LMFDB - Group of Dirichlet characters of modulus 6300

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6300)

pari: g = idealstar(,6300,2)

Character group

sage: G.order() pari: g.no
Order	=	1440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6300}(3151,\cdot)$, $\chi_{6300}(2801,\cdot)$, $\chi_{6300}(3277,\cdot)$, $\chi_{6300}(3601,\cdot)$

First 32 of 1440 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{6300}(1,\cdot)$	6300.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6300}(11,\cdot)$	6300.hj	30	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{6300}(13,\cdot)$	6300.iq	60	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{6300}(17,\cdot)$	6300.ik	60	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{6300}(19,\cdot)$	6300.gc	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{6300}(23,\cdot)$	6300.iy	60	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{6300}(29,\cdot)$	6300.gd	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{6300}(31,\cdot)$	6300.ht	30	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6300}(37,\cdot)$	6300.iv	60	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{4}{5}\right)$	$-i$
$\chi_{6300}(41,\cdot)$	6300.ge	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6300}(43,\cdot)$	6300.fb	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{6300}(47,\cdot)$	6300.ib	60	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{6300}(53,\cdot)$	6300.ig	60	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{6300}(59,\cdot)$	6300.fx	30	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6300}(61,\cdot)$	6300.fs	30	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6300}(67,\cdot)$	6300.je	60	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{6300}(71,\cdot)$	6300.dn	10	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$
$\chi_{6300}(73,\cdot)$	6300.iz	60	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{6300}(79,\cdot)$	6300.hs	30	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6300}(83,\cdot)$	6300.jb	60	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{6300}(89,\cdot)$	6300.fz	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{6300}(97,\cdot)$	6300.iq	60	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{6300}(101,\cdot)$	6300.cv	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6300}(103,\cdot)$	6300.ih	60	yes	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{6300}(107,\cdot)$	6300.ej	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{6300}(109,\cdot)$	6300.hp	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{6300}(113,\cdot)$	6300.ip	60	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{6300}(121,\cdot)$	6300.fj	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6300}(127,\cdot)$	6300.fp	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{6300}(131,\cdot)$	6300.hf	30	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6300}(137,\cdot)$	6300.ii	60	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{6300}(139,\cdot)$	6300.gl	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$

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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	$6300$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{60}\)
Order	$1440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{6300}(1,\cdot)\)	6300.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6300}(11,\cdot)\)	6300.hj	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6300}(13,\cdot)\)	6300.iq	60	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{6300}(17,\cdot)\)	6300.ik	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{6300}(19,\cdot)\)	6300.gc	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{6300}(23,\cdot)\)	6300.iy	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{6300}(29,\cdot)\)	6300.gd	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6300}(31,\cdot)\)	6300.ht	30	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6300}(37,\cdot)\)	6300.iv	60	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)
\(\chi_{6300}(41,\cdot)\)	6300.ge	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6300}(43,\cdot)\)	6300.fb	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{6300}(47,\cdot)\)	6300.ib	60	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{6300}(53,\cdot)\)	6300.ig	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{6300}(59,\cdot)\)	6300.fx	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6300}(61,\cdot)\)	6300.fs	30	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6300}(67,\cdot)\)	6300.je	60	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{6300}(71,\cdot)\)	6300.dn	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)
\(\chi_{6300}(73,\cdot)\)	6300.iz	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)
\(\chi_{6300}(79,\cdot)\)	6300.hs	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6300}(83,\cdot)\)	6300.jb	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{6300}(89,\cdot)\)	6300.fz	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{6300}(97,\cdot)\)	6300.iq	60	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{6300}(101,\cdot)\)	6300.cv	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6300}(103,\cdot)\)	6300.ih	60	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{6300}(107,\cdot)\)	6300.ej	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{6300}(109,\cdot)\)	6300.hp	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{6300}(113,\cdot)\)	6300.ip	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{6300}(121,\cdot)\)	6300.fj	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6300}(127,\cdot)\)	6300.fp	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{6300}(131,\cdot)\)	6300.hf	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6300}(137,\cdot)\)	6300.ii	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{6300}(139,\cdot)\)	6300.gl	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.