LMFDB - Group of Dirichlet characters of modulus 6020

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6020)

pari: g = idealstar(,6020,2)

Character group

sage: G.order() pari: g.no
Order	=	2016
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6020}(3011,\cdot)$, $\chi_{6020}(4817,\cdot)$, $\chi_{6020}(4301,\cdot)$, $\chi_{6020}(1121,\cdot)$

First 32 of 2016 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{6020}(1,\cdot)$	6020.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6020}(3,\cdot)$	6020.if	84	yes	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{6020}(9,\cdot)$	6020.gn	42	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{6020}(11,\cdot)$	6020.gd	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{6020}(13,\cdot)$	6020.ic	84	no	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{6020}(17,\cdot)$	6020.je	84	no	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{6020}(19,\cdot)$	6020.fu	42	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{6020}(23,\cdot)$	6020.ja	84	yes	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{6020}(27,\cdot)$	6020.fo	28	yes	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{6020}(29,\cdot)$	6020.gx	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{6020}(31,\cdot)$	6020.hc	42	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{6020}(33,\cdot)$	6020.jd	84	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{6020}(37,\cdot)$	6020.dl	12	no	$1$	$1$	$i$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{6020}(39,\cdot)$	6020.gk	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{6020}(41,\cdot)$	6020.fb	14	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{6020}(47,\cdot)$	6020.ih	84	yes	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{6020}(51,\cdot)$	6020.hb	42	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{6020}(53,\cdot)$	6020.is	84	no	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{6020}(57,\cdot)$	6020.ia	84	no	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{6020}(59,\cdot)$	6020.ge	42	yes	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{6020}(61,\cdot)$	6020.hj	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{6020}(67,\cdot)$	6020.ie	84	yes	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{6020}(69,\cdot)$	6020.gc	42	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{6020}(71,\cdot)$	6020.hr	42	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{6020}(73,\cdot)$	6020.jd	84	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{6020}(79,\cdot)$	6020.by	6	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{6020}(81,\cdot)$	6020.fj	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{6020}(83,\cdot)$	6020.iu	84	yes	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{6020}(87,\cdot)$	6020.ej	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{6020}(89,\cdot)$	6020.hz	42	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{6020}(93,\cdot)$	6020.ed	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6020}(97,\cdot)$	6020.fl	28	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$

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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	$6020$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{84}\)
Order	$2016$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{6020}(1,\cdot)\)	6020.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6020}(3,\cdot)\)	6020.if	84	yes	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{6020}(9,\cdot)\)	6020.gn	42	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{6020}(11,\cdot)\)	6020.gd	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{6020}(13,\cdot)\)	6020.ic	84	no	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{6020}(17,\cdot)\)	6020.je	84	no	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{6020}(19,\cdot)\)	6020.fu	42	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{6020}(23,\cdot)\)	6020.ja	84	yes	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{6020}(27,\cdot)\)	6020.fo	28	yes	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{6020}(29,\cdot)\)	6020.gx	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{6020}(31,\cdot)\)	6020.hc	42	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{6020}(33,\cdot)\)	6020.jd	84	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{6020}(37,\cdot)\)	6020.dl	12	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{6020}(39,\cdot)\)	6020.gk	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{6020}(41,\cdot)\)	6020.fb	14	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{6020}(47,\cdot)\)	6020.ih	84	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{6020}(51,\cdot)\)	6020.hb	42	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{6020}(53,\cdot)\)	6020.is	84	no	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{6020}(57,\cdot)\)	6020.ia	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{6020}(59,\cdot)\)	6020.ge	42	yes	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{6020}(61,\cdot)\)	6020.hj	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{6020}(67,\cdot)\)	6020.ie	84	yes	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{6020}(69,\cdot)\)	6020.gc	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{6020}(71,\cdot)\)	6020.hr	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{6020}(73,\cdot)\)	6020.jd	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{6020}(79,\cdot)\)	6020.by	6	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6020}(81,\cdot)\)	6020.fj	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{6020}(83,\cdot)\)	6020.iu	84	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{6020}(87,\cdot)\)	6020.ej	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6020}(89,\cdot)\)	6020.hz	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{6020}(93,\cdot)\)	6020.ed	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6020}(97,\cdot)\)	6020.fl	28	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)

Introduction

L-functions

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First 32 of 2016 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.