\cdot)\)	1690.y	39	no	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{1690}(83,\cdot)\)	1690.ba	52	no	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(i\)	\(e\left(\frac{33}{52}\right)\)	\(-i\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)

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