LMFDB - Group of Dirichlet characters of modulus 3744

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(3744)

gp:g = idealstar(,3744,2)

magma:G := FullDirichletGroup(3744);

Character group

Order	=	1152	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{24}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{3744}(703,\cdot)$, $\chi_{3744}(2341,\cdot)$, $\chi_{3744}(2081,\cdot)$, $\chi_{3744}(2017,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1152 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{3744}(1,\cdot)$	3744.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3744}(5,\cdot)$	3744.ke	24	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{3744}(7,\cdot)$	3744.ia	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{3744}(11,\cdot)$	3744.km	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{3744}(17,\cdot)$	3744.bz	6	no	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{3744}(19,\cdot)$	3744.kh	24	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{24}\right)$	$i$	$e\left(\frac{11}{24}\right)$
$\chi_{3744}(23,\cdot)$	3744.fi	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{3744}(25,\cdot)$	3744.fv	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$
$\chi_{3744}(29,\cdot)$	3744.jh	24	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{3744}(31,\cdot)$	3744.fw	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$
$\chi_{3744}(35,\cdot)$	3744.jd	24	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{11}{24}\right)$
$\chi_{3744}(37,\cdot)$	3744.io	24	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{1}{24}\right)$
$\chi_{3744}(41,\cdot)$	3744.fb	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3744}(43,\cdot)$	3744.jq	24	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{3744}(47,\cdot)$	3744.ha	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$
$\chi_{3744}(49,\cdot)$	3744.ca	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3744}(53,\cdot)$	3744.ek	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{3744}(55,\cdot)$	3744.fm	12	no	$-1$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$
$\chi_{3744}(59,\cdot)$	3744.km	24	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{3744}(61,\cdot)$	3744.jr	24	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{3744}(67,\cdot)$	3744.ij	24	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$-1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{3744}(71,\cdot)$	3744.es	12	no	$-1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{3744}(73,\cdot)$	3744.bo	4	no	$-1$	$1$	$1$	$i$	$-1$	$-1$	$-1$	$1$	$1$	$i$	$i$	$i$
$\chi_{3744}(77,\cdot)$	3744.kd	24	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{3744}(79,\cdot)$	3744.dk	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{3744}(83,\cdot)$	3744.kf	24	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3744}(85,\cdot)$	3744.ip	24	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{3744}(89,\cdot)$	3744.ig	12	no	$1$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{3744}(95,\cdot)$	3744.cf	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{3744}(97,\cdot)$	3744.gm	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{3744}(101,\cdot)$	3744.jl	24	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{3744}(103,\cdot)$	3744.hm	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$3744$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{24}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3744}(1,\cdot)\)	3744.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3744}(5,\cdot)\)	3744.ke	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{3744}(7,\cdot)\)	3744.ia	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{3744}(11,\cdot)\)	3744.km	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{3744}(17,\cdot)\)	3744.bz	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3744}(19,\cdot)\)	3744.kh	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{7}{24}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{3744}(23,\cdot)\)	3744.fi	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{3744}(25,\cdot)\)	3744.fv	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)
\(\chi_{3744}(29,\cdot)\)	3744.jh	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{3744}(31,\cdot)\)	3744.fw	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)
\(\chi_{3744}(35,\cdot)\)	3744.jd	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{3744}(37,\cdot)\)	3744.io	24	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{3744}(41,\cdot)\)	3744.fb	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3744}(43,\cdot)\)	3744.jq	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{3744}(47,\cdot)\)	3744.ha	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)
\(\chi_{3744}(49,\cdot)\)	3744.ca	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3744}(53,\cdot)\)	3744.ek	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3744}(55,\cdot)\)	3744.fm	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3744}(59,\cdot)\)	3744.km	24	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{3744}(61,\cdot)\)	3744.jr	24	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{3744}(67,\cdot)\)	3744.ij	24	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{3744}(71,\cdot)\)	3744.es	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3744}(73,\cdot)\)	3744.bo	4	no	\(-1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(i\)	\(i\)
\(\chi_{3744}(77,\cdot)\)	3744.kd	24	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3744}(79,\cdot)\)	3744.dk	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{3744}(83,\cdot)\)	3744.kf	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3744}(85,\cdot)\)	3744.ip	24	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{3744}(89,\cdot)\)	3744.ig	12	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{3744}(95,\cdot)\)	3744.cf	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3744}(97,\cdot)\)	3744.gm	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3744}(101,\cdot)\)	3744.jl	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{3744}(103,\cdot)\)	3744.hm	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)

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