LMFDB - Group of Dirichlet characters of modulus 3332

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3332)

pari: g = idealstar(,3332,2)

Character group

sage: G.order() pari: g.no
Order	=	1344
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3332}(1667,\cdot)$, $\chi_{3332}(885,\cdot)$, $\chi_{3332}(785,\cdot)$

First 32 of 1344 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{3332}(1,\cdot)$	3332.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3332}(3,\cdot)$	3332.da	336	yes	$-1$	$1$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{85}{112}\right)$
$\chi_{3332}(5,\cdot)$	3332.db	336	no	$1$	$1$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{3332}(9,\cdot)$	3332.cw	168	no	$1$	$1$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{3332}(11,\cdot)$	3332.cy	336	yes	$1$	$1$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{3332}(13,\cdot)$	3332.bw	28	no	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{3332}(15,\cdot)$	3332.ck	56	yes	$-1$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$-i$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{3332}(19,\cdot)$	3332.bs	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3332}(23,\cdot)$	3332.cy	336	yes	$1$	$1$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{317}{336}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{3332}(25,\cdot)$	3332.cw	168	no	$1$	$1$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{3332}(27,\cdot)$	3332.cr	112	yes	$-1$	$1$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{3332}(29,\cdot)$	3332.cs	112	no	$-1$	$1$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{3332}(31,\cdot)$	3332.ce	48	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{3332}(33,\cdot)$	3332.cd	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{3332}(37,\cdot)$	3332.cz	336	no	$-1$	$1$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{53}{112}\right)$
$\chi_{3332}(39,\cdot)$	3332.cy	336	yes	$1$	$1$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{97}{112}\right)$
$\chi_{3332}(41,\cdot)$	3332.cq	112	no	$1$	$1$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{15}{112}\right)$
$\chi_{3332}(43,\cdot)$	3332.ck	56	yes	$-1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{3332}(45,\cdot)$	3332.db	336	no	$1$	$1$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{59}{112}\right)$
$\chi_{3332}(47,\cdot)$	3332.co	84	yes	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{3332}(53,\cdot)$	3332.cw	168	no	$1$	$1$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{3332}(55,\cdot)$	3332.bv	28	yes	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{3332}(57,\cdot)$	3332.cs	112	no	$-1$	$1$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{43}{112}\right)$
$\chi_{3332}(59,\cdot)$	3332.cu	168	yes	$1$	$1$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{3332}(61,\cdot)$	3332.db	336	no	$1$	$1$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{3332}(65,\cdot)$	3332.cz	336	no	$-1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{3332}(67,\cdot)$	3332.o	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{3332}(69,\cdot)$	3332.bi	14	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{3332}(71,\cdot)$	3332.ct	112	yes	$1$	$1$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{45}{112}\right)$
$\chi_{3332}(73,\cdot)$	3332.db	336	no	$1$	$1$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{65}{112}\right)$
$\chi_{3332}(75,\cdot)$	3332.da	336	yes	$-1$	$1$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{169}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{87}{112}\right)$
$\chi_{3332}(79,\cdot)$	3332.cg	48	no	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{48}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{16}\right)$

Click here to search among the remaining 1312 characters.

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	$3332$
Structure	\(C_{2}\times C_{2}\times C_{336}\)
Order	$1344$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{3332}(1,\cdot)\)	3332.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3332}(3,\cdot)\)	3332.da	336	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{85}{112}\right)\)
\(\chi_{3332}(5,\cdot)\)	3332.db	336	no	\(1\)	\(1\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{3332}(9,\cdot)\)	3332.cw	168	no	\(1\)	\(1\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{3332}(11,\cdot)\)	3332.cy	336	yes	\(1\)	\(1\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{3332}(13,\cdot)\)	3332.bw	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{3332}(15,\cdot)\)	3332.ck	56	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{3332}(19,\cdot)\)	3332.bs	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3332}(23,\cdot)\)	3332.cy	336	yes	\(1\)	\(1\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{317}{336}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{3332}(25,\cdot)\)	3332.cw	168	no	\(1\)	\(1\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{3332}(27,\cdot)\)	3332.cr	112	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{3332}(29,\cdot)\)	3332.cs	112	no	\(-1\)	\(1\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{3332}(31,\cdot)\)	3332.ce	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{3332}(33,\cdot)\)	3332.cd	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{3332}(37,\cdot)\)	3332.cz	336	no	\(-1\)	\(1\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{53}{112}\right)\)
\(\chi_{3332}(39,\cdot)\)	3332.cy	336	yes	\(1\)	\(1\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)
\(\chi_{3332}(41,\cdot)\)	3332.cq	112	no	\(1\)	\(1\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)
\(\chi_{3332}(43,\cdot)\)	3332.ck	56	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{3332}(45,\cdot)\)	3332.db	336	no	\(1\)	\(1\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{59}{112}\right)\)
\(\chi_{3332}(47,\cdot)\)	3332.co	84	yes	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{3332}(53,\cdot)\)	3332.cw	168	no	\(1\)	\(1\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{3332}(55,\cdot)\)	3332.bv	28	yes	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{3332}(57,\cdot)\)	3332.cs	112	no	\(-1\)	\(1\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{43}{112}\right)\)
\(\chi_{3332}(59,\cdot)\)	3332.cu	168	yes	\(1\)	\(1\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{3332}(61,\cdot)\)	3332.db	336	no	\(1\)	\(1\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{3332}(65,\cdot)\)	3332.cz	336	no	\(-1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{3332}(67,\cdot)\)	3332.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{3332}(69,\cdot)\)	3332.bi	14	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{3332}(71,\cdot)\)	3332.ct	112	yes	\(1\)	\(1\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{45}{112}\right)\)
\(\chi_{3332}(73,\cdot)\)	3332.db	336	no	\(1\)	\(1\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{65}{112}\right)\)
\(\chi_{3332}(75,\cdot)\)	3332.da	336	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{169}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{87}{112}\right)\)
\(\chi_{3332}(79,\cdot)\)	3332.cg	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1344 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.