LMFDB - Group of Dirichlet characters of modulus 3381

sage:H = DirichletGroup(3381)

pari:g = idealstar(,3381,2)

Character group

sage:G.order() pari:g.no
Order	=	1848
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{462}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{3381}(2255,\cdot)$, $\chi_{3381}(346,\cdot)$, $\chi_{3381}(442,\cdot)$

First 32 of 1848 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{3381}(1,\cdot)$	3381.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3381}(2,\cdot)$	3381.cl	462	yes	$-1$	$1$	$e\left(\frac{359}{462}\right)$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{251}{462}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{283}{462}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{3381}(4,\cdot)$	3381.ce	231	no	$1$	$1$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{20}{231}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{50}{231}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{3381}(5,\cdot)$	3381.ck	462	yes	$-1$	$1$	$e\left(\frac{251}{462}\right)$	$e\left(\frac{20}{231}\right)$	$e\left(\frac{263}{462}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{3381}(8,\cdot)$	3381.bx	154	yes	$-1$	$1$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{3381}(10,\cdot)$	3381.cf	462	no	$1$	$1$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{3381}(11,\cdot)$	3381.ci	462	yes	$1$	$1$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{3381}(13,\cdot)$	3381.cc	154	no	$-1$	$1$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{3381}(16,\cdot)$	3381.ce	231	no	$1$	$1$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{50}{231}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{104}{231}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{3381}(17,\cdot)$	3381.ck	462	yes	$-1$	$1$	$e\left(\frac{283}{462}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{104}{231}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{3381}(19,\cdot)$	3381.bv	66	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{3381}(20,\cdot)$	3381.by	154	yes	$-1$	$1$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{3381}(22,\cdot)$	3381.u	14	no	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{3381}(25,\cdot)$	3381.ce	231	no	$1$	$1$	$e\left(\frac{20}{231}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{3381}(26,\cdot)$	3381.cj	462	yes	$1$	$1$	$e\left(\frac{221}{462}\right)$	$e\left(\frac{221}{231}\right)$	$e\left(\frac{223}{231}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{205}{462}\right)$	$e\left(\frac{109}{462}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{211}{231}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{3381}(29,\cdot)$	3381.bx	154	yes	$-1$	$1$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{3381}(31,\cdot)$	3381.bu	66	no	$-1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{3381}(32,\cdot)$	3381.cl	462	yes	$-1$	$1$	$e\left(\frac{409}{462}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{331}{462}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{185}{462}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{29}{462}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{3381}(34,\cdot)$	3381.cd	154	no	$1$	$1$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{3381}(37,\cdot)$	3381.ch	462	no	$-1$	$1$	$e\left(\frac{166}{231}\right)$	$e\left(\frac{101}{231}\right)$	$e\left(\frac{23}{462}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{355}{462}\right)$	$e\left(\frac{31}{462}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{3381}(38,\cdot)$	3381.ck	462	yes	$-1$	$1$	$e\left(\frac{373}{462}\right)$	$e\left(\frac{142}{231}\right)$	$e\left(\frac{181}{462}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{46}{231}\right)$	$e\left(\frac{127}{231}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{53}{231}\right)$	$e\left(\frac{101}{462}\right)$	$e\left(\frac{14}{33}\right)$
$\chi_{3381}(40,\cdot)$	3381.cf	462	no	$1$	$1$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{173}{231}\right)$	$e\left(\frac{46}{231}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{17}{231}\right)$	$e\left(\frac{355}{462}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{3381}(41,\cdot)$	3381.bz	154	yes	$1$	$1$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{3381}(43,\cdot)$	3381.cb	154	no	$-1$	$1$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{3381}(44,\cdot)$	3381.ci	462	yes	$1$	$1$	$e\left(\frac{293}{462}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{142}{231}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{115}{462}\right)$	$e\left(\frac{101}{231}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{92}{231}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{3381}(47,\cdot)$	3381.bk	42	no	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3381}(50,\cdot)$	3381.bg	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{3381}(52,\cdot)$	3381.cg	462	no	$-1$	$1$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{118}{231}\right)$	$e\left(\frac{235}{462}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{353}{462}\right)$	$e\left(\frac{73}{231}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{5}{231}\right)$	$e\left(\frac{149}{462}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{3381}(53,\cdot)$	3381.ci	462	yes	$1$	$1$	$e\left(\frac{193}{462}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{317}{462}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{3381}(55,\cdot)$	3381.cc	154	no	$-1$	$1$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{3381}(58,\cdot)$	3381.ce	231	no	$1$	$1$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{67}{231}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{20}{231}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{3381}(59,\cdot)$	3381.cj	462	yes	$1$	$1$	$e\left(\frac{379}{462}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{431}{462}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{25}{66}\right)$

