LMFDB - Group of Dirichlet characters of modulus 2656

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2656)

pari: g = idealstar(,2656,2)

Character group

sage: G.order() pari: g.no
Order	=	1312
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{328}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2656}(831,\cdot)$, $\chi_{2656}(997,\cdot)$, $\chi_{2656}(417,\cdot)$

First 32 of 1312 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2656}(1,\cdot)$	2656.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2656}(3,\cdot)$	2656.bd	328	yes	$-1$	$1$	$e\left(\frac{277}{328}\right)$	$e\left(\frac{27}{328}\right)$	$e\left(\frac{45}{164}\right)$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{147}{328}\right)$	$e\left(\frac{77}{328}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{129}{328}\right)$	$e\left(\frac{39}{328}\right)$
$\chi_{2656}(5,\cdot)$	2656.bc	328	yes	$-1$	$1$	$e\left(\frac{27}{328}\right)$	$e\left(\frac{5}{328}\right)$	$e\left(\frac{145}{164}\right)$	$e\left(\frac{27}{164}\right)$	$e\left(\frac{173}{328}\right)$	$e\left(\frac{75}{328}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{115}{328}\right)$	$e\left(\frac{317}{328}\right)$
$\chi_{2656}(7,\cdot)$	2656.z	164	no	$-1$	$1$	$e\left(\frac{45}{164}\right)$	$e\left(\frac{145}{164}\right)$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{15}{164}\right)$	$e\left(\frac{43}{164}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{137}{164}\right)$	$e\left(\frac{9}{164}\right)$
$\chi_{2656}(9,\cdot)$	2656.ba	164	no	$1$	$1$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{27}{164}\right)$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{147}{164}\right)$	$e\left(\frac{77}{164}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{129}{164}\right)$	$e\left(\frac{39}{164}\right)$
$\chi_{2656}(11,\cdot)$	2656.bd	328	yes	$-1$	$1$	$e\left(\frac{147}{328}\right)$	$e\left(\frac{173}{328}\right)$	$e\left(\frac{15}{164}\right)$	$e\left(\frac{147}{164}\right)$	$e\left(\frac{213}{328}\right)$	$e\left(\frac{299}{328}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{73}{82}\right)$	$e\left(\frac{207}{328}\right)$	$e\left(\frac{177}{328}\right)$
$\chi_{2656}(13,\cdot)$	2656.bc	328	yes	$-1$	$1$	$e\left(\frac{77}{328}\right)$	$e\left(\frac{75}{328}\right)$	$e\left(\frac{43}{164}\right)$	$e\left(\frac{77}{164}\right)$	$e\left(\frac{299}{328}\right)$	$e\left(\frac{141}{328}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{7}{82}\right)$	$e\left(\frac{85}{328}\right)$	$e\left(\frac{163}{328}\right)$
$\chi_{2656}(15,\cdot)$	2656.r	82	no	$1$	$1$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{7}{82}\right)$
$\chi_{2656}(17,\cdot)$	2656.w	82	no	$1$	$1$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{73}{82}\right)$	$e\left(\frac{7}{82}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{11}{82}\right)$
$\chi_{2656}(19,\cdot)$	2656.bf	328	yes	$1$	$1$	$e\left(\frac{129}{328}\right)$	$e\left(\frac{115}{328}\right)$	$e\left(\frac{137}{164}\right)$	$e\left(\frac{129}{164}\right)$	$e\left(\frac{207}{328}\right)$	$e\left(\frac{85}{328}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{185}{328}\right)$	$e\left(\frac{75}{328}\right)$
$\chi_{2656}(21,\cdot)$	2656.be	328	yes	$1$	$1$	$e\left(\frac{39}{328}\right)$	$e\left(\frac{317}{328}\right)$	$e\left(\frac{9}{164}\right)$	$e\left(\frac{39}{164}\right)$	$e\left(\frac{177}{328}\right)$	$e\left(\frac{163}{328}\right)$	$e\left(\frac{7}{82}\right)$	$e\left(\frac{11}{82}\right)$	$e\left(\frac{75}{328}\right)$	$e\left(\frac{57}{328}\right)$
