LMFDB - Group of Dirichlet characters of modulus 3960

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3960)

pari: g = idealstar(,3960,2)

Character group

sage: G.order() pari: g.no
Order	=	960
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3960}(991,\cdot)$, $\chi_{3960}(1981,\cdot)$, $\chi_{3960}(3521,\cdot)$, $\chi_{3960}(2377,\cdot)$, $\chi_{3960}(2521,\cdot)$

First 32 of 960 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{3960}(1,\cdot)$	3960.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3960}(7,\cdot)$	3960.hg	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3960}(13,\cdot)$	3960.he	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{3960}(17,\cdot)$	3960.fd	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{3960}(19,\cdot)$	3960.ed	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$
$\chi_{3960}(23,\cdot)$	3960.et	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3960}(29,\cdot)$	3960.gj	30	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3960}(31,\cdot)$	3960.ga	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3960}(37,\cdot)$	3960.ez	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$i$
$\chi_{3960}(41,\cdot)$	3960.fs	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3960}(43,\cdot)$	3960.ex	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3960}(47,\cdot)$	3960.gy	60	no	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{3960}(49,\cdot)$	3960.fu	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3960}(53,\cdot)$	3960.fe	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{3960}(59,\cdot)$	3960.gn	30	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3960}(61,\cdot)$	3960.gb	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3960}(67,\cdot)$	3960.ek	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3960}(71,\cdot)$	3960.dz	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{3960}(73,\cdot)$	3960.fa	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{3960}(79,\cdot)$	3960.fx	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3960}(83,\cdot)$	3960.gz	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3960}(89,\cdot)$	3960.i	2	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$
$\chi_{3960}(91,\cdot)$	3960.ea	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{3960}(97,\cdot)$	3960.hf	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3960}(101,\cdot)$	3960.fy	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3960}(103,\cdot)$	3960.gv	60	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3960}(107,\cdot)$	3960.fb	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$i$
$\chi_{3960}(109,\cdot)$	3960.x	2	no	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$
$\chi_{3960}(113,\cdot)$	3960.hi	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{3960}(119,\cdot)$	3960.gi	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3960}(127,\cdot)$	3960.fk	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{3960}(131,\cdot)$	3960.cc	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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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	$3960$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{3960}(1,\cdot)\)	3960.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3960}(7,\cdot)\)	3960.hg	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3960}(13,\cdot)\)	3960.he	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{3960}(17,\cdot)\)	3960.fd	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{3960}(19,\cdot)\)	3960.ed	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)
\(\chi_{3960}(23,\cdot)\)	3960.et	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3960}(29,\cdot)\)	3960.gj	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3960}(31,\cdot)\)	3960.ga	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3960}(37,\cdot)\)	3960.ez	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)
\(\chi_{3960}(41,\cdot)\)	3960.fs	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3960}(43,\cdot)\)	3960.ex	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3960}(47,\cdot)\)	3960.gy	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{3960}(49,\cdot)\)	3960.fu	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3960}(53,\cdot)\)	3960.fe	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{3960}(59,\cdot)\)	3960.gn	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3960}(61,\cdot)\)	3960.gb	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3960}(67,\cdot)\)	3960.ek	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3960}(71,\cdot)\)	3960.dz	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{3960}(73,\cdot)\)	3960.fa	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)
\(\chi_{3960}(79,\cdot)\)	3960.fx	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3960}(83,\cdot)\)	3960.gz	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3960}(89,\cdot)\)	3960.i	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{3960}(91,\cdot)\)	3960.ea	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{3960}(97,\cdot)\)	3960.hf	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3960}(101,\cdot)\)	3960.fy	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3960}(103,\cdot)\)	3960.gv	60	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3960}(107,\cdot)\)	3960.fb	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)
\(\chi_{3960}(109,\cdot)\)	3960.x	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{3960}(113,\cdot)\)	3960.hi	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{3960}(119,\cdot)\)	3960.gi	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3960}(127,\cdot)\)	3960.fk	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)
\(\chi_{3960}(131,\cdot)\)	3960.cc	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.