LMFDB - Group of Dirichlet characters of modulus 5070

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5070)

pari: g = idealstar(,5070,2)

Character group

sage: G.order() pari: g.no
Order	=	1248
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5070}(1691,\cdot)$, $\chi_{5070}(4057,\cdot)$, $\chi_{5070}(1861,\cdot)$

First 32 of 1248 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{5070}(1,\cdot)$	5070.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5070}(7,\cdot)$	5070.da	156	no	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{67}{156}\right)$
$\chi_{5070}(11,\cdot)$	5070.cw	156	no	$1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{5070}(17,\cdot)$	5070.cy	156	no	$1$	$1$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{145}{156}\right)$
$\chi_{5070}(19,\cdot)$	5070.bg	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5070}(23,\cdot)$	5070.be	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{5070}(29,\cdot)$	5070.cj	78	no	$-1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{5070}(31,\cdot)$	5070.cd	52	no	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{26}\right)$	$-i$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{5070}(37,\cdot)$	5070.da	156	no	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{131}{156}\right)$
$\chi_{5070}(41,\cdot)$	5070.cw	156	no	$1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{5070}(43,\cdot)$	5070.cs	156	no	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{103}{156}\right)$
$\chi_{5070}(47,\cdot)$	5070.bx	52	no	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{37}{52}\right)$	$-i$	$-i$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{5070}(49,\cdot)$	5070.co	78	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{5070}(53,\cdot)$	5070.cf	52	no	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{52}\right)$	$-1$	$-i$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{5070}(59,\cdot)$	5070.cu	156	no	$1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{5070}(61,\cdot)$	5070.bw	39	no	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{5070}(67,\cdot)$	5070.cq	156	no	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{107}{156}\right)$
$\chi_{5070}(71,\cdot)$	5070.cw	156	no	$1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{5070}(73,\cdot)$	5070.ci	52	no	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{25}{52}\right)$	$-i$	$-i$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{5070}(77,\cdot)$	5070.ca	52	no	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{15}{52}\right)$	$1$	$i$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{5070}(79,\cdot)$	5070.bt	26	no	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{26}\right)$	$1$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{5070}(83,\cdot)$	5070.bx	52	no	$-1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{19}{52}\right)$	$i$	$i$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{5070}(89,\cdot)$	5070.bj	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5070}(97,\cdot)$	5070.cq	156	no	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{7}{156}\right)$
$\chi_{5070}(101,\cdot)$	5070.cm	78	no	$-1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{5070}(103,\cdot)$	5070.cg	52	no	$-1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{52}\right)$	$1$	$i$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{5070}(107,\cdot)$	5070.ct	156	no	$1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{149}{156}\right)$
$\chi_{5070}(109,\cdot)$	5070.cb	52	no	$-1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{13}\right)$	$-i$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{5070}(113,\cdot)$	5070.ct	156	no	$1$	$1$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{43}{156}\right)$
$\chi_{5070}(119,\cdot)$	5070.cu	156	no	$1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{5070}(121,\cdot)$	5070.ck	78	no	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{5070}(127,\cdot)$	5070.cs	156	no	$-1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{29}{156}\right)$

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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	$5070$
Structure	\(C_{2}\times C_{4}\times C_{156}\)
Order	$1248$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{5070}(1,\cdot)\)	5070.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5070}(7,\cdot)\)	5070.da	156	no	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)
\(\chi_{5070}(11,\cdot)\)	5070.cw	156	no	\(1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{5070}(17,\cdot)\)	5070.cy	156	no	\(1\)	\(1\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)
\(\chi_{5070}(19,\cdot)\)	5070.bg	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5070}(23,\cdot)\)	5070.be	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{5070}(29,\cdot)\)	5070.cj	78	no	\(-1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{5070}(31,\cdot)\)	5070.cd	52	no	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{5070}(37,\cdot)\)	5070.da	156	no	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)
\(\chi_{5070}(41,\cdot)\)	5070.cw	156	no	\(1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{5070}(43,\cdot)\)	5070.cs	156	no	\(-1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)
\(\chi_{5070}(47,\cdot)\)	5070.bx	52	no	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{5070}(49,\cdot)\)	5070.co	78	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{5070}(53,\cdot)\)	5070.cf	52	no	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{5070}(59,\cdot)\)	5070.cu	156	no	\(1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{5070}(61,\cdot)\)	5070.bw	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{5070}(67,\cdot)\)	5070.cq	156	no	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{107}{156}\right)\)
\(\chi_{5070}(71,\cdot)\)	5070.cw	156	no	\(1\)	\(1\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{5070}(73,\cdot)\)	5070.ci	52	no	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{5070}(77,\cdot)\)	5070.ca	52	no	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(1\)	\(i\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{5070}(79,\cdot)\)	5070.bt	26	no	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{5070}(83,\cdot)\)	5070.bx	52	no	\(-1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{5070}(89,\cdot)\)	5070.bj	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5070}(97,\cdot)\)	5070.cq	156	no	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{7}{156}\right)\)
\(\chi_{5070}(101,\cdot)\)	5070.cm	78	no	\(-1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{5070}(103,\cdot)\)	5070.cg	52	no	\(-1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(1\)	\(i\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{5070}(107,\cdot)\)	5070.ct	156	no	\(1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)
\(\chi_{5070}(109,\cdot)\)	5070.cb	52	no	\(-1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{5070}(113,\cdot)\)	5070.ct	156	no	\(1\)	\(1\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{43}{156}\right)\)
\(\chi_{5070}(119,\cdot)\)	5070.cu	156	no	\(1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{5070}(121,\cdot)\)	5070.ck	78	no	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{5070}(127,\cdot)\)	5070.cs	156	no	\(-1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)

Introduction

L-functions

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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.