LMFDB - Group of Dirichlet characters of modulus 229320

Show commands: PariGP / SageMath

sage: H = DirichletGroup(229320)

pari: g = idealstar(,229320,2)

Character group

sage: G.order() pari: g.no
Order	=	48384
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{12}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{229320}(171991,\cdot)$, $\chi_{229320}(114661,\cdot)$, $\chi_{229320}(25481,\cdot)$, $\chi_{229320}(183457,\cdot)$, $\chi_{229320}(18721,\cdot)$, $\chi_{229320}(211681,\cdot)$

First 32 of 48384 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	$-1$	$1$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{229320}(1,\cdot)$	229320.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{229320}(11,\cdot)$	229320.gfa	84	no	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{10}{21}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{229320}(17,\cdot)$	229320.gmf	84	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{229320}(19,\cdot)$	229320.cwb	12	no	$-1$	$1$	$i$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{229320}(23,\cdot)$	229320.gpu	84	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{20}{21}\right)$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{229320}(29,\cdot)$	229320.dsk	42	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{229320}(31,\cdot)$	229320.cbm	12	no	$-1$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{229320}(37,\cdot)$	229320.fxk	84	no	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{229320}(41,\cdot)$	229320.ffe	84	no	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{229320}(43,\cdot)$	229320.eyx	84	yes	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{229320}(47,\cdot)$	229320.fvo	84	no	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{229320}(53,\cdot)$	229320.gkx	84	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{229320}(59,\cdot)$	229320.fdp	84	yes	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{229320}(61,\cdot)$	229320.dyw	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{37}{42}\right)$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{229320}(67,\cdot)$	229320.cgg	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{229320}(71,\cdot)$	229320.gcc	84	no	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{42}\right)$	$i$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{229320}(73,\cdot)$	229320.fyq	84	no	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{229320}(79,\cdot)$	229320.ko	6	no	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{229320}(83,\cdot)$	229320.fru	84	yes	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{3}{28}\right)$	$-i$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{229320}(89,\cdot)$	229320.feo	84	no	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{229320}(97,\cdot)$	229320.cnj	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{229320}(101,\cdot)$	229320.dzq	42	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{229320}(103,\cdot)$	229320.gjq	84	no	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{42}\right)$	$-1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{229320}(107,\cdot)$	229320.faf	84	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{229320}(109,\cdot)$	229320.gew	84	no	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{229320}(113,\cdot)$	229320.gpc	84	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{229320}(121,\cdot)$	229320.dzd	42	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{229320}(127,\cdot)$	229320.glw	84	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{42}\right)$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{229320}(131,\cdot)$	229320.eby	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{21}\right)$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{229320}(137,\cdot)$	229320.ftf	84	no	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{21}\right)$	$i$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{229320}(139,\cdot)$	229320.dsm	42	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{229320}(149,\cdot)$	229320.fjl	84	yes	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{13}{42}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{28}\right)$

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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	$229320$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{12}\times C_{84}\)
Order	$48384$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{229320}(1,\cdot)\)	229320.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{229320}(11,\cdot)\)	229320.gfa	84	no	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{229320}(17,\cdot)\)	229320.gmf	84	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{229320}(19,\cdot)\)	229320.cwb	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{229320}(23,\cdot)\)	229320.gpu	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{229320}(29,\cdot)\)	229320.dsk	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{229320}(31,\cdot)\)	229320.cbm	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{229320}(37,\cdot)\)	229320.fxk	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{229320}(41,\cdot)\)	229320.ffe	84	no	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{229320}(43,\cdot)\)	229320.eyx	84	yes	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{229320}(47,\cdot)\)	229320.fvo	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{229320}(53,\cdot)\)	229320.gkx	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{229320}(59,\cdot)\)	229320.fdp	84	yes	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{229320}(61,\cdot)\)	229320.dyw	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{229320}(67,\cdot)\)	229320.cgg	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{229320}(71,\cdot)\)	229320.gcc	84	no	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(i\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{229320}(73,\cdot)\)	229320.fyq	84	no	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{229320}(79,\cdot)\)	229320.ko	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{229320}(83,\cdot)\)	229320.fru	84	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-i\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{229320}(89,\cdot)\)	229320.feo	84	no	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{229320}(97,\cdot)\)	229320.cnj	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{229320}(101,\cdot)\)	229320.dzq	42	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{229320}(103,\cdot)\)	229320.gjq	84	no	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{229320}(107,\cdot)\)	229320.faf	84	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{229320}(109,\cdot)\)	229320.gew	84	no	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{229320}(113,\cdot)\)	229320.gpc	84	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{229320}(121,\cdot)\)	229320.dzd	42	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{229320}(127,\cdot)\)	229320.glw	84	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{229320}(131,\cdot)\)	229320.eby	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{229320}(137,\cdot)\)	229320.ftf	84	no	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(i\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{229320}(139,\cdot)\)	229320.dsm	42	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{229320}(149,\cdot)\)	229320.fjl	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)

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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.