LMFDB - Group of Dirichlet characters of modulus 43120

Show commands: PariGP / SageMath

sage: H = DirichletGroup(43120)

pari: g = idealstar(,43120,2)

Character group

sage: G.order() pari: g.no
Order	=	13440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{43120}(5391,\cdot)$, $\chi_{43120}(32341,\cdot)$, $\chi_{43120}(34497,\cdot)$, $\chi_{43120}(42241,\cdot)$, $\chi_{43120}(11761,\cdot)$

First 32 of 13440 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	$-1$	$1$	$3$	$9$	$13$	$17$	$19$	$23$	$27$	$29$	$31$	$37$
$\chi_{43120}(1,\cdot)$	43120.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{43120}(3,\cdot)$	43120.yp	420	yes	$-1$	$1$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{181}{210}\right)$
$\chi_{43120}(9,\cdot)$	43120.wa	210	no	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{43120}(13,\cdot)$	43120.vk	140	yes	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{43120}(17,\cdot)$	43120.xp	420	no	$-1$	$1$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{420}\right)$
$\chi_{43120}(19,\cdot)$	43120.pj	60	no	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{43120}(23,\cdot)$	43120.sx	84	no	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{43120}(27,\cdot)$	43120.tx	140	yes	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{43120}(29,\cdot)$	43120.va	140	yes	$-1$	$1$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{140}\right)$
$\chi_{43120}(31,\cdot)$	43120.nj	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{43120}(37,\cdot)$	43120.yk	420	yes	$-1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{210}\right)$
$\chi_{43120}(39,\cdot)$	43120.wf	210	no	$1$	$1$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{43120}(41,\cdot)$	43120.ro	70	no	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{43120}(43,\cdot)$	43120.mh	28	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$i$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{4}{7}\right)$
$\chi_{43120}(47,\cdot)$	43120.xl	420	no	$-1$	$1$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{277}{420}\right)$
$\chi_{43120}(51,\cdot)$	43120.yf	420	no	$1$	$1$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{403}{420}\right)$
$\chi_{43120}(53,\cdot)$	43120.xb	420	yes	$-1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{43120}(57,\cdot)$	43120.uu	140	no	$1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{140}\right)$
$\chi_{43120}(59,\cdot)$	43120.xe	420	yes	$1$	$1$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{420}\right)$
$\chi_{43120}(61,\cdot)$	43120.xc	420	no	$1$	$1$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{391}{420}\right)$
$\chi_{43120}(67,\cdot)$	43120.hj	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{43120}(69,\cdot)$	43120.vb	140	yes	$-1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{140}\right)$
$\chi_{43120}(71,\cdot)$	43120.rl	70	no	$-1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{43120}(73,\cdot)$	43120.xs	420	no	$-1$	$1$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{353}{420}\right)$
$\chi_{43120}(79,\cdot)$	43120.ng	30	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{43120}(81,\cdot)$	43120.ts	105	no	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{43120}(83,\cdot)$	43120.tt	140	yes	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{70}\right)$
$\chi_{43120}(87,\cdot)$	43120.sy	84	no	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{43120}(89,\cdot)$	43120.od	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{43120}(93,\cdot)$	43120.yk	420	yes	$-1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{83}{210}\right)$
$\chi_{43120}(97,\cdot)$	43120.jn	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{43120}(101,\cdot)$	43120.xc	420	no	$1$	$1$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{420}\right)$

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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	$43120$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{420}\)
Order	$13440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)	\(37\)
\(\chi_{43120}(1,\cdot)\)	43120.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{43120}(3,\cdot)\)	43120.yp	420	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{181}{210}\right)\)
\(\chi_{43120}(9,\cdot)\)	43120.wa	210	no	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{43120}(13,\cdot)\)	43120.vk	140	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{43120}(17,\cdot)\)	43120.xp	420	no	\(-1\)	\(1\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{420}\right)\)
\(\chi_{43120}(19,\cdot)\)	43120.pj	60	no	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{43120}(23,\cdot)\)	43120.sx	84	no	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{43120}(27,\cdot)\)	43120.tx	140	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{43120}(29,\cdot)\)	43120.va	140	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{140}\right)\)
\(\chi_{43120}(31,\cdot)\)	43120.nj	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{43120}(37,\cdot)\)	43120.yk	420	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{210}\right)\)
\(\chi_{43120}(39,\cdot)\)	43120.wf	210	no	\(1\)	\(1\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{43120}(41,\cdot)\)	43120.ro	70	no	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{43120}(43,\cdot)\)	43120.mh	28	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(i\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{43120}(47,\cdot)\)	43120.xl	420	no	\(-1\)	\(1\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{277}{420}\right)\)
\(\chi_{43120}(51,\cdot)\)	43120.yf	420	no	\(1\)	\(1\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{403}{420}\right)\)
\(\chi_{43120}(53,\cdot)\)	43120.xb	420	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{43120}(57,\cdot)\)	43120.uu	140	no	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{140}\right)\)
\(\chi_{43120}(59,\cdot)\)	43120.xe	420	yes	\(1\)	\(1\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{420}\right)\)
\(\chi_{43120}(61,\cdot)\)	43120.xc	420	no	\(1\)	\(1\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{391}{420}\right)\)
\(\chi_{43120}(67,\cdot)\)	43120.hj	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{43120}(69,\cdot)\)	43120.vb	140	yes	\(-1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{140}\right)\)
\(\chi_{43120}(71,\cdot)\)	43120.rl	70	no	\(-1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{43120}(73,\cdot)\)	43120.xs	420	no	\(-1\)	\(1\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{353}{420}\right)\)
\(\chi_{43120}(79,\cdot)\)	43120.ng	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{43120}(81,\cdot)\)	43120.ts	105	no	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{43120}(83,\cdot)\)	43120.tt	140	yes	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{70}\right)\)
\(\chi_{43120}(87,\cdot)\)	43120.sy	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{43120}(89,\cdot)\)	43120.od	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{43120}(93,\cdot)\)	43120.yk	420	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{83}{210}\right)\)
\(\chi_{43120}(97,\cdot)\)	43120.jn	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{43120}(101,\cdot)\)	43120.xc	420	no	\(1\)	\(1\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{420}\right)\)

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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.