LMFDB - Group of Dirichlet characters of modulus 6975

sage:H = DirichletGroup(6975)

pari:g = idealstar(,6975,2)

Character group

sage:G.order() pari:g.no
Order	=	3600
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{30}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6975}(776,\cdot)$, $\chi_{6975}(5302,\cdot)$, $\chi_{6975}(1801,\cdot)$

First 32 of 3600 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{6975}(1,\cdot)$	6975.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6975}(2,\cdot)$	6975.px	60	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{60}\right)$	$i$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{10}\right)$
$\chi_{6975}(4,\cdot)$	6975.mb	30	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{5}\right)$
$\chi_{6975}(7,\cdot)$	6975.nx	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{6975}(8,\cdot)$	6975.fe	20	no	$1$	$1$	$i$	$-1$	$e\left(\frac{19}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$1$	$i$	$e\left(\frac{3}{10}\right)$
$\chi_{6975}(11,\cdot)$	6975.ii	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{30}\right)$	$-1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{6975}(13,\cdot)$	6975.pu	60	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$	$i$	$e\left(\frac{29}{30}\right)$	$-i$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{6975}(14,\cdot)$	6975.js	30	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6975}(16,\cdot)$	6975.eg	15	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{5}\right)$
$\chi_{6975}(17,\cdot)$	6975.mp	60	no	$-1$	$1$	$-i$	$-1$	$e\left(\frac{47}{60}\right)$	$i$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{15}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{6975}(19,\cdot)$	6975.lj	30	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{6975}(22,\cdot)$	6975.ni	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{6975}(23,\cdot)$	6975.mu	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{20}\right)$	$-1$
$\chi_{6975}(26,\cdot)$	6975.w	6	no	$1$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6975}(28,\cdot)$	6975.pp	60	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{6975}(29,\cdot)$	6975.jt	30	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$1$
$\chi_{6975}(32,\cdot)$	6975.dy	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-1$
$\chi_{6975}(34,\cdot)$	6975.mh	30	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{19}{30}\right)$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{6975}(37,\cdot)$	6975.pd	60	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{6975}(38,\cdot)$	6975.ov	60	yes	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6975}(41,\cdot)$	6975.hk	30	yes	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{6975}(43,\cdot)$	6975.nh	60	no	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{6975}(44,\cdot)$	6975.go	30	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6975}(46,\cdot)$	6975.ch	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{6975}(47,\cdot)$	6975.nf	60	yes	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{6975}(49,\cdot)$	6975.jc	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{6975}(52,\cdot)$	6975.qd	60	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{60}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{6975}(53,\cdot)$	6975.po	60	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{6975}(56,\cdot)$	6975.ji	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{6975}(58,\cdot)$	6975.nj	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{6975}(59,\cdot)$	6975.gi	30	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{6975}(61,\cdot)$	6975.jm	30	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$6975$
Structure	\(C_{2}\times C_{30}\times C_{60}\)
Order	$3600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{6975}(1,\cdot)\)	6975.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6975}(2,\cdot)\)	6975.px	60	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(i\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{6975}(4,\cdot)\)	6975.mb	30	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{6975}(7,\cdot)\)	6975.nx	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{6975}(8,\cdot)\)	6975.fe	20	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{6975}(11,\cdot)\)	6975.ii	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{6975}(13,\cdot)\)	6975.pu	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(i\)	\(e\left(\frac{29}{30}\right)\)	\(-i\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{6975}(14,\cdot)\)	6975.js	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6975}(16,\cdot)\)	6975.eg	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{6975}(17,\cdot)\)	6975.mp	60	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{47}{60}\right)\)	\(i\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{6975}(19,\cdot)\)	6975.lj	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{6975}(22,\cdot)\)	6975.ni	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{6975}(23,\cdot)\)	6975.mu	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)
\(\chi_{6975}(26,\cdot)\)	6975.w	6	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6975}(28,\cdot)\)	6975.pp	60	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{6975}(29,\cdot)\)	6975.jt	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)
\(\chi_{6975}(32,\cdot)\)	6975.dy	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-1\)
\(\chi_{6975}(34,\cdot)\)	6975.mh	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{19}{30}\right)\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{6975}(37,\cdot)\)	6975.pd	60	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{6975}(38,\cdot)\)	6975.ov	60	yes	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6975}(41,\cdot)\)	6975.hk	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{6975}(43,\cdot)\)	6975.nh	60	no	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{6975}(44,\cdot)\)	6975.go	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6975}(46,\cdot)\)	6975.ch	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{6975}(47,\cdot)\)	6975.nf	60	yes	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{6975}(49,\cdot)\)	6975.jc	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{6975}(52,\cdot)\)	6975.qd	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{6975}(53,\cdot)\)	6975.po	60	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{6975}(56,\cdot)\)	6975.ji	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{6975}(58,\cdot)\)	6975.nj	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{6975}(59,\cdot)\)	6975.gi	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{6975}(61,\cdot)\)	6975.jm	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)

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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.