LMFDB - Group of Dirichlet characters of modulus 1216

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1216)

pari: g = idealstar(,1216,2)

Character group

sage: G.order() pari: g.no
Order	=	576
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{144}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1216}(191,\cdot)$, $\chi_{1216}(837,\cdot)$, $\chi_{1216}(705,\cdot)$

First 32 of 576 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{1216}(1,\cdot)$	1216.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1216}(3,\cdot)$	1216.ch	144	yes	$1$	$1$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{1216}(5,\cdot)$	1216.cg	144	yes	$1$	$1$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{1216}(7,\cdot)$	1216.bo	24	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{24}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1216}(9,\cdot)$	1216.ca	72	no	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{1216}(11,\cdot)$	1216.bz	48	yes	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{1216}(13,\cdot)$	1216.cf	144	yes	$-1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{1216}(15,\cdot)$	1216.bs	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1216}(17,\cdot)$	1216.bu	36	no	$1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1216}(21,\cdot)$	1216.cf	144	yes	$-1$	$1$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{1216}(23,\cdot)$	1216.cc	72	no	$-1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{1216}(25,\cdot)$	1216.ca	72	no	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{1216}(27,\cdot)$	1216.bw	48	yes	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{1216}(29,\cdot)$	1216.cf	144	yes	$-1$	$1$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{1216}(31,\cdot)$	1216.s	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1216}(33,\cdot)$	1216.bi	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1216}(35,\cdot)$	1216.ce	144	yes	$-1$	$1$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{1216}(37,\cdot)$	1216.bg	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1216}(39,\cdot)$	1216.x	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{1216}(41,\cdot)$	1216.cd	72	no	$-1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{1216}(43,\cdot)$	1216.ce	144	yes	$-1$	$1$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{1216}(45,\cdot)$	1216.bx	48	yes	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{1216}(47,\cdot)$	1216.bt	36	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1216}(49,\cdot)$	1216.z	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1216}(51,\cdot)$	1216.ch	144	yes	$1$	$1$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{1216}(53,\cdot)$	1216.cf	144	yes	$-1$	$1$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{1216}(55,\cdot)$	1216.cc	72	no	$-1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{1216}(59,\cdot)$	1216.ch	144	yes	$1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{1216}(61,\cdot)$	1216.cg	144	yes	$1$	$1$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{1216}(63,\cdot)$	1216.bn	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{1216}(65,\cdot)$	1216.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1216}(67,\cdot)$	1216.ch	144	yes	$1$	$1$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{1}{72}\right)$

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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	$1216$
Structure	\(C_{2}\times C_{2}\times C_{144}\)
Order	$576$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{1216}(1,\cdot)\)	1216.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1216}(3,\cdot)\)	1216.ch	144	yes	\(1\)	\(1\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)
\(\chi_{1216}(5,\cdot)\)	1216.cg	144	yes	\(1\)	\(1\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{47}{72}\right)\)
\(\chi_{1216}(7,\cdot)\)	1216.bo	24	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1216}(9,\cdot)\)	1216.ca	72	no	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{1216}(11,\cdot)\)	1216.bz	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{1216}(13,\cdot)\)	1216.cf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{1216}(15,\cdot)\)	1216.bs	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1216}(17,\cdot)\)	1216.bu	36	no	\(1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1216}(21,\cdot)\)	1216.cf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{1216}(23,\cdot)\)	1216.cc	72	no	\(-1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{1216}(25,\cdot)\)	1216.ca	72	no	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{1216}(27,\cdot)\)	1216.bw	48	yes	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{1216}(29,\cdot)\)	1216.cf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{37}{72}\right)\)
\(\chi_{1216}(31,\cdot)\)	1216.s	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1216}(33,\cdot)\)	1216.bi	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1216}(35,\cdot)\)	1216.ce	144	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)
\(\chi_{1216}(37,\cdot)\)	1216.bg	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1216}(39,\cdot)\)	1216.x	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{1216}(41,\cdot)\)	1216.cd	72	no	\(-1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{1216}(43,\cdot)\)	1216.ce	144	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{47}{72}\right)\)
\(\chi_{1216}(45,\cdot)\)	1216.bx	48	yes	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{1216}(47,\cdot)\)	1216.bt	36	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1216}(49,\cdot)\)	1216.z	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1216}(51,\cdot)\)	1216.ch	144	yes	\(1\)	\(1\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{13}{72}\right)\)
\(\chi_{1216}(53,\cdot)\)	1216.cf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{1216}(55,\cdot)\)	1216.cc	72	no	\(-1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{1216}(59,\cdot)\)	1216.ch	144	yes	\(1\)	\(1\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{1216}(61,\cdot)\)	1216.cg	144	yes	\(1\)	\(1\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)
\(\chi_{1216}(63,\cdot)\)	1216.bn	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{1216}(65,\cdot)\)	1216.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1216}(67,\cdot)\)	1216.ch	144	yes	\(1\)	\(1\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{1}{72}\right)\)

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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.