LMFDB - Group of Dirichlet characters of modulus 129360

Show commands: PariGP / SageMath

sage: H = DirichletGroup(129360)

pari: g = idealstar(,129360,2)

Character group

sage: G.order() pari: g.no
Order	=	26880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{129360}(48511,\cdot)$, $\chi_{129360}(32341,\cdot)$, $\chi_{129360}(43121,\cdot)$, $\chi_{129360}(77617,\cdot)$, $\chi_{129360}(42241,\cdot)$, $\chi_{129360}(11761,\cdot)$

First 32 of 26880 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	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{129360}(1,\cdot)$	129360.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{129360}(13,\cdot)$	129360.bnu	140	no	$-1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{129360}(17,\cdot)$	129360.buv	420	no	$1$	$1$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{389}{420}\right)$
$\chi_{129360}(19,\cdot)$	129360.bet	60	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{17}{30}\right)$
$\chi_{129360}(23,\cdot)$	129360.bmd	84	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{129360}(29,\cdot)$	129360.bok	140	yes	$1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{129360}(31,\cdot)$	129360.bak	30	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{2}{15}\right)$
$\chi_{129360}(37,\cdot)$	129360.bua	420	no	$-1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{277}{420}\right)$
$\chi_{129360}(41,\cdot)$	129360.bht	70	no	$-1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{129360}(43,\cdot)$	129360.yd	28	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$i$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{129360}(47,\cdot)$	129360.bvi	420	no	$1$	$1$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{103}{420}\right)$
$\chi_{129360}(53,\cdot)$	129360.bxb	420	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{101}{420}\right)$
$\chi_{129360}(59,\cdot)$	129360.bwm	420	yes	$-1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{420}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{68}{105}\right)$
$\chi_{129360}(61,\cdot)$	129360.buf	420	no	$1$	$1$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{107}{210}\right)$
$\chi_{129360}(67,\cdot)$	129360.on	12	no	$1$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$
$\chi_{129360}(71,\cdot)$	129360.bhj	70	no	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{129360}(73,\cdot)$	129360.bvn	420	no	$-1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{317}{420}\right)$
$\chi_{129360}(79,\cdot)$	129360.zr	30	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{7}{15}\right)$
$\chi_{129360}(83,\cdot)$	129360.bnn	140	yes	$-1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{140}\right)$
$\chi_{129360}(89,\cdot)$	129360.bco	42	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{129360}(97,\cdot)$	129360.tb	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$
$\chi_{129360}(101,\cdot)$	129360.bwk	420	no	$-1$	$1$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{129360}(103,\cdot)$	129360.bvw	420	no	$-1$	$1$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{127}{420}\right)$
$\chi_{129360}(107,\cdot)$	129360.bwv	420	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{373}{420}\right)$
$\chi_{129360}(109,\cdot)$	129360.bmm	84	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{129360}(113,\cdot)$	129360.bpq	140	no	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{31}{140}\right)$
$\chi_{129360}(127,\cdot)$	129360.bpu	140	no	$-1$	$1$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{140}\right)$
$\chi_{129360}(131,\cdot)$	129360.bki	84	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{129360}(137,\cdot)$	129360.bvp	420	no	$1$	$1$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{419}{420}\right)$
$\chi_{129360}(139,\cdot)$	129360.boj	140	no	$-1$	$1$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{129360}(149,\cdot)$	129360.bwe	420	yes	$1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{129360}(151,\cdot)$	129360.btb	210	no	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{210}\right)$

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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	$129360$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{420}\)
Order	$26880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{129360}(1,\cdot)\)	129360.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{129360}(13,\cdot)\)	129360.bnu	140	no	\(-1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{129360}(17,\cdot)\)	129360.buv	420	no	\(1\)	\(1\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{389}{420}\right)\)
\(\chi_{129360}(19,\cdot)\)	129360.bet	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{129360}(23,\cdot)\)	129360.bmd	84	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{129360}(29,\cdot)\)	129360.bok	140	yes	\(1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{129360}(31,\cdot)\)	129360.bak	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{129360}(37,\cdot)\)	129360.bua	420	no	\(-1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{277}{420}\right)\)
\(\chi_{129360}(41,\cdot)\)	129360.bht	70	no	\(-1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{129360}(43,\cdot)\)	129360.yd	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(i\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{129360}(47,\cdot)\)	129360.bvi	420	no	\(1\)	\(1\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{103}{420}\right)\)
\(\chi_{129360}(53,\cdot)\)	129360.bxb	420	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{101}{420}\right)\)
\(\chi_{129360}(59,\cdot)\)	129360.bwm	420	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{420}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{68}{105}\right)\)
\(\chi_{129360}(61,\cdot)\)	129360.buf	420	no	\(1\)	\(1\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{107}{210}\right)\)
\(\chi_{129360}(67,\cdot)\)	129360.on	12	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{129360}(71,\cdot)\)	129360.bhj	70	no	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{129360}(73,\cdot)\)	129360.bvn	420	no	\(-1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{317}{420}\right)\)
\(\chi_{129360}(79,\cdot)\)	129360.zr	30	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{129360}(83,\cdot)\)	129360.bnn	140	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{140}\right)\)
\(\chi_{129360}(89,\cdot)\)	129360.bco	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{129360}(97,\cdot)\)	129360.tb	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{129360}(101,\cdot)\)	129360.bwk	420	no	\(-1\)	\(1\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{129360}(103,\cdot)\)	129360.bvw	420	no	\(-1\)	\(1\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{127}{420}\right)\)
\(\chi_{129360}(107,\cdot)\)	129360.bwv	420	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{373}{420}\right)\)
\(\chi_{129360}(109,\cdot)\)	129360.bmm	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{129360}(113,\cdot)\)	129360.bpq	140	no	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{31}{140}\right)\)
\(\chi_{129360}(127,\cdot)\)	129360.bpu	140	no	\(-1\)	\(1\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{140}\right)\)
\(\chi_{129360}(131,\cdot)\)	129360.bki	84	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{129360}(137,\cdot)\)	129360.bvp	420	no	\(1\)	\(1\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{419}{420}\right)\)
\(\chi_{129360}(139,\cdot)\)	129360.boj	140	no	\(-1\)	\(1\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{129360}(149,\cdot)\)	129360.bwe	420	yes	\(1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{129360}(151,\cdot)\)	129360.btb	210	no	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{210}\right)\)

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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.