LMFDB - Group of Dirichlet characters of modulus 4176

sage:H = DirichletGroup(4176)

pari:g = idealstar(,4176,2)

Character group

sage:G.order() pari:g.no
Order	=	1344
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{84}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{4176}(1567,\cdot)$, $\chi_{4176}(1045,\cdot)$, $\chi_{4176}(929,\cdot)$, $\chi_{4176}(4033,\cdot)$

First 32 of 1344 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$31$	$35$
$\chi_{4176}(1,\cdot)$	4176.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4176}(5,\cdot)$	4176.fp	84	yes	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{47}{84}\right)$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4176}(7,\cdot)$	4176.et	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{23}{42}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4176}(11,\cdot)$	4176.fy	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{84}\right)$	$i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{4176}(13,\cdot)$	4176.fm	84	yes	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{41}{84}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{4176}(17,\cdot)$	4176.bn	4	no	$1$	$1$	$1$	$1$	$i$	$-1$	$i$	$-i$	$-1$	$1$	$-i$	$1$
$\chi_{4176}(19,\cdot)$	4176.dy	28	no	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$-i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(23,\cdot)$	4176.ez	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{42}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{4176}(25,\cdot)$	4176.ev	42	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{42}\right)$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{4176}(31,\cdot)$	4176.fg	84	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{42}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4176}(35,\cdot)$	4176.ec	28	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{28}\right)$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{4176}(37,\cdot)$	4176.el	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{28}\right)$	$i$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{4176}(41,\cdot)$	4176.cz	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$
$\chi_{4176}(43,\cdot)$	4176.fs	84	yes	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{37}{84}\right)$	$-i$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{4176}(47,\cdot)$	4176.ga	84	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{42}\right)$	$-i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{4176}(49,\cdot)$	4176.ds	21	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4176}(53,\cdot)$	4176.eh	28	no	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4176}(55,\cdot)$	4176.dv	28	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{7}\right)$	$i$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{4176}(59,\cdot)$	4176.cm	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$
$\chi_{4176}(61,\cdot)$	4176.fk	84	yes	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{67}{84}\right)$	$-i$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{4176}(65,\cdot)$	4176.ew	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{21}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{4176}(67,\cdot)$	4176.fv	84	yes	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{29}{84}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{4176}(71,\cdot)$	4176.dh	14	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{4176}(73,\cdot)$	4176.dt	28	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{6}{7}\right)$	$i$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{4176}(77,\cdot)$	4176.fq	84	yes	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{84}\right)$	$i$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(79,\cdot)$	4176.fg	84	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{42}\right)$	$-i$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4176}(83,\cdot)$	4176.fu	84	yes	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{73}{84}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(85,\cdot)$	4176.fk	84	yes	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{84}\right)$	$i$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4176}(89,\cdot)$	4176.en	28	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$	$i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{4176}(91,\cdot)$	4176.dz	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(95,\cdot)$	4176.ga	84	no	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{25}{42}\right)$	$-i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{4176}(97,\cdot)$	4176.fi	84	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{42}\right)$	$i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{14}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$4176$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{84}\)
Order	$1344$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\(\chi_{4176}(1,\cdot)\)	4176.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4176}(5,\cdot)\)	4176.fp	84	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4176}(7,\cdot)\)	4176.et	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{4176}(11,\cdot)\)	4176.fy	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{4176}(13,\cdot)\)	4176.fm	84	yes	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{4176}(17,\cdot)\)	4176.bn	4	no	\(1\)	\(1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(1\)
\(\chi_{4176}(19,\cdot)\)	4176.dy	28	no	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(23,\cdot)\)	4176.ez	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{4176}(25,\cdot)\)	4176.ev	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{4176}(31,\cdot)\)	4176.fg	84	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4176}(35,\cdot)\)	4176.ec	28	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{4176}(37,\cdot)\)	4176.el	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(i\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{4176}(41,\cdot)\)	4176.cz	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)
\(\chi_{4176}(43,\cdot)\)	4176.fs	84	yes	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(-i\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{4176}(47,\cdot)\)	4176.ga	84	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(-i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{4176}(49,\cdot)\)	4176.ds	21	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{4176}(53,\cdot)\)	4176.eh	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4176}(55,\cdot)\)	4176.dv	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(i\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{4176}(59,\cdot)\)	4176.cm	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)
\(\chi_{4176}(61,\cdot)\)	4176.fk	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{4176}(65,\cdot)\)	4176.ew	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{4176}(67,\cdot)\)	4176.fv	84	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{4176}(71,\cdot)\)	4176.dh	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{4176}(73,\cdot)\)	4176.dt	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(i\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{4176}(77,\cdot)\)	4176.fq	84	yes	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(79,\cdot)\)	4176.fg	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-i\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{4176}(83,\cdot)\)	4176.fu	84	yes	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(85,\cdot)\)	4176.fk	84	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(i\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4176}(89,\cdot)\)	4176.en	28	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{4176}(91,\cdot)\)	4176.dz	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(95,\cdot)\)	4176.ga	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{4176}(97,\cdot)\)	4176.fi	84	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)

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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.