$\chi_{2656}(23,\cdot)$	2656.z	164	no	$-1$	$1$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{83}{164}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{71}{82}\right)$	$e\left(\frac{133}{164}\right)$	$e\left(\frac{97}{164}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{47}{164}\right)$
$\chi_{2656}(25,\cdot)$	2656.ba	164	no	$1$	$1$	$e\left(\frac{27}{164}\right)$	$e\left(\frac{5}{164}\right)$	$e\left(\frac{63}{82}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{9}{164}\right)$	$e\left(\frac{75}{164}\right)$	$e\left(\frac{8}{41}\right)$	$e\left(\frac{36}{41}\right)$	$e\left(\frac{115}{164}\right)$	$e\left(\frac{153}{164}\right)$
$\chi_{2656}(27,\cdot)$	2656.bd	328	yes	$-1$	$1$	$e\left(\frac{175}{328}\right)$	$e\left(\frac{81}{328}\right)$	$e\left(\frac{135}{164}\right)$	$e\left(\frac{11}{164}\right)$	$e\left(\frac{113}{328}\right)$	$e\left(\frac{231}{328}\right)$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{59}{328}\right)$	$e\left(\frac{117}{328}\right)$
$\chi_{2656}(29,\cdot)$	2656.be	328	yes	$1$	$1$	$e\left(\frac{217}{328}\right)$	$e\left(\frac{107}{328}\right)$	$e\left(\frac{151}{164}\right)$	$e\left(\frac{53}{164}\right)$	$e\left(\frac{127}{328}\right)$	$e\left(\frac{293}{328}\right)$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{57}{82}\right)$	$e\left(\frac{165}{328}\right)$	$e\left(\frac{191}{328}\right)$
$\chi_{2656}(31,\cdot)$	2656.v	82	no	$-1$	$1$	$e\left(\frac{71}{82}\right)$	$e\left(\frac{21}{41}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{3}{41}\right)$
$\chi_{2656}(33,\cdot)$	2656.q	41	no	$1$	$1$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{15}{41}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{6}{41}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{27}{41}\right)$
$\chi_{2656}(35,\cdot)$	2656.bf	328	yes	$1$	$1$	$e\left(\frac{117}{328}\right)$	$e\left(\frac{295}{328}\right)$	$e\left(\frac{109}{164}\right)$	$e\left(\frac{117}{164}\right)$	$e\left(\frac{203}{328}\right)$	$e\left(\frac{161}{328}\right)$	$e\left(\frac{21}{82}\right)$	$e\left(\frac{33}{82}\right)$	$e\left(\frac{61}{328}\right)$	$e\left(\frac{7}{328}\right)$
$\chi_{2656}(37,\cdot)$	2656.be	328	yes	$1$	$1$	$e\left(\frac{307}{328}\right)$	$e\left(\frac{233}{328}\right)$	$e\left(\frac{33}{164}\right)$	$e\left(\frac{143}{164}\right)$	$e\left(\frac{157}{328}\right)$	$e\left(\frac{215}{328}\right)$	$e\left(\frac{53}{82}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{111}{328}\right)$	$e\left(\frac{45}{328}\right)$
$\chi_{2656}(39,\cdot)$	2656.y	164	no	$1$	$1$	$e\left(\frac{13}{164}\right)$	$e\left(\frac{51}{164}\right)$	$e\left(\frac{22}{41}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{59}{164}\right)$	$e\left(\frac{109}{164}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{31}{41}\right)$	$e\left(\frac{107}{164}\right)$	$e\left(\frac{101}{164}\right)$
$\chi_{2656}(41,\cdot)$	2656.ba	164	no	$1$	$1$	$e\left(\frac{61}{164}\right)$	$e\left(\frac{151}{164}\right)$	$e\left(\frac{33}{82}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{75}{164}\right)$	$e\left(\frac{133}{164}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{29}{164}\right)$	$e\left(\frac{127}{164}\right)$
$\chi_{2656}(43,\cdot)$	2656.bf	328	yes	$1$	$1$	$e\left(\frac{235}{328}\right)$	$e\left(\frac{1}{328}\right)$	$e\left(\frac{111}{164}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{133}{328}\right)$	$e\left(\frac{15}{328}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{187}{328}\right)$	$e\left(\frac{129}{328}\right)$
