LMFDB - Group of Dirichlet characters of modulus 4020

sage:H = DirichletGroup(4020)

pari:g = idealstar(,4020,2)

Character group

sage:G.order() pari:g.no
Order	=	1056
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{132}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{4020}(2011,\cdot)$, $\chi_{4020}(2681,\cdot)$, $\chi_{4020}(3217,\cdot)$, $\chi_{4020}(1141,\cdot)$

First 32 of 1056 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{4020}(1,\cdot)$	4020.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4020}(7,\cdot)$	4020.dr	132	no	$-1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{4020}(11,\cdot)$	4020.de	66	no	$-1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{4020}(13,\cdot)$	4020.dl	132	no	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{4020}(17,\cdot)$	4020.dk	132	no	$1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{4020}(19,\cdot)$	4020.dd	66	no	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{4020}(23,\cdot)$	4020.dq	132	yes	$-1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{4020}(29,\cdot)$	4020.bn	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4020}(31,\cdot)$	4020.dh	66	no	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{4020}(37,\cdot)$	4020.bs	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4020}(41,\cdot)$	4020.da	66	no	$1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{4020}(43,\cdot)$	4020.cn	44	no	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$-1$	$e\left(\frac{10}{11}\right)$	$-i$	$e\left(\frac{5}{22}\right)$
$\chi_{4020}(47,\cdot)$	4020.dq	132	yes	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{4020}(49,\cdot)$	4020.cz	66	no	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{4020}(53,\cdot)$	4020.cq	44	no	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{44}\right)$	$1$	$e\left(\frac{13}{22}\right)$	$-i$	$e\left(\frac{3}{11}\right)$
$\chi_{4020}(59,\cdot)$	4020.by	22	yes	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{22}\right)$	$-1$	$e\left(\frac{3}{22}\right)$	$-1$	$e\left(\frac{9}{22}\right)$
$\chi_{4020}(61,\cdot)$	4020.cv	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{4020}(71,\cdot)$	4020.dc	66	no	$1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{4020}(73,\cdot)$	4020.dp	132	no	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{4020}(77,\cdot)$	4020.dk	132	no	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{4020}(79,\cdot)$	4020.db	66	no	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{4020}(83,\cdot)$	4020.dq	132	yes	$-1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{4020}(89,\cdot)$	4020.ck	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{11}\right)$	$-1$	$e\left(\frac{8}{11}\right)$	$-1$	$e\left(\frac{15}{22}\right)$
$\chi_{4020}(91,\cdot)$	4020.cj	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{9}{22}\right)$	$1$	$e\left(\frac{8}{11}\right)$
$\chi_{4020}(97,\cdot)$	4020.bw	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4020}(101,\cdot)$	4020.da	66	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{4020}(103,\cdot)$	4020.dn	132	no	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{4020}(107,\cdot)$	4020.co	44	yes	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{44}\right)$	$1$	$e\left(\frac{7}{22}\right)$	$i$	$e\left(\frac{21}{22}\right)$
$\chi_{4020}(109,\cdot)$	4020.cb	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{22}\right)$	$1$	$e\left(\frac{19}{22}\right)$	$-1$	$e\left(\frac{13}{22}\right)$
$\chi_{4020}(113,\cdot)$	4020.do	132	no	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{4020}(119,\cdot)$	4020.ci	22	yes	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$	$-1$	$e\left(\frac{5}{11}\right)$	$-1$	$e\left(\frac{4}{11}\right)$
$\chi_{4020}(121,\cdot)$	4020.cm	33	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{33}\right)$

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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	$4020$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{132}\)
Order	$1056$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4020}(1,\cdot)\)	4020.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4020}(7,\cdot)\)	4020.dr	132	no	\(-1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{4020}(11,\cdot)\)	4020.de	66	no	\(-1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{4020}(13,\cdot)\)	4020.dl	132	no	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{4020}(17,\cdot)\)	4020.dk	132	no	\(1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{4020}(19,\cdot)\)	4020.dd	66	no	\(-1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{4020}(23,\cdot)\)	4020.dq	132	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{4020}(29,\cdot)\)	4020.bn	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4020}(31,\cdot)\)	4020.dh	66	no	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{4020}(37,\cdot)\)	4020.bs	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4020}(41,\cdot)\)	4020.da	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{4020}(43,\cdot)\)	4020.cn	44	no	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(-1\)	\(e\left(\frac{10}{11}\right)\)	\(-i\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{4020}(47,\cdot)\)	4020.dq	132	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{4020}(49,\cdot)\)	4020.cz	66	no	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{4020}(53,\cdot)\)	4020.cq	44	no	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(-i\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{4020}(59,\cdot)\)	4020.by	22	yes	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(-1\)	\(e\left(\frac{3}{22}\right)\)	\(-1\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{4020}(61,\cdot)\)	4020.cv	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{4020}(71,\cdot)\)	4020.dc	66	no	\(1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{4020}(73,\cdot)\)	4020.dp	132	no	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{4020}(77,\cdot)\)	4020.dk	132	no	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{4020}(79,\cdot)\)	4020.db	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{4020}(83,\cdot)\)	4020.dq	132	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{4020}(89,\cdot)\)	4020.ck	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(-1\)	\(e\left(\frac{8}{11}\right)\)	\(-1\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{4020}(91,\cdot)\)	4020.cj	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(1\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{4020}(97,\cdot)\)	4020.bw	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4020}(101,\cdot)\)	4020.da	66	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{4020}(103,\cdot)\)	4020.dn	132	no	\(1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{4020}(107,\cdot)\)	4020.co	44	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(i\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{4020}(109,\cdot)\)	4020.cb	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(-1\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{4020}(113,\cdot)\)	4020.do	132	no	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{4020}(119,\cdot)\)	4020.ci	22	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(-1\)	\(e\left(\frac{5}{11}\right)\)	\(-1\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{4020}(121,\cdot)\)	4020.cm	33	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{33}\right)\)

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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.