LMFDB - Group of Dirichlet characters of modulus 4056

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4056)

pari: g = idealstar(,4056,2)

Character group

sage: G.order() pari: g.no
Order	=	1248
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4056}(1015,\cdot)$, $\chi_{4056}(2029,\cdot)$, $\chi_{4056}(2705,\cdot)$, $\chi_{4056}(3889,\cdot)$

First 32 of 1248 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{4056}(1,\cdot)$	4056.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4056}(5,\cdot)$	4056.cp	52	yes	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$i$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4056}(7,\cdot)$	4056.dl	156	no	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{4056}(11,\cdot)$	4056.dr	156	yes	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{4056}(17,\cdot)$	4056.cx	78	no	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{4056}(19,\cdot)$	4056.bt	12	no	$1$	$1$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{4056}(23,\cdot)$	4056.bj	6	no	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{4056}(25,\cdot)$	4056.ck	26	no	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4056}(29,\cdot)$	4056.db	78	yes	$-1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{4056}(31,\cdot)$	4056.ct	52	no	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{26}\right)$	$i$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{4056}(35,\cdot)$	4056.cv	78	yes	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{4056}(37,\cdot)$	4056.dm	156	no	$-1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{4056}(41,\cdot)$	4056.do	156	no	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{4056}(43,\cdot)$	4056.da	78	no	$-1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{4056}(47,\cdot)$	4056.co	52	no	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4056}(49,\cdot)$	4056.dd	78	no	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{4056}(53,\cdot)$	4056.bx	26	yes	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{21}{26}\right)$	$-1$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4056}(55,\cdot)$	4056.cw	78	no	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{4056}(59,\cdot)$	4056.dr	156	yes	$-1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{4056}(61,\cdot)$	4056.dh	78	no	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{4056}(67,\cdot)$	4056.dk	156	no	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{4056}(71,\cdot)$	4056.dq	156	no	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{4056}(73,\cdot)$	4056.cr	52	no	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{26}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4056}(77,\cdot)$	4056.cl	26	yes	$-1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{26}\right)$	$1$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4056}(79,\cdot)$	4056.cc	26	no	$-1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{6}{13}\right)$	$-1$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{4056}(83,\cdot)$	4056.cn	52	yes	$-1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{8}{13}\right)$	$-i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{4056}(85,\cdot)$	4056.dm	156	no	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{4056}(89,\cdot)$	4056.bp	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{4056}(95,\cdot)$	4056.cz	78	no	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{4056}(97,\cdot)$	4056.dn	156	no	$-1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{4056}(101,\cdot)$	4056.dc	78	yes	$-1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{4056}(103,\cdot)$	4056.ce	26	no	$-1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{26}\right)$

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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	$4056$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{156}\)
Order	$1248$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{4056}(1,\cdot)\)	4056.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4056}(5,\cdot)\)	4056.cp	52	yes	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4056}(7,\cdot)\)	4056.dl	156	no	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{4056}(11,\cdot)\)	4056.dr	156	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{4056}(17,\cdot)\)	4056.cx	78	no	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{4056}(19,\cdot)\)	4056.bt	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4056}(23,\cdot)\)	4056.bj	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4056}(25,\cdot)\)	4056.ck	26	no	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4056}(29,\cdot)\)	4056.db	78	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{4056}(31,\cdot)\)	4056.ct	52	no	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(i\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{4056}(35,\cdot)\)	4056.cv	78	yes	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{4056}(37,\cdot)\)	4056.dm	156	no	\(-1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{4056}(41,\cdot)\)	4056.do	156	no	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{4056}(43,\cdot)\)	4056.da	78	no	\(-1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{4056}(47,\cdot)\)	4056.co	52	no	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4056}(49,\cdot)\)	4056.dd	78	no	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{4056}(53,\cdot)\)	4056.bx	26	yes	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4056}(55,\cdot)\)	4056.cw	78	no	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{4056}(59,\cdot)\)	4056.dr	156	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{4056}(61,\cdot)\)	4056.dh	78	no	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{4056}(67,\cdot)\)	4056.dk	156	no	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{4056}(71,\cdot)\)	4056.dq	156	no	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{4056}(73,\cdot)\)	4056.cr	52	no	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4056}(77,\cdot)\)	4056.cl	26	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4056}(79,\cdot)\)	4056.cc	26	no	\(-1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{4056}(83,\cdot)\)	4056.cn	52	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{4056}(85,\cdot)\)	4056.dm	156	no	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{4056}(89,\cdot)\)	4056.bp	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4056}(95,\cdot)\)	4056.cz	78	no	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{4056}(97,\cdot)\)	4056.dn	156	no	\(-1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{4056}(101,\cdot)\)	4056.dc	78	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{4056}(103,\cdot)\)	4056.ce	26	no	\(-1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)

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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.