LMFDB - Group of Dirichlet characters of modulus 4026

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4026)

pari: g = idealstar(,4026,2)

Character group

sage: G.order() pari: g.no
Order	=	1200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{10}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4026}(1343,\cdot)$, $\chi_{4026}(1465,\cdot)$, $\chi_{4026}(3235,\cdot)$

First 32 of 1200 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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{4026}(1,\cdot)$	4026.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4026}(5,\cdot)$	4026.fl	30	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{4026}(7,\cdot)$	4026.fr	60	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{4026}(13,\cdot)$	4026.ez	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4026}(17,\cdot)$	4026.fo	60	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{4026}(19,\cdot)$	4026.ev	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{4026}(23,\cdot)$	4026.dl	20	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{4026}(25,\cdot)$	4026.cu	15	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{4026}(29,\cdot)$	4026.ge	60	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{4}{15}\right)$	$-i$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{4026}(31,\cdot)$	4026.fw	60	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4026}(35,\cdot)$	4026.gd	60	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{4026}(37,\cdot)$	4026.dn	20	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{4026}(41,\cdot)$	4026.bb	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4026}(43,\cdot)$	4026.fz	60	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{4026}(47,\cdot)$	4026.ep	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$-1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4026}(49,\cdot)$	4026.fj	30	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4026}(53,\cdot)$	4026.dw	20	no	$1$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{4026}(59,\cdot)$	4026.fp	60	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{4026}(65,\cdot)$	4026.es	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4026}(67,\cdot)$	4026.fq	60	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{4026}(71,\cdot)$	4026.gi	60	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{4026}(73,\cdot)$	4026.ey	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4026}(79,\cdot)$	4026.gk	60	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{4026}(83,\cdot)$	4026.eg	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4026}(85,\cdot)$	4026.db	20	no	$1$	$1$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{4026}(89,\cdot)$	4026.dl	20	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{4026}(91,\cdot)$	4026.gl	60	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{4026}(95,\cdot)$	4026.ci	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{4026}(97,\cdot)$	4026.fb	30	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4026}(101,\cdot)$	4026.ge	60	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{2}{15}\right)$	$i$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{4026}(103,\cdot)$	4026.cu	15	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{4026}(107,\cdot)$	4026.en	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{30}\right)$

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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	$4026$
Structure	\(C_{2}\times C_{10}\times C_{60}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{4026}(1,\cdot)\)	4026.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4026}(5,\cdot)\)	4026.fl	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{4026}(7,\cdot)\)	4026.fr	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{4026}(13,\cdot)\)	4026.ez	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4026}(17,\cdot)\)	4026.fo	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{4026}(19,\cdot)\)	4026.ev	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{4026}(23,\cdot)\)	4026.dl	20	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{4026}(25,\cdot)\)	4026.cu	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{4026}(29,\cdot)\)	4026.ge	60	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(-i\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{4026}(31,\cdot)\)	4026.fw	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4026}(35,\cdot)\)	4026.gd	60	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{4026}(37,\cdot)\)	4026.dn	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{4026}(41,\cdot)\)	4026.bb	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4026}(43,\cdot)\)	4026.fz	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{4026}(47,\cdot)\)	4026.ep	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(-1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4026}(49,\cdot)\)	4026.fj	30	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4026}(53,\cdot)\)	4026.dw	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{4026}(59,\cdot)\)	4026.fp	60	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{4026}(65,\cdot)\)	4026.es	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4026}(67,\cdot)\)	4026.fq	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{4026}(71,\cdot)\)	4026.gi	60	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{4026}(73,\cdot)\)	4026.ey	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4026}(79,\cdot)\)	4026.gk	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{4026}(83,\cdot)\)	4026.eg	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4026}(85,\cdot)\)	4026.db	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{4026}(89,\cdot)\)	4026.dl	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{4026}(91,\cdot)\)	4026.gl	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{4026}(95,\cdot)\)	4026.ci	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{4026}(97,\cdot)\)	4026.fb	30	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4026}(101,\cdot)\)	4026.ge	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(i\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{4026}(103,\cdot)\)	4026.cu	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{4026}(107,\cdot)\)	4026.en	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)

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.