LMFDB - Group of Dirichlet characters of modulus 3312

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3312)

pari: g = idealstar(,3312,2)

Character group

sage: G.order() pari: g.no
Order	=	1056
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{132}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3312}(415,\cdot)$, $\chi_{3312}(2485,\cdot)$, $\chi_{3312}(2945,\cdot)$, $\chi_{3312}(2305,\cdot)$

First 32 of 1056 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$35$
$\chi_{3312}(1,\cdot)$	3312.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3312}(5,\cdot)$	3312.dp	132	yes	$1$	$1$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{3312}(7,\cdot)$	3312.dh	66	no	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{3312}(11,\cdot)$	3312.dk	132	yes	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{3312}(13,\cdot)$	3312.dl	132	yes	$1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{3312}(17,\cdot)$	3312.ca	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{3312}(19,\cdot)$	3312.cu	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{3312}(25,\cdot)$	3312.cz	66	no	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{3312}(29,\cdot)$	3312.dn	132	yes	$-1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{3312}(31,\cdot)$	3312.de	66	no	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{3312}(35,\cdot)$	3312.cq	44	no	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{3312}(37,\cdot)$	3312.cp	44	no	$-1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{3312}(41,\cdot)$	3312.dj	66	no	$-1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{3312}(43,\cdot)$	3312.dm	132	yes	$1$	$1$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{3312}(47,\cdot)$	3312.bk	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{3312}(49,\cdot)$	3312.cm	33	no	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{3312}(53,\cdot)$	3312.cn	44	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{3312}(55,\cdot)$	3312.cj	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{3312}(59,\cdot)$	3312.dq	132	yes	$1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{3312}(61,\cdot)$	3312.dr	132	yes	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{3312}(65,\cdot)$	3312.dg	66	no	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{3312}(67,\cdot)$	3312.dm	132	yes	$1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{3312}(71,\cdot)$	3312.cd	22	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{3312}(73,\cdot)$	3312.ch	22	no	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{3312}(77,\cdot)$	3312.dn	132	yes	$-1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{3312}(79,\cdot)$	3312.dc	66	no	$1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{3312}(83,\cdot)$	3312.dk	132	yes	$-1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{3312}(85,\cdot)$	3312.dl	132	yes	$1$	$1$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{3312}(89,\cdot)$	3312.cl	22	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{3312}(91,\cdot)$	3312.r	4	no	$1$	$1$	$-i$	$-1$	$i$	$-i$	$-1$	$-i$	$-1$	$-i$	$-1$	$i$
$\chi_{3312}(95,\cdot)$	3312.cy	66	no	$1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{3312}(97,\cdot)$	3312.cw	66	no	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{11}\right)$

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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	$3312$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{132}\)
Order	$1056$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3312}(1,\cdot)\)	3312.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3312}(5,\cdot)\)	3312.dp	132	yes	\(1\)	\(1\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{3312}(7,\cdot)\)	3312.dh	66	no	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{3312}(11,\cdot)\)	3312.dk	132	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{3312}(13,\cdot)\)	3312.dl	132	yes	\(1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{3312}(17,\cdot)\)	3312.ca	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{3312}(19,\cdot)\)	3312.cu	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{3312}(25,\cdot)\)	3312.cz	66	no	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{3312}(29,\cdot)\)	3312.dn	132	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{3312}(31,\cdot)\)	3312.de	66	no	\(-1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{3312}(35,\cdot)\)	3312.cq	44	no	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{3312}(37,\cdot)\)	3312.cp	44	no	\(-1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{3312}(41,\cdot)\)	3312.dj	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{3312}(43,\cdot)\)	3312.dm	132	yes	\(1\)	\(1\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{3312}(47,\cdot)\)	3312.bk	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{3312}(49,\cdot)\)	3312.cm	33	no	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{3312}(53,\cdot)\)	3312.cn	44	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{3312}(55,\cdot)\)	3312.cj	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{3312}(59,\cdot)\)	3312.dq	132	yes	\(1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{3312}(61,\cdot)\)	3312.dr	132	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{3312}(65,\cdot)\)	3312.dg	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{3312}(67,\cdot)\)	3312.dm	132	yes	\(1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{3312}(71,\cdot)\)	3312.cd	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{3312}(73,\cdot)\)	3312.ch	22	no	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{3312}(77,\cdot)\)	3312.dn	132	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{3312}(79,\cdot)\)	3312.dc	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{3312}(83,\cdot)\)	3312.dk	132	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{3312}(85,\cdot)\)	3312.dl	132	yes	\(1\)	\(1\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{3312}(89,\cdot)\)	3312.cl	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{3312}(91,\cdot)\)	3312.r	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{3312}(95,\cdot)\)	3312.cy	66	no	\(1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{3312}(97,\cdot)\)	3312.cw	66	no	\(-1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)

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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.