LMFDB - Group of Dirichlet characters of modulus 297

Show commands: PariGP / SageMath

sage: H = DirichletGroup(297)

pari: g = idealstar(,297,2)

Character group

sage: G.order() pari: g.no
Order	=	180
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{90}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{297}(56,\cdot)$, $\chi_{297}(244,\cdot)$

First 32 of 180 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{297}(1,\cdot)$	297.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{297}(2,\cdot)$	297.x	90	yes	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{297}(4,\cdot)$	297.u	45	yes	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{297}(5,\cdot)$	297.v	90	yes	$-1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{297}(7,\cdot)$	297.w	90	yes	$-1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{297}(8,\cdot)$	297.t	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{297}(10,\cdot)$	297.h	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{297}(13,\cdot)$	297.w	90	yes	$-1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{297}(14,\cdot)$	297.v	90	yes	$-1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{297}(16,\cdot)$	297.u	45	yes	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{297}(17,\cdot)$	297.t	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{297}(19,\cdot)$	297.s	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{297}(20,\cdot)$	297.v	90	yes	$-1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{297}(23,\cdot)$	297.p	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{297}(25,\cdot)$	297.u	45	yes	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{297}(26,\cdot)$	297.m	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{297}(28,\cdot)$	297.l	10	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{297}(29,\cdot)$	297.x	90	yes	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{297}(31,\cdot)$	297.u	45	yes	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{297}(32,\cdot)$	297.o	18	yes	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{297}(34,\cdot)$	297.j	9	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{297}(35,\cdot)$	297.t	30	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{297}(37,\cdot)$	297.n	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{297}(38,\cdot)$	297.v	90	yes	$-1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{297}(40,\cdot)$	297.w	90	yes	$-1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{297}(41,\cdot)$	297.x	90	yes	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{297}(43,\cdot)$	297.q	18	yes	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{297}(46,\cdot)$	297.s	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{297}(47,\cdot)$	297.v	90	yes	$-1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{297}(49,\cdot)$	297.u	45	yes	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{297}(50,\cdot)$	297.x	90	yes	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{297}(52,\cdot)$	297.w	90	yes	$-1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{30}\right)$

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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	$297$
Structure	\(C_{2}\times C_{90}\)
Order	$180$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{297}(1,\cdot)\)	297.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{297}(2,\cdot)\)	297.x	90	yes	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{297}(4,\cdot)\)	297.u	45	yes	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{297}(5,\cdot)\)	297.v	90	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{297}(7,\cdot)\)	297.w	90	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{297}(8,\cdot)\)	297.t	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{297}(10,\cdot)\)	297.h	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{297}(13,\cdot)\)	297.w	90	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{297}(14,\cdot)\)	297.v	90	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{297}(16,\cdot)\)	297.u	45	yes	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{297}(17,\cdot)\)	297.t	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{297}(19,\cdot)\)	297.s	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{297}(20,\cdot)\)	297.v	90	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{297}(23,\cdot)\)	297.p	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{297}(25,\cdot)\)	297.u	45	yes	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{297}(26,\cdot)\)	297.m	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{297}(28,\cdot)\)	297.l	10	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{297}(29,\cdot)\)	297.x	90	yes	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{297}(31,\cdot)\)	297.u	45	yes	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{297}(32,\cdot)\)	297.o	18	yes	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{297}(34,\cdot)\)	297.j	9	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{297}(35,\cdot)\)	297.t	30	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{297}(37,\cdot)\)	297.n	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{297}(38,\cdot)\)	297.v	90	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{297}(40,\cdot)\)	297.w	90	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{297}(41,\cdot)\)	297.x	90	yes	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{297}(43,\cdot)\)	297.q	18	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{297}(46,\cdot)\)	297.s	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{297}(47,\cdot)\)	297.v	90	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{297}(49,\cdot)\)	297.u	45	yes	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{297}(50,\cdot)\)	297.x	90	yes	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{297}(52,\cdot)\)	297.w	90	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)

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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.