LMFDB - Group of Dirichlet characters of modulus 1300

sage:H = DirichletGroup(1300)

pari:g = idealstar(,1300,2)

Character group

sage:G.order() pari:g.no
Order	=	480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1300}(651,\cdot)$, $\chi_{1300}(677,\cdot)$, $\chi_{1300}(301,\cdot)$

First 32 of 480 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{1300}(1,\cdot)$	1300.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1300}(3,\cdot)$	1300.cu	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{1300}(7,\cdot)$	1300.bt	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{1300}(9,\cdot)$	1300.cm	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1300}(11,\cdot)$	1300.cq	60	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1300}(17,\cdot)$	1300.cv	60	no	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1300}(19,\cdot)$	1300.db	60	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1300}(21,\cdot)$	1300.by	20	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1300}(23,\cdot)$	1300.cx	60	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{1300}(27,\cdot)$	1300.cd	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1300}(29,\cdot)$	1300.cm	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1300}(31,\cdot)$	1300.ci	20	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1300}(33,\cdot)$	1300.cz	60	no	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1300}(37,\cdot)$	1300.cs	60	no	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1300}(41,\cdot)$	1300.da	60	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1300}(43,\cdot)$	1300.bo	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{1300}(47,\cdot)$	1300.ca	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1300}(49,\cdot)$	1300.ba	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{1300}(51,\cdot)$	1300.e	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{1300}(53,\cdot)$	1300.cb	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1300}(57,\cdot)$	1300.m	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$i$	$i$	$i$	$i$	$-1$
$\chi_{1300}(59,\cdot)$	1300.db	60	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1300}(61,\cdot)$	1300.bw	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1300}(63,\cdot)$	1300.ct	60	yes	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1300}(67,\cdot)$	1300.ct	60	yes	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1300}(69,\cdot)$	1300.cj	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1300}(71,\cdot)$	1300.cq	60	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1300}(73,\cdot)$	1300.bz	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1300}(77,\cdot)$	1300.ce	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1300}(79,\cdot)$	1300.bf	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1300}(81,\cdot)$	1300.bw	15	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1300}(83,\cdot)$	1300.ca	20	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$

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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	$1300$
Structure	\(C_{2}\times C_{4}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1300}(1,\cdot)\)	1300.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1300}(3,\cdot)\)	1300.cu	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{1300}(7,\cdot)\)	1300.bt	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1300}(9,\cdot)\)	1300.cm	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1300}(11,\cdot)\)	1300.cq	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1300}(17,\cdot)\)	1300.cv	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1300}(19,\cdot)\)	1300.db	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1300}(21,\cdot)\)	1300.by	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1300}(23,\cdot)\)	1300.cx	60	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{1300}(27,\cdot)\)	1300.cd	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1300}(29,\cdot)\)	1300.cm	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1300}(31,\cdot)\)	1300.ci	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1300}(33,\cdot)\)	1300.cz	60	no	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1300}(37,\cdot)\)	1300.cs	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1300}(41,\cdot)\)	1300.da	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1300}(43,\cdot)\)	1300.bo	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1300}(47,\cdot)\)	1300.ca	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1300}(49,\cdot)\)	1300.ba	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1300}(51,\cdot)\)	1300.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1300}(53,\cdot)\)	1300.cb	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1300}(57,\cdot)\)	1300.m	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{1300}(59,\cdot)\)	1300.db	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1300}(61,\cdot)\)	1300.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1300}(63,\cdot)\)	1300.ct	60	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1300}(67,\cdot)\)	1300.ct	60	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1300}(69,\cdot)\)	1300.cj	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1300}(71,\cdot)\)	1300.cq	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1300}(73,\cdot)\)	1300.bz	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1300}(77,\cdot)\)	1300.ce	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1300}(79,\cdot)\)	1300.bf	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1300}(81,\cdot)\)	1300.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1300}(83,\cdot)\)	1300.ca	20	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)

Introduction

L-functions

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Character group

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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.