Click here to search among the remaining 1816 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	$3381$
Structure	\(C_{2}\times C_{2}\times C_{462}\)
Order	$1848$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{3381}(1,\cdot)\)	3381.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3381}(2,\cdot)\)	3381.cl	462	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{462}\right)\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{251}{462}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{283}{462}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{3381}(4,\cdot)\)	3381.ce	231	no	\(1\)	\(1\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{20}{231}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{50}{231}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{3381}(5,\cdot)\)	3381.ck	462	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{462}\right)\)	\(e\left(\frac{20}{231}\right)\)	\(e\left(\frac{263}{462}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{3381}(8,\cdot)\)	3381.bx	154	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{3381}(10,\cdot)\)	3381.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{3381}(11,\cdot)\)	3381.ci	462	yes	\(1\)	\(1\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{3381}(13,\cdot)\)	3381.cc	154	no	\(-1\)	\(1\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{3381}(16,\cdot)\)	3381.ce	231	no	\(1\)	\(1\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{50}{231}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{104}{231}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{3381}(17,\cdot)\)	3381.ck	462	yes	\(-1\)	\(1\)	\(e\left(\frac{283}{462}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{104}{231}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{3381}(19,\cdot)\)	3381.bv	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{3381}(20,\cdot)\)	3381.by	154	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{3381}(22,\cdot)\)	3381.u	14	no	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{3381}(25,\cdot)\)	3381.ce	231	no	\(1\)	\(1\)	\(e\left(\frac{20}{231}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{3381}(26,\cdot)\)	3381.cj	462	yes	\(1\)	\(1\)	\(e\left(\frac{221}{462}\right)\)	\(e\left(\frac{221}{231}\right)\)	\(e\left(\frac{223}{231}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{205}{462}\right)\)	\(e\left(\frac{109}{462}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{211}{231}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{3381}(29,\cdot)\)	3381.bx	154	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{3381}(31,\cdot)\)	3381.bu	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{3381}(32,\cdot)\)	3381.cl	462	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{462}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{331}{462}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{185}{462}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{29}{462}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{3381}(34,\cdot)\)	3381.cd	154	no	\(1\)	\(1\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{3381}(37,\cdot)\)	3381.ch	462	no	\(-1\)	\(1\)	\(e\left(\frac{166}{231}\right)\)	\(e\left(\frac{101}{231}\right)\)	\(e\left(\frac{23}{462}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{355}{462}\right)\)	\(e\left(\frac{31}{462}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{3381}(38,\cdot)\)	3381.ck	462	yes	\(-1\)	\(1\)	\(e\left(\frac{373}{462}\right)\)	\(e\left(\frac{142}{231}\right)\)	\(e\left(\frac{181}{462}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{46}{231}\right)\)	\(e\left(\frac{127}{231}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{53}{231}\right)\)	\(e\left(\frac{101}{462}\right)\)	\(e\left(\frac{14}{33}\right)\)
\(\chi_{3381}(40,\cdot)\)	3381.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{173}{231}\right)\)	\(e\left(\frac{46}{231}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{17}{231}\right)\)	\(e\left(\frac{355}{462}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{3381}(41,\cdot)\)	3381.bz	154	yes	\(1\)	\(1\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{3381}(43,\cdot)\)	3381.cb	154	no	\(-1\)	\(1\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{3381}(44,\cdot)\)	3381.ci	462	yes	\(1\)	\(1\)	\(e\left(\frac{293}{462}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{142}{231}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{115}{462}\right)\)	\(e\left(\frac{101}{231}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{92}{231}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{3381}(47,\cdot)\)	3381.bk	42	no	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3381}(50,\cdot)\)	3381.bg	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{3381}(52,\cdot)\)	3381.cg	462	no	\(-1\)	\(1\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{118}{231}\right)\)	\(e\left(\frac{235}{462}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{353}{462}\right)\)	\(e\left(\frac{73}{231}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{5}{231}\right)\)	\(e\left(\frac{149}{462}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{3381}(53,\cdot)\)	3381.ci	462	yes	\(1\)	\(1\)	\(e\left(\frac{193}{462}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{317}{462}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{3381}(55,\cdot)\)	3381.cc	154	no	\(-1\)	\(1\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{3381}(58,\cdot)\)	3381.ce	231	no	\(1\)	\(1\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{67}{231}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{20}{231}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{3381}(59,\cdot)\)	3381.cj	462	yes	\(1\)	\(1\)	\(e\left(\frac{379}{462}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{431}{462}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{25}{66}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1848 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.