LMFDB - Group of Dirichlet characters of modulus 3100

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3100)

pari: g = idealstar(,3100,2)

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	=	$\chi_{3100}(1551,\cdot)$, $\chi_{3100}(2977,\cdot)$, $\chi_{3100}(1801,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{3100}(1,\cdot)$	3100.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3100}(3,\cdot)$	3100.gh	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{19}{20}\right)$
$\chi_{3100}(7,\cdot)$	3100.fw	60	no	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{3100}(9,\cdot)$	3100.eh	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{9}{10}\right)$
$\chi_{3100}(11,\cdot)$	3100.fc	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{5}\right)$
$\chi_{3100}(13,\cdot)$	3100.fq	60	no	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{3100}(17,\cdot)$	3100.fq	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{3100}(19,\cdot)$	3100.fe	30	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{4}{5}\right)$
$\chi_{3100}(21,\cdot)$	3100.fn	30	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{3100}(23,\cdot)$	3100.dd	20	yes	$-1$	$1$	$i$	$e\left(\frac{9}{20}\right)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$-i$
$\chi_{3100}(27,\cdot)$	3100.de	20	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-i$	$e\left(\frac{17}{20}\right)$
$\chi_{3100}(29,\cdot)$	3100.co	10	no	$-1$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$
$\chi_{3100}(33,\cdot)$	3100.dn	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$i$	$e\left(\frac{11}{20}\right)$
$\chi_{3100}(37,\cdot)$	3100.fr	60	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{3100}(39,\cdot)$	3100.cn	10	yes	$-1$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$
$\chi_{3100}(41,\cdot)$	3100.cz	15	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3100}(43,\cdot)$	3100.gf	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{3100}(47,\cdot)$	3100.ds	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$i$	$e\left(\frac{19}{20}\right)$
$\chi_{3100}(49,\cdot)$	3100.ej	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{3100}(51,\cdot)$	3100.ef	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3100}(53,\cdot)$	3100.fo	60	no	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{3100}(57,\cdot)$	3100.ct	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-i$
$\chi_{3100}(59,\cdot)$	3100.fh	30	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3100}(61,\cdot)$	3100.cm	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3100}(63,\cdot)$	3100.do	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{3100}(67,\cdot)$	3100.fx	60	yes	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{3100}(69,\cdot)$	3100.ei	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{3100}(71,\cdot)$	3100.eg	30	yes	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3100}(73,\cdot)$	3100.fs	60	no	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{17}{20}\right)$
$\chi_{3100}(77,\cdot)$	3100.dx	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{3100}(79,\cdot)$	3100.er	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3100}(81,\cdot)$	3100.cx	15	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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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	$3100$
Structure	\(C_{2}\times C_{10}\times C_{60}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{3100}(1,\cdot)\)	3100.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3100}(3,\cdot)\)	3100.gh	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{3100}(7,\cdot)\)	3100.fw	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{3100}(9,\cdot)\)	3100.eh	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{3100}(11,\cdot)\)	3100.fc	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3100}(13,\cdot)\)	3100.fq	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{3100}(17,\cdot)\)	3100.fq	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{3100}(19,\cdot)\)	3100.fe	30	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3100}(21,\cdot)\)	3100.fn	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{3100}(23,\cdot)\)	3100.dd	20	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)
\(\chi_{3100}(27,\cdot)\)	3100.de	20	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{3100}(29,\cdot)\)	3100.co	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)
\(\chi_{3100}(33,\cdot)\)	3100.dn	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{3100}(37,\cdot)\)	3100.fr	60	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{3100}(39,\cdot)\)	3100.cn	10	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)
\(\chi_{3100}(41,\cdot)\)	3100.cz	15	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3100}(43,\cdot)\)	3100.gf	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{3100}(47,\cdot)\)	3100.ds	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{3100}(49,\cdot)\)	3100.ej	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{3100}(51,\cdot)\)	3100.ef	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3100}(53,\cdot)\)	3100.fo	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{3100}(57,\cdot)\)	3100.ct	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-i\)
\(\chi_{3100}(59,\cdot)\)	3100.fh	30	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3100}(61,\cdot)\)	3100.cm	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3100}(63,\cdot)\)	3100.do	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{3100}(67,\cdot)\)	3100.fx	60	yes	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{3100}(69,\cdot)\)	3100.ei	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{3100}(71,\cdot)\)	3100.eg	30	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3100}(73,\cdot)\)	3100.fs	60	no	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{3100}(77,\cdot)\)	3100.dx	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{3100}(79,\cdot)\)	3100.er	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3100}(81,\cdot)\)	3100.cx	15	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)

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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.