LMFDB - Group of Dirichlet characters of modulus 8624

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8624)

pari: g = idealstar(,8624,2)

Character group

sage: G.order() pari: g.no
Order	=	3360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8624}(5391,\cdot)$, $\chi_{8624}(6469,\cdot)$, $\chi_{8624}(7745,\cdot)$, $\chi_{8624}(3137,\cdot)$

First 32 of 3360 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	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{8624}(1,\cdot)$	8624.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8624}(3,\cdot)$	8624.hf	420	yes	$1$	$1$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{73}{140}\right)$
$\chi_{8624}(5,\cdot)$	8624.hi	420	yes	$-1$	$1$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{129}{140}\right)$
$\chi_{8624}(9,\cdot)$	8624.gy	210	no	$1$	$1$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{3}{70}\right)$
$\chi_{8624}(13,\cdot)$	8624.gm	140	yes	$1$	$1$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{71}{140}\right)$
$\chi_{8624}(15,\cdot)$	8624.fo	70	no	$-1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{8624}(17,\cdot)$	8624.ha	210	no	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{8624}(19,\cdot)$	8624.fg	60	no	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8624}(23,\cdot)$	8624.ev	42	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{8624}(25,\cdot)$	8624.gy	210	no	$1$	$1$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{8624}(27,\cdot)$	8624.gf	140	yes	$1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{8624}(29,\cdot)$	8624.gj	140	yes	$-1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{117}{140}\right)$
$\chi_{8624}(31,\cdot)$	8624.ee	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{8624}(37,\cdot)$	8624.hh	420	yes	$1$	$1$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{47}{140}\right)$
$\chi_{8624}(39,\cdot)$	8624.gt	210	no	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{8624}(41,\cdot)$	8624.fu	70	no	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{8624}(43,\cdot)$	8624.ds	28	yes	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$-i$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{8624}(45,\cdot)$	8624.fx	84	no	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{8624}(47,\cdot)$	8624.gr	210	no	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{8624}(51,\cdot)$	8624.he	420	yes	$1$	$1$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{127}{140}\right)$
$\chi_{8624}(53,\cdot)$	8624.hh	420	yes	$1$	$1$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{51}{140}\right)$
$\chi_{8624}(57,\cdot)$	8624.fj	70	no	$-1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{8624}(59,\cdot)$	8624.hf	420	yes	$1$	$1$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{8624}(61,\cdot)$	8624.hg	420	yes	$1$	$1$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{19}{140}\right)$
$\chi_{8624}(65,\cdot)$	8624.ex	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{8624}(67,\cdot)$	8624.cg	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$
$\chi_{8624}(69,\cdot)$	8624.gk	140	yes	$-1$	$1$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{33}{140}\right)$
$\chi_{8624}(71,\cdot)$	8624.fq	70	no	$-1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{8624}(73,\cdot)$	8624.gn	210	no	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{8624}(75,\cdot)$	8624.hf	420	yes	$1$	$1$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{51}{140}\right)$
$\chi_{8624}(79,\cdot)$	8624.ea	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{8624}(81,\cdot)$	8624.ge	105	no	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{3}{35}\right)$

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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	$8624$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{420}\)
Order	$3360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{8624}(1,\cdot)\)	8624.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8624}(3,\cdot)\)	8624.hf	420	yes	\(1\)	\(1\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{73}{140}\right)\)
\(\chi_{8624}(5,\cdot)\)	8624.hi	420	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{129}{140}\right)\)
\(\chi_{8624}(9,\cdot)\)	8624.gy	210	no	\(1\)	\(1\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)
\(\chi_{8624}(13,\cdot)\)	8624.gm	140	yes	\(1\)	\(1\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)
\(\chi_{8624}(15,\cdot)\)	8624.fo	70	no	\(-1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{8624}(17,\cdot)\)	8624.ha	210	no	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{8624}(19,\cdot)\)	8624.fg	60	no	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8624}(23,\cdot)\)	8624.ev	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{8624}(25,\cdot)\)	8624.gy	210	no	\(1\)	\(1\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{8624}(27,\cdot)\)	8624.gf	140	yes	\(1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{8624}(29,\cdot)\)	8624.gj	140	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{117}{140}\right)\)
\(\chi_{8624}(31,\cdot)\)	8624.ee	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{8624}(37,\cdot)\)	8624.hh	420	yes	\(1\)	\(1\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{47}{140}\right)\)
\(\chi_{8624}(39,\cdot)\)	8624.gt	210	no	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{8624}(41,\cdot)\)	8624.fu	70	no	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{8624}(43,\cdot)\)	8624.ds	28	yes	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-i\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{8624}(45,\cdot)\)	8624.fx	84	no	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{8624}(47,\cdot)\)	8624.gr	210	no	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{8624}(51,\cdot)\)	8624.he	420	yes	\(1\)	\(1\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{127}{140}\right)\)
\(\chi_{8624}(53,\cdot)\)	8624.hh	420	yes	\(1\)	\(1\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{51}{140}\right)\)
\(\chi_{8624}(57,\cdot)\)	8624.fj	70	no	\(-1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)
\(\chi_{8624}(59,\cdot)\)	8624.hf	420	yes	\(1\)	\(1\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{8624}(61,\cdot)\)	8624.hg	420	yes	\(1\)	\(1\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{19}{140}\right)\)
\(\chi_{8624}(65,\cdot)\)	8624.ex	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{8624}(67,\cdot)\)	8624.cg	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)
\(\chi_{8624}(69,\cdot)\)	8624.gk	140	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{33}{140}\right)\)
\(\chi_{8624}(71,\cdot)\)	8624.fq	70	no	\(-1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{8624}(73,\cdot)\)	8624.gn	210	no	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{8624}(75,\cdot)\)	8624.hf	420	yes	\(1\)	\(1\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{51}{140}\right)\)
\(\chi_{8624}(79,\cdot)\)	8624.ea	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{8624}(81,\cdot)\)	8624.ge	105	no	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)

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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.