$\chi_{2656}(45,\cdot)$	2656.bc	328	yes	$-1$	$1$	$e\left(\frac{253}{328}\right)$	$e\left(\frac{59}{328}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{89}{164}\right)$	$e\left(\frac{139}{328}\right)$	$e\left(\frac{229}{328}\right)$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{45}{328}\right)$	$e\left(\frac{67}{328}\right)$
$\chi_{2656}(47,\cdot)$	2656.r	82	no	$1$	$1$	$e\left(\frac{8}{41}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{29}{41}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{77}{82}\right)$
$\chi_{2656}(49,\cdot)$	2656.w	82	no	$1$	$1$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{63}{82}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{43}{82}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{9}{82}\right)$
$\chi_{2656}(51,\cdot)$	2656.bd	328	yes	$-1$	$1$	$e\left(\frac{169}{328}\right)$	$e\left(\frac{7}{328}\right)$	$e\left(\frac{121}{164}\right)$	$e\left(\frac{5}{164}\right)$	$e\left(\frac{111}{328}\right)$	$e\left(\frac{105}{328}\right)$	$e\left(\frac{22}{41}\right)$	$e\left(\frac{75}{82}\right)$	$e\left(\frac{325}{328}\right)$	$e\left(\frac{83}{328}\right)$
$\chi_{2656}(53,\cdot)$	2656.bc	328	yes	$-1$	$1$	$e\left(\frac{223}{328}\right)$	$e\left(\frac{17}{328}\right)$	$e\left(\frac{1}{164}\right)$	$e\left(\frac{59}{164}\right)$	$e\left(\frac{129}{328}\right)$	$e\left(\frac{255}{328}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{65}{82}\right)$	$e\left(\frac{63}{328}\right)$	$e\left(\frac{225}{328}\right)$
$\chi_{2656}(55,\cdot)$	2656.y	164	no	$1$	$1$	$e\left(\frac{87}{164}\right)$	$e\left(\frac{89}{164}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{5}{82}\right)$	$e\left(\frac{29}{164}\right)$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{34}{41}\right)$	$e\left(\frac{161}{164}\right)$	$e\left(\frac{83}{164}\right)$
$\chi_{2656}(57,\cdot)$	2656.bb	164	no	$-1$	$1$	$e\left(\frac{39}{164}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{9}{82}\right)$	$e\left(\frac{39}{82}\right)$	$e\left(\frac{13}{164}\right)$	$e\left(\frac{81}{164}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{157}{164}\right)$	$e\left(\frac{57}{164}\right)$
$\chi_{2656}(59,\cdot)$	2656.bd	328	yes	$-1$	$1$	$e\left(\frac{239}{328}\right)$	$e\left(\frac{105}{328}\right)$	$e\left(\frac{11}{164}\right)$	$e\left(\frac{75}{164}\right)$	$e\left(\frac{25}{328}\right)$	$e\left(\frac{263}{328}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{283}{328}\right)$	$e\left(\frac{261}{328}\right)$
$\chi_{2656}(61,\cdot)$	2656.be	328	yes	$1$	$1$	$e\left(\frac{25}{328}\right)$	$e\left(\frac{35}{328}\right)$	$e\left(\frac{31}{164}\right)$	$e\left(\frac{25}{164}\right)$	$e\left(\frac{63}{328}\right)$	$e\left(\frac{197}{328}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{149}{328}\right)$	$e\left(\frac{87}{328}\right)$
$\chi_{2656}(63,\cdot)$	2656.v	82	no	$-1$	$1$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{33}{41}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{12}{41}\right)$

Click here to search among the remaining 1280 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	$2656$
Structure	\(C_{2}\times C_{2}\times C_{328}\)
