LMFDB - Group of Dirichlet characters of modulus 1215

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1215)

pari: g = idealstar(,1215,2)

Character group

sage: G.order() pari: g.no
Order	=	648
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{324}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1215}(731,\cdot)$, $\chi_{1215}(487,\cdot)$

First 32 of 648 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1215}(1,\cdot)$	1215.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1215}(2,\cdot)$	1215.bd	324	yes	$1$	$1$	$e\left(\frac{83}{324}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{259}{324}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{1215}(4,\cdot)$	1215.ba	162	yes	$1$	$1$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{1215}(7,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{161}{324}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{67}{324}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{1215}(8,\cdot)$	1215.y	108	no	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1215}(11,\cdot)$	1215.z	162	no	$-1$	$1$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{1215}(13,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{259}{324}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{67}{324}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{209}{324}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{1215}(14,\cdot)$	1215.bb	162	yes	$-1$	$1$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{1215}(16,\cdot)$	1215.w	81	no	$1$	$1$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{1215}(17,\cdot)$	1215.y	108	no	$1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{1215}(19,\cdot)$	1215.t	54	no	$1$	$1$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1215}(22,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{313}{324}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{251}{324}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{1215}(23,\cdot)$	1215.bd	324	yes	$1$	$1$	$e\left(\frac{49}{324}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{149}{324}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{1215}(26,\cdot)$	1215.o	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1215}(28,\cdot)$	1215.s	36	no	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1215}(29,\cdot)$	1215.bb	162	yes	$-1$	$1$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{79}{162}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{1215}(31,\cdot)$	1215.w	81	no	$1$	$1$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{1215}(32,\cdot)$	1215.bd	324	yes	$1$	$1$	$e\left(\frac{91}{324}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{133}{324}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{323}{324}\right)$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{1215}(34,\cdot)$	1215.ba	162	yes	$1$	$1$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{34}{81}\right)$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{1215}(37,\cdot)$	1215.x	108	no	$-1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1215}(38,\cdot)$	1215.bd	324	yes	$1$	$1$	$e\left(\frac{233}{324}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{191}{324}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{1215}(41,\cdot)$	1215.z	162	no	$-1$	$1$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{1215}(43,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{179}{324}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{299}{324}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{217}{324}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{1215}(44,\cdot)$	1215.v	54	no	$-1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1215}(46,\cdot)$	1215.q	27	no	$1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1215}(47,\cdot)$	1215.bd	324	yes	$1$	$1$	$e\left(\frac{203}{324}\right)$	$e\left(\frac{41}{162}\right)$	$e\left(\frac{197}{324}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{247}{324}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{1215}(49,\cdot)$	1215.ba	162	yes	$1$	$1$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{1215}(52,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{101}{324}\right)$	$e\left(\frac{101}{162}\right)$	$e\left(\frac{185}{324}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{79}{324}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{1215}(53,\cdot)$	1215.r	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1215}(56,\cdot)$	1215.z	162	no	$-1$	$1$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{1215}(58,\cdot)$	1215.bc	324	yes	$-1$	$1$	$e\left(\frac{319}{324}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{55}{324}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{41}{324}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{1215}(59,\cdot)$	1215.bb	162	yes	$-1$	$1$	$e\left(\frac{34}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{27}\right)$

Click here to search among the remaining 616 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	$1215$
Structure	\(C_{2}\times C_{324}\)
Order	$648$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1215}(1,\cdot)\)	1215.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1215}(2,\cdot)\)	1215.bd	324	yes	\(1\)	\(1\)	\(e\left(\frac{83}{324}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{221}{324}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{259}{324}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{1215}(4,\cdot)\)	1215.ba	162	yes	\(1\)	\(1\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{1215}(7,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{324}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{161}{324}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{67}{324}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{1215}(8,\cdot)\)	1215.y	108	no	\(1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1215}(11,\cdot)\)	1215.z	162	no	\(-1\)	\(1\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{61}{162}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{1215}(13,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{259}{324}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{67}{324}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{209}{324}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{1215}(14,\cdot)\)	1215.bb	162	yes	\(-1\)	\(1\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{1215}(16,\cdot)\)	1215.w	81	no	\(1\)	\(1\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{1215}(17,\cdot)\)	1215.y	108	no	\(1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1215}(19,\cdot)\)	1215.t	54	no	\(1\)	\(1\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1215}(22,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{313}{324}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{251}{324}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{1215}(23,\cdot)\)	1215.bd	324	yes	\(1\)	\(1\)	\(e\left(\frac{49}{324}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{271}{324}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{149}{324}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{1215}(26,\cdot)\)	1215.o	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1215}(28,\cdot)\)	1215.s	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1215}(29,\cdot)\)	1215.bb	162	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{79}{162}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{35}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{1215}(31,\cdot)\)	1215.w	81	no	\(1\)	\(1\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{1215}(32,\cdot)\)	1215.bd	324	yes	\(1\)	\(1\)	\(e\left(\frac{91}{324}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{133}{324}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{323}{324}\right)\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{1215}(34,\cdot)\)	1215.ba	162	yes	\(1\)	\(1\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{34}{81}\right)\)	\(e\left(\frac{31}{162}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{1215}(37,\cdot)\)	1215.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1215}(38,\cdot)\)	1215.bd	324	yes	\(1\)	\(1\)	\(e\left(\frac{233}{324}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{191}{324}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{1215}(41,\cdot)\)	1215.z	162	no	\(-1\)	\(1\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{1215}(43,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{324}\right)\)	\(e\left(\frac{17}{162}\right)\)	\(e\left(\frac{299}{324}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{217}{324}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{1215}(44,\cdot)\)	1215.v	54	no	\(-1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1215}(46,\cdot)\)	1215.q	27	no	\(1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1215}(47,\cdot)\)	1215.bd	324	yes	\(1\)	\(1\)	\(e\left(\frac{203}{324}\right)\)	\(e\left(\frac{41}{162}\right)\)	\(e\left(\frac{197}{324}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{247}{324}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{1215}(49,\cdot)\)	1215.ba	162	yes	\(1\)	\(1\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{1215}(52,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{324}\right)\)	\(e\left(\frac{101}{162}\right)\)	\(e\left(\frac{185}{324}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{79}{324}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{1215}(53,\cdot)\)	1215.r	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1215}(56,\cdot)\)	1215.z	162	no	\(-1\)	\(1\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{1215}(58,\cdot)\)	1215.bc	324	yes	\(-1\)	\(1\)	\(e\left(\frac{319}{324}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{55}{324}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{41}{324}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{1215}(59,\cdot)\)	1215.bb	162	yes	\(-1\)	\(1\)	\(e\left(\frac{34}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 648 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.