LMFDB - Group of Dirichlet characters of modulus 975

Show commands: PariGP / SageMath

sage: H = DirichletGroup(975)

pari: g = idealstar(,975,2)

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	=	$\chi_{975}(326,\cdot)$, $\chi_{975}(352,\cdot)$, $\chi_{975}(301,\cdot)$

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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{975}(1,\cdot)$	975.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{975}(2,\cdot)$	975.cr	60	yes	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{975}(4,\cdot)$	975.cn	30	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{975}(7,\cdot)$	975.bu	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{975}(8,\cdot)$	975.ch	20	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{975}(11,\cdot)$	975.cx	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{975}(14,\cdot)$	975.be	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{975}(16,\cdot)$	975.bw	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{975}(17,\cdot)$	975.cy	60	yes	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{975}(19,\cdot)$	975.cv	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{975}(22,\cdot)$	975.cz	60	no	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{975}(23,\cdot)$	975.cy	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{975}(28,\cdot)$	975.cq	60	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{975}(29,\cdot)$	975.co	30	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{975}(31,\cdot)$	975.cc	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{975}(32,\cdot)$	975.bv	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{975}(34,\cdot)$	975.cb	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{975}(37,\cdot)$	975.cq	60	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{975}(38,\cdot)$	975.bz	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{975}(41,\cdot)$	975.cx	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{975}(43,\cdot)$	975.bs	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{975}(44,\cdot)$	975.ce	20	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{975}(46,\cdot)$	975.cu	60	no	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{975}(47,\cdot)$	975.by	20	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{975}(49,\cdot)$	975.w	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{975}(53,\cdot)$	975.cf	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{975}(56,\cdot)$	975.cp	30	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{975}(58,\cdot)$	975.cq	60	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{975}(59,\cdot)$	975.cw	60	yes	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{975}(61,\cdot)$	975.bw	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{975}(62,\cdot)$	975.cy	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{975}(64,\cdot)$	975.bf	10	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$

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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 $\F_{q}$

Modulus	$975$
Structure	\(C_{2}\times C_{4}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{975}(1,\cdot)\)	975.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{975}(2,\cdot)\)	975.cr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{975}(4,\cdot)\)	975.cn	30	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{975}(7,\cdot)\)	975.bu	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{975}(8,\cdot)\)	975.ch	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{975}(11,\cdot)\)	975.cx	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{975}(14,\cdot)\)	975.be	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{975}(16,\cdot)\)	975.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{975}(17,\cdot)\)	975.cy	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{975}(19,\cdot)\)	975.cv	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{975}(22,\cdot)\)	975.cz	60	no	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{975}(23,\cdot)\)	975.cy	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{975}(28,\cdot)\)	975.cq	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{975}(29,\cdot)\)	975.co	30	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{975}(31,\cdot)\)	975.cc	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{975}(32,\cdot)\)	975.bv	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{975}(34,\cdot)\)	975.cb	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{975}(37,\cdot)\)	975.cq	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{975}(38,\cdot)\)	975.bz	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{975}(41,\cdot)\)	975.cx	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{975}(43,\cdot)\)	975.bs	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{975}(44,\cdot)\)	975.ce	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{975}(46,\cdot)\)	975.cu	60	no	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{975}(47,\cdot)\)	975.by	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{975}(49,\cdot)\)	975.w	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{975}(53,\cdot)\)	975.cf	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{975}(56,\cdot)\)	975.cp	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{975}(58,\cdot)\)	975.cq	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{975}(59,\cdot)\)	975.cw	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{975}(61,\cdot)\)	975.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{975}(62,\cdot)\)	975.cy	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{975}(64,\cdot)\)	975.bf	10	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)

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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.