LMFDB - Group of Dirichlet characters of modulus 1859

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	$-1$	$1$	$e\left(\frac{131}{780}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{133}{260}\right)$	$e\left(\frac{619}{780}\right)$	$e\left(\frac{757}{780}\right)$	$e\left(\frac{131}{260}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{25}{26}\right)$

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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 $\F_{q}$

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

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	\(-1\)	\(1\)	\(e\left(\frac{131}{780}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{133}{260}\right)\)	\(e\left(\frac{619}{780}\right)\)	\(e\left(\frac{757}{780}\right)\)	\(e\left(\frac{131}{260}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)

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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.