Order	$1312$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2656}(1,\cdot)\)	2656.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2656}(3,\cdot)\)	2656.bd	328	yes	\(-1\)	\(1\)	\(e\left(\frac{277}{328}\right)\)	\(e\left(\frac{27}{328}\right)\)	\(e\left(\frac{45}{164}\right)\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{147}{328}\right)\)	\(e\left(\frac{77}{328}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{129}{328}\right)\)	\(e\left(\frac{39}{328}\right)\)
\(\chi_{2656}(5,\cdot)\)	2656.bc	328	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{328}\right)\)	\(e\left(\frac{5}{328}\right)\)	\(e\left(\frac{145}{164}\right)\)	\(e\left(\frac{27}{164}\right)\)	\(e\left(\frac{173}{328}\right)\)	\(e\left(\frac{75}{328}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{115}{328}\right)\)	\(e\left(\frac{317}{328}\right)\)
\(\chi_{2656}(7,\cdot)\)	2656.z	164	no	\(-1\)	\(1\)	\(e\left(\frac{45}{164}\right)\)	\(e\left(\frac{145}{164}\right)\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{15}{164}\right)\)	\(e\left(\frac{43}{164}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{137}{164}\right)\)	\(e\left(\frac{9}{164}\right)\)
\(\chi_{2656}(9,\cdot)\)	2656.ba	164	no	\(1\)	\(1\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{27}{164}\right)\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{31}{82}\right)\)	\(e\left(\frac{147}{164}\right)\)	\(e\left(\frac{77}{164}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{129}{164}\right)\)	\(e\left(\frac{39}{164}\right)\)
\(\chi_{2656}(11,\cdot)\)	2656.bd	328	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{328}\right)\)	\(e\left(\frac{173}{328}\right)\)	\(e\left(\frac{15}{164}\right)\)	\(e\left(\frac{147}{164}\right)\)	\(e\left(\frac{213}{328}\right)\)	\(e\left(\frac{299}{328}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{73}{82}\right)\)	\(e\left(\frac{207}{328}\right)\)	\(e\left(\frac{177}{328}\right)\)
\(\chi_{2656}(13,\cdot)\)	2656.bc	328	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{328}\right)\)	\(e\left(\frac{75}{328}\right)\)	\(e\left(\frac{43}{164}\right)\)	\(e\left(\frac{77}{164}\right)\)	\(e\left(\frac{299}{328}\right)\)	\(e\left(\frac{141}{328}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{7}{82}\right)\)	\(e\left(\frac{85}{328}\right)\)	\(e\left(\frac{163}{328}\right)\)
\(\chi_{2656}(15,\cdot)\)	2656.r	82	no	\(1\)	\(1\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{7}{82}\right)\)
\(\chi_{2656}(17,\cdot)\)	2656.w	82	no	\(1\)	\(1\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{73}{82}\right)\)	\(e\left(\frac{7}{82}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{11}{82}\right)\)
\(\chi_{2656}(19,\cdot)\)	2656.bf	328	yes	\(1\)	\(1\)	\(e\left(\frac{129}{328}\right)\)	\(e\left(\frac{115}{328}\right)\)	\(e\left(\frac{137}{164}\right)\)	\(e\left(\frac{129}{164}\right)\)	\(e\left(\frac{207}{328}\right)\)	\(e\left(\frac{85}{328}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{185}{328}\right)\)	\(e\left(\frac{75}{328}\right)\)
\(\chi_{2656}(21,\cdot)\)	2656.be	328	yes	\(1\)	\(1\)	\(e\left(\frac{39}{328}\right)\)	\(e\left(\frac{317}{328}\right)\)	\(e\left(\frac{9}{164}\right)\)	\(e\left(\frac{39}{164}\right)\)	\(e\left(\frac{177}{328}\right)\)	\(e\left(\frac{163}{328}\right)\)	\(e\left(\frac{7}{82}\right)\)	\(e\left(\frac{11}{82}\right)\)	\(e\left(\frac{75}{328}\right)\)	\(e\left(\frac{57}{328}\right)\)
\(\chi_{2656}(23,\cdot)\)	2656.z	164	no	\(-1\)	\(1\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{83}{164}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{71}{82}\right)\)	\(e\left(\frac{133}{164}\right)\)	\(e\left(\frac{97}{164}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{47}{164}\right)\)
