LMFDB - Group of Dirichlet characters of modulus 8216

sage:H = DirichletGroup(8216)

pari:g = idealstar(,8216,2)

Character group

sage:G.order() pari:g.no
Order	=	3744
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{156}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{8216}(2055,\cdot)$, $\chi_{8216}(4109,\cdot)$, $\chi_{8216}(3161,\cdot)$, $\chi_{8216}(3953,\cdot)$

First 32 of 3744 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{8216}(1,\cdot)$	8216.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8216}(3,\cdot)$	8216.hu	78	yes	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(5,\cdot)$	8216.ip	156	yes	$-1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(7,\cdot)$	8216.ic	156	no	$-1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(9,\cdot)$	8216.fg	39	no	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(11,\cdot)$	8216.iv	156	yes	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{17}{52}\right)$	$1$
$\chi_{8216}(15,\cdot)$	8216.ix	156	no	$-1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(17,\cdot)$	8216.gt	78	no	$-1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(19,\cdot)$	8216.ia	156	yes	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(21,\cdot)$	8216.fq	52	yes	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$-1$
$\chi_{8216}(23,\cdot)$	8216.cx	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$
$\chi_{8216}(25,\cdot)$	8216.hc	78	no	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(27,\cdot)$	8216.fd	26	no	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{15}{26}\right)$	$-1$
$\chi_{8216}(29,\cdot)$	8216.hg	78	yes	$-1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{3}{26}\right)$	$1$
$\chi_{8216}(31,\cdot)$	8216.io	156	no	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(33,\cdot)$	8216.im	156	no	$1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(35,\cdot)$	8216.gd	78	yes	$1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{26}\right)$	$-1$
$\chi_{8216}(37,\cdot)$	8216.id	156	yes	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(41,\cdot)$	8216.im	156	no	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(43,\cdot)$	8216.gr	78	yes	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{12}{13}\right)$	$-1$
$\chi_{8216}(45,\cdot)$	8216.ig	156	yes	$-1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{3}{52}\right)$	$-1$
$\chi_{8216}(47,\cdot)$	8216.iq	156	no	$-1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(49,\cdot)$	8216.ft	78	no	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(51,\cdot)$	8216.hj	78	yes	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(53,\cdot)$	8216.hd	78	no	$-1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(55,\cdot)$	8216.be	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(57,\cdot)$	8216.fo	52	no	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{52}\right)$	$-1$
$\chi_{8216}(59,\cdot)$	8216.in	156	yes	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{37}{52}\right)$	$1$
$\chi_{8216}(61,\cdot)$	8216.ho	78	yes	$-1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(63,\cdot)$	8216.ic	156	no	$-1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8216}(67,\cdot)$	8216.it	156	yes	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8216}(69,\cdot)$	8216.gz	78	yes	$-1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$

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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	$8216$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{156}\)
Order	$3744$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8216}(1,\cdot)\)	8216.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8216}(3,\cdot)\)	8216.hu	78	yes	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(5,\cdot)\)	8216.ip	156	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(7,\cdot)\)	8216.ic	156	no	\(-1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(9,\cdot)\)	8216.fg	39	no	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(11,\cdot)\)	8216.iv	156	yes	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(1\)
\(\chi_{8216}(15,\cdot)\)	8216.ix	156	no	\(-1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(17,\cdot)\)	8216.gt	78	no	\(-1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(19,\cdot)\)	8216.ia	156	yes	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(21,\cdot)\)	8216.fq	52	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(-1\)
\(\chi_{8216}(23,\cdot)\)	8216.cx	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{8216}(25,\cdot)\)	8216.hc	78	no	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(27,\cdot)\)	8216.fd	26	no	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(-1\)
\(\chi_{8216}(29,\cdot)\)	8216.hg	78	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(1\)
\(\chi_{8216}(31,\cdot)\)	8216.io	156	no	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(33,\cdot)\)	8216.im	156	no	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(35,\cdot)\)	8216.gd	78	yes	\(1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(-1\)
\(\chi_{8216}(37,\cdot)\)	8216.id	156	yes	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(41,\cdot)\)	8216.im	156	no	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(43,\cdot)\)	8216.gr	78	yes	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-1\)
\(\chi_{8216}(45,\cdot)\)	8216.ig	156	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)
\(\chi_{8216}(47,\cdot)\)	8216.iq	156	no	\(-1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(49,\cdot)\)	8216.ft	78	no	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(51,\cdot)\)	8216.hj	78	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(53,\cdot)\)	8216.hd	78	no	\(-1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(55,\cdot)\)	8216.be	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(57,\cdot)\)	8216.fo	52	no	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)
\(\chi_{8216}(59,\cdot)\)	8216.in	156	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(1\)
\(\chi_{8216}(61,\cdot)\)	8216.ho	78	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(63,\cdot)\)	8216.ic	156	no	\(-1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8216}(67,\cdot)\)	8216.it	156	yes	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8216}(69,\cdot)\)	8216.gz	78	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)

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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.