LMFDB - Group of Dirichlet characters of modulus 3298

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(3298)

gp:g = idealstar(,3298,2)

magma:G = FullDirichletGroup(3298);

Character group

Order	=	1536	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{16}\times C_{96}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{3298}(1941,\cdot)$, $\chi_{3298}(2721,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1536 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$23$
$\chi_{3298}(1,\cdot)$	3298.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3298}(3,\cdot)$	3298.do	48	no	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3298}(5,\cdot)$	3298.eg	96	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3298}(7,\cdot)$	3298.eg	96	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{17}{96}\right)$
$\chi_{3298}(9,\cdot)$	3298.cj	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3298}(11,\cdot)$	3298.du	48	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{3298}(13,\cdot)$	3298.ek	96	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{77}{96}\right)$
$\chi_{3298}(15,\cdot)$	3298.em	96	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{55}{96}\right)$
$\chi_{3298}(19,\cdot)$	3298.da	32	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3298}(21,\cdot)$	3298.en	96	no	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{25}{96}\right)$
$\chi_{3298}(23,\cdot)$	3298.er	96	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{79}{96}\right)$
$\chi_{3298}(25,\cdot)$	3298.eb	48	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{3298}(27,\cdot)$	3298.bx	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$
$\chi_{3298}(29,\cdot)$	3298.ef	96	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{59}{96}\right)$
$\chi_{3298}(31,\cdot)$	3298.dl	48	no	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{3298}(33,\cdot)$	3298.q	8	no	$1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3298}(35,\cdot)$	3298.e	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3298}(37,\cdot)$	3298.es	96	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{89}{96}\right)$
$\chi_{3298}(39,\cdot)$	3298.er	96	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{85}{96}\right)$
$\chi_{3298}(41,\cdot)$	3298.ee	96	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3298}(43,\cdot)$	3298.cf	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3298}(45,\cdot)$	3298.cr	32	no	$1$	$1$	$i$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{32}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3298}(47,\cdot)$	3298.o	8	no	$1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{3298}(49,\cdot)$	3298.eb	48	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{3298}(53,\cdot)$	3298.ed	48	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{3298}(55,\cdot)$	3298.cw	32	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3298}(57,\cdot)$	3298.eq	96	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{17}{96}\right)$
$\chi_{3298}(59,\cdot)$	3298.ej	96	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{11}{96}\right)$
$\chi_{3298}(61,\cdot)$	3298.dm	48	no	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{3298}(63,\cdot)$	3298.cq	32	no	$1$	$1$	$-1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{32}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3298}(65,\cdot)$	3298.dv	48	no	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{3298}(67,\cdot)$	3298.cu	32	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{32}\right)$

Click here to search among the remaining 1504 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 $\F_{q}$
Belyi maps

Modulus	$3298$
Structure	\(C_{16}\times C_{96}\)
Order	$1536$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\(\chi_{3298}(1,\cdot)\)	3298.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3298}(3,\cdot)\)	3298.do	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3298}(5,\cdot)\)	3298.eg	96	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3298}(7,\cdot)\)	3298.eg	96	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{3298}(9,\cdot)\)	3298.cj	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3298}(11,\cdot)\)	3298.du	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{3298}(13,\cdot)\)	3298.ek	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{3298}(15,\cdot)\)	3298.em	96	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{3298}(19,\cdot)\)	3298.da	32	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3298}(21,\cdot)\)	3298.en	96	no	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)
\(\chi_{3298}(23,\cdot)\)	3298.er	96	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{3298}(25,\cdot)\)	3298.eb	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{3298}(27,\cdot)\)	3298.bx	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)
\(\chi_{3298}(29,\cdot)\)	3298.ef	96	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{3298}(31,\cdot)\)	3298.dl	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3298}(33,\cdot)\)	3298.q	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3298}(35,\cdot)\)	3298.e	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3298}(37,\cdot)\)	3298.es	96	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{3298}(39,\cdot)\)	3298.er	96	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)
\(\chi_{3298}(41,\cdot)\)	3298.ee	96	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3298}(43,\cdot)\)	3298.cf	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3298}(45,\cdot)\)	3298.cr	32	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3298}(47,\cdot)\)	3298.o	8	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3298}(49,\cdot)\)	3298.eb	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{3298}(53,\cdot)\)	3298.ed	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{3298}(55,\cdot)\)	3298.cw	32	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3298}(57,\cdot)\)	3298.eq	96	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{3298}(59,\cdot)\)	3298.ej	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)
\(\chi_{3298}(61,\cdot)\)	3298.dm	48	no	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{3298}(63,\cdot)\)	3298.cq	32	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3298}(65,\cdot)\)	3298.dv	48	no	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{3298}(67,\cdot)\)	3298.cu	32	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 1536 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.