\(\chi_{2656}(25,\cdot)\)	2656.ba	164	no	\(1\)	\(1\)	\(e\left(\frac{27}{164}\right)\)	\(e\left(\frac{5}{164}\right)\)	\(e\left(\frac{63}{82}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{9}{164}\right)\)	\(e\left(\frac{75}{164}\right)\)	\(e\left(\frac{8}{41}\right)\)	\(e\left(\frac{36}{41}\right)\)	\(e\left(\frac{115}{164}\right)\)	\(e\left(\frac{153}{164}\right)\)
\(\chi_{2656}(27,\cdot)\)	2656.bd	328	yes	\(-1\)	\(1\)	\(e\left(\frac{175}{328}\right)\)	\(e\left(\frac{81}{328}\right)\)	\(e\left(\frac{135}{164}\right)\)	\(e\left(\frac{11}{164}\right)\)	\(e\left(\frac{113}{328}\right)\)	\(e\left(\frac{231}{328}\right)\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{59}{328}\right)\)	\(e\left(\frac{117}{328}\right)\)
\(\chi_{2656}(29,\cdot)\)	2656.be	328	yes	\(1\)	\(1\)	\(e\left(\frac{217}{328}\right)\)	\(e\left(\frac{107}{328}\right)\)	\(e\left(\frac{151}{164}\right)\)	\(e\left(\frac{53}{164}\right)\)	\(e\left(\frac{127}{328}\right)\)	\(e\left(\frac{293}{328}\right)\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{57}{82}\right)\)	\(e\left(\frac{165}{328}\right)\)	\(e\left(\frac{191}{328}\right)\)
\(\chi_{2656}(31,\cdot)\)	2656.v	82	no	\(-1\)	\(1\)	\(e\left(\frac{71}{82}\right)\)	\(e\left(\frac{21}{41}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{31}{82}\right)\)	\(e\left(\frac{39}{41}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{3}{41}\right)\)
\(\chi_{2656}(33,\cdot)\)	2656.q	41	no	\(1\)	\(1\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{15}{41}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{6}{41}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{27}{41}\right)\)
\(\chi_{2656}(35,\cdot)\)	2656.bf	328	yes	\(1\)	\(1\)	\(e\left(\frac{117}{328}\right)\)	\(e\left(\frac{295}{328}\right)\)	\(e\left(\frac{109}{164}\right)\)	\(e\left(\frac{117}{164}\right)\)	\(e\left(\frac{203}{328}\right)\)	\(e\left(\frac{161}{328}\right)\)	\(e\left(\frac{21}{82}\right)\)	\(e\left(\frac{33}{82}\right)\)	\(e\left(\frac{61}{328}\right)\)	\(e\left(\frac{7}{328}\right)\)
\(\chi_{2656}(37,\cdot)\)	2656.be	328	yes	\(1\)	\(1\)	\(e\left(\frac{307}{328}\right)\)	\(e\left(\frac{233}{328}\right)\)	\(e\left(\frac{33}{164}\right)\)	\(e\left(\frac{143}{164}\right)\)	\(e\left(\frac{157}{328}\right)\)	\(e\left(\frac{215}{328}\right)\)	\(e\left(\frac{53}{82}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{111}{328}\right)\)	\(e\left(\frac{45}{328}\right)\)
\(\chi_{2656}(39,\cdot)\)	2656.y	164	no	\(1\)	\(1\)	\(e\left(\frac{13}{164}\right)\)	\(e\left(\frac{51}{164}\right)\)	\(e\left(\frac{22}{41}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{59}{164}\right)\)	\(e\left(\frac{109}{164}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{31}{41}\right)\)	\(e\left(\frac{107}{164}\right)\)	\(e\left(\frac{101}{164}\right)\)
\(\chi_{2656}(41,\cdot)\)	2656.ba	164	no	\(1\)	\(1\)	\(e\left(\frac{61}{164}\right)\)	\(e\left(\frac{151}{164}\right)\)	\(e\left(\frac{33}{82}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{75}{164}\right)\)	\(e\left(\frac{133}{164}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{29}{164}\right)\)	\(e\left(\frac{127}{164}\right)\)
\(\chi_{2656}(43,\cdot)\)	2656.bf	328	yes	\(1\)	\(1\)	\(e\left(\frac{235}{328}\right)\)	\(e\left(\frac{1}{328}\right)\)	\(e\left(\frac{111}{164}\right)\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{133}{328}\right)\)	\(e\left(\frac{15}{328}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{187}{328}\right)\)	\(e\left(\frac{129}{328}\right)\)
