LMFDB - Group of Dirichlet characters of modulus 8775

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(8775)

gp:g = idealstar(,8775,2)

magma:G = FullDirichletGroup(8775);

Character group

Order	=	4320	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{12}\times C_{180}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{8775}(326,\cdot)$, $\chi_{8775}(352,\cdot)$, $\chi_{8775}(8101,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 4320 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{8775}(1,\cdot)$	8775.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8775}(2,\cdot)$	8775.kz	180	yes	$-1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{53}{180}\right)$
$\chi_{8775}(4,\cdot)$	8775.kx	90	yes	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{8775}(7,\cdot)$	8775.ia	36	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{36}\right)$
$\chi_{8775}(8,\cdot)$	8775.in	60	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{8775}(11,\cdot)$	8775.lf	180	yes	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{8775}(14,\cdot)$	8775.kv	90	no	$-1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{8775}(16,\cdot)$	8775.ie	45	yes	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{8775}(17,\cdot)$	8775.jo	60	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{8775}(19,\cdot)$	8775.jd	60	no	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{8775}(22,\cdot)$	8775.lm	180	yes	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{121}{180}\right)$
$\chi_{8775}(23,\cdot)$	8775.lk	180	yes	$1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{103}{180}\right)$
$\chi_{8775}(28,\cdot)$	8775.il	60	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{8775}(29,\cdot)$	8775.kp	90	yes	$-1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{8775}(31,\cdot)$	8775.lg	180	yes	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{8775}(32,\cdot)$	8775.ic	36	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8775}(34,\cdot)$	8775.lz	180	yes	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{8775}(37,\cdot)$	8775.io	60	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{8775}(38,\cdot)$	8775.lr	180	yes	$1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{8775}(41,\cdot)$	8775.ly	180	yes	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{8775}(43,\cdot)$	8775.hq	36	no	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{36}\right)$
$\chi_{8775}(44,\cdot)$	8775.ja	60	no	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{8775}(46,\cdot)$	8775.jc	60	no	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{8775}(47,\cdot)$	8775.mc	180	yes	$-1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{161}{180}\right)$
$\chi_{8775}(49,\cdot)$	8775.ep	18	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{18}\right)$
$\chi_{8775}(53,\cdot)$	8775.fo	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8775}(56,\cdot)$	8775.ks	90	yes	$-1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{8775}(58,\cdot)$	8775.lc	180	yes	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{79}{180}\right)$
$\chi_{8775}(59,\cdot)$	8775.ma	180	yes	$1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{8775}(61,\cdot)$	8775.if	45	yes	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{8775}(62,\cdot)$	8775.jo	60	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8775}(64,\cdot)$	8775.gk	30	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$8775$
Structure	\(C_{2}\times C_{12}\times C_{180}\)
Order	$4320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{8775}(1,\cdot)\)	8775.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8775}(2,\cdot)\)	8775.kz	180	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{53}{180}\right)\)
\(\chi_{8775}(4,\cdot)\)	8775.kx	90	yes	\(1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{8775}(7,\cdot)\)	8775.ia	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8775}(8,\cdot)\)	8775.in	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{8775}(11,\cdot)\)	8775.lf	180	yes	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{8775}(14,\cdot)\)	8775.kv	90	no	\(-1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{8775}(16,\cdot)\)	8775.ie	45	yes	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{8775}(17,\cdot)\)	8775.jo	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{8775}(19,\cdot)\)	8775.jd	60	no	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{8775}(22,\cdot)\)	8775.lm	180	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{121}{180}\right)\)
\(\chi_{8775}(23,\cdot)\)	8775.lk	180	yes	\(1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{103}{180}\right)\)
\(\chi_{8775}(28,\cdot)\)	8775.il	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{8775}(29,\cdot)\)	8775.kp	90	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{8775}(31,\cdot)\)	8775.lg	180	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{8775}(32,\cdot)\)	8775.ic	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8775}(34,\cdot)\)	8775.lz	180	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{8775}(37,\cdot)\)	8775.io	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{8775}(38,\cdot)\)	8775.lr	180	yes	\(1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{8775}(41,\cdot)\)	8775.ly	180	yes	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{8775}(43,\cdot)\)	8775.hq	36	no	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8775}(44,\cdot)\)	8775.ja	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{8775}(46,\cdot)\)	8775.jc	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{8775}(47,\cdot)\)	8775.mc	180	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{161}{180}\right)\)
\(\chi_{8775}(49,\cdot)\)	8775.ep	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{8775}(53,\cdot)\)	8775.fo	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8775}(56,\cdot)\)	8775.ks	90	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{8775}(58,\cdot)\)	8775.lc	180	yes	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{79}{180}\right)\)
\(\chi_{8775}(59,\cdot)\)	8775.ma	180	yes	\(1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{8775}(61,\cdot)\)	8775.if	45	yes	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{8775}(62,\cdot)\)	8775.jo	60	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8775}(64,\cdot)\)	8775.gk	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)

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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.