\(\chi_{2656}(45,\cdot)\)	2656.bc	328	yes	\(-1\)	\(1\)	\(e\left(\frac{253}{328}\right)\)	\(e\left(\frac{59}{328}\right)\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{89}{164}\right)\)	\(e\left(\frac{139}{328}\right)\)	\(e\left(\frac{229}{328}\right)\)	\(e\left(\frac{39}{41}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{45}{328}\right)\)	\(e\left(\frac{67}{328}\right)\)
\(\chi_{2656}(47,\cdot)\)	2656.r	82	no	\(1\)	\(1\)	\(e\left(\frac{8}{41}\right)\)	\(e\left(\frac{3}{41}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{29}{41}\right)\)	\(e\left(\frac{15}{82}\right)\)	\(e\left(\frac{77}{82}\right)\)
\(\chi_{2656}(49,\cdot)\)	2656.w	82	no	\(1\)	\(1\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{63}{82}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{15}{82}\right)\)	\(e\left(\frac{43}{82}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{9}{82}\right)\)
\(\chi_{2656}(51,\cdot)\)	2656.bd	328	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{328}\right)\)	\(e\left(\frac{7}{328}\right)\)	\(e\left(\frac{121}{164}\right)\)	\(e\left(\frac{5}{164}\right)\)	\(e\left(\frac{111}{328}\right)\)	\(e\left(\frac{105}{328}\right)\)	\(e\left(\frac{22}{41}\right)\)	\(e\left(\frac{75}{82}\right)\)	\(e\left(\frac{325}{328}\right)\)	\(e\left(\frac{83}{328}\right)\)
\(\chi_{2656}(53,\cdot)\)	2656.bc	328	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{328}\right)\)	\(e\left(\frac{17}{328}\right)\)	\(e\left(\frac{1}{164}\right)\)	\(e\left(\frac{59}{164}\right)\)	\(e\left(\frac{129}{328}\right)\)	\(e\left(\frac{255}{328}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{65}{82}\right)\)	\(e\left(\frac{63}{328}\right)\)	\(e\left(\frac{225}{328}\right)\)
\(\chi_{2656}(55,\cdot)\)	2656.y	164	no	\(1\)	\(1\)	\(e\left(\frac{87}{164}\right)\)	\(e\left(\frac{89}{164}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{5}{82}\right)\)	\(e\left(\frac{29}{164}\right)\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{3}{41}\right)\)	\(e\left(\frac{34}{41}\right)\)	\(e\left(\frac{161}{164}\right)\)	\(e\left(\frac{83}{164}\right)\)
\(\chi_{2656}(57,\cdot)\)	2656.bb	164	no	\(-1\)	\(1\)	\(e\left(\frac{39}{164}\right)\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{9}{82}\right)\)	\(e\left(\frac{39}{82}\right)\)	\(e\left(\frac{13}{164}\right)\)	\(e\left(\frac{81}{164}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{157}{164}\right)\)	\(e\left(\frac{57}{164}\right)\)
\(\chi_{2656}(59,\cdot)\)	2656.bd	328	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{328}\right)\)	\(e\left(\frac{105}{328}\right)\)	\(e\left(\frac{11}{164}\right)\)	\(e\left(\frac{75}{164}\right)\)	\(e\left(\frac{25}{328}\right)\)	\(e\left(\frac{263}{328}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{283}{328}\right)\)	\(e\left(\frac{261}{328}\right)\)
\(\chi_{2656}(61,\cdot)\)	2656.be	328	yes	\(1\)	\(1\)	\(e\left(\frac{25}{328}\right)\)	\(e\left(\frac{35}{328}\right)\)	\(e\left(\frac{31}{164}\right)\)	\(e\left(\frac{25}{164}\right)\)	\(e\left(\frac{63}{328}\right)\)	\(e\left(\frac{197}{328}\right)\)	\(e\left(\frac{15}{82}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{149}{328}\right)\)	\(e\left(\frac{87}{328}\right)\)
\(\chi_{2656}(63,\cdot)\)	2656.v	82	no	\(-1\)	\(1\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{33}{41}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{12}{41}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1312 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.