LMFDB - Group of Dirichlet characters of modulus 227

Show commands: PariGP / SageMath

sage: H = DirichletGroup(227)

pari: g = idealstar(,227,2)

Character group

sage: G.order() pari: g.no
Order	=	226
sage: H.invariants() pari: g.cyc
Structure	=	$C_{226}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{227}(2,\cdot)$

First 32 of 226 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{227}(1,\cdot)$	227.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{227}(2,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{1}{226}\right)$	$e\left(\frac{23}{113}\right)$	$e\left(\frac{1}{113}\right)$	$e\left(\frac{11}{226}\right)$	$e\left(\frac{47}{226}\right)$	$e\left(\frac{77}{113}\right)$	$e\left(\frac{3}{226}\right)$	$e\left(\frac{46}{113}\right)$	$e\left(\frac{6}{113}\right)$	$e\left(\frac{14}{113}\right)$
$\chi_{227}(3,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{23}{113}\right)$	$e\left(\frac{41}{113}\right)$	$e\left(\frac{46}{113}\right)$	$e\left(\frac{27}{113}\right)$	$e\left(\frac{64}{113}\right)$	$e\left(\frac{39}{113}\right)$	$e\left(\frac{69}{113}\right)$	$e\left(\frac{82}{113}\right)$	$e\left(\frac{50}{113}\right)$	$e\left(\frac{79}{113}\right)$
$\chi_{227}(4,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{1}{113}\right)$	$e\left(\frac{46}{113}\right)$	$e\left(\frac{2}{113}\right)$	$e\left(\frac{11}{113}\right)$	$e\left(\frac{47}{113}\right)$	$e\left(\frac{41}{113}\right)$	$e\left(\frac{3}{113}\right)$	$e\left(\frac{92}{113}\right)$	$e\left(\frac{12}{113}\right)$	$e\left(\frac{28}{113}\right)$
$\chi_{227}(5,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{11}{226}\right)$	$e\left(\frac{27}{113}\right)$	$e\left(\frac{11}{113}\right)$	$e\left(\frac{121}{226}\right)$	$e\left(\frac{65}{226}\right)$	$e\left(\frac{56}{113}\right)$	$e\left(\frac{33}{226}\right)$	$e\left(\frac{54}{113}\right)$	$e\left(\frac{66}{113}\right)$	$e\left(\frac{41}{113}\right)$
$\chi_{227}(6,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{47}{226}\right)$	$e\left(\frac{64}{113}\right)$	$e\left(\frac{47}{113}\right)$	$e\left(\frac{65}{226}\right)$	$e\left(\frac{175}{226}\right)$	$e\left(\frac{3}{113}\right)$	$e\left(\frac{141}{226}\right)$	$e\left(\frac{15}{113}\right)$	$e\left(\frac{56}{113}\right)$	$e\left(\frac{93}{113}\right)$
$\chi_{227}(7,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{77}{113}\right)$	$e\left(\frac{39}{113}\right)$	$e\left(\frac{41}{113}\right)$	$e\left(\frac{56}{113}\right)$	$e\left(\frac{3}{113}\right)$	$e\left(\frac{106}{113}\right)$	$e\left(\frac{5}{113}\right)$	$e\left(\frac{78}{113}\right)$	$e\left(\frac{20}{113}\right)$	$e\left(\frac{9}{113}\right)$
$\chi_{227}(8,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{3}{226}\right)$	$e\left(\frac{69}{113}\right)$	$e\left(\frac{3}{113}\right)$	$e\left(\frac{33}{226}\right)$	$e\left(\frac{141}{226}\right)$	$e\left(\frac{5}{113}\right)$	$e\left(\frac{9}{226}\right)$	$e\left(\frac{25}{113}\right)$	$e\left(\frac{18}{113}\right)$	$e\left(\frac{42}{113}\right)$
$\chi_{227}(9,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{46}{113}\right)$	$e\left(\frac{82}{113}\right)$	$e\left(\frac{92}{113}\right)$	$e\left(\frac{54}{113}\right)$	$e\left(\frac{15}{113}\right)$	$e\left(\frac{78}{113}\right)$	$e\left(\frac{25}{113}\right)$	$e\left(\frac{51}{113}\right)$	$e\left(\frac{100}{113}\right)$	$e\left(\frac{45}{113}\right)$
$\chi_{227}(10,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{6}{113}\right)$	$e\left(\frac{50}{113}\right)$	$e\left(\frac{12}{113}\right)$	$e\left(\frac{66}{113}\right)$	$e\left(\frac{56}{113}\right)$	$e\left(\frac{20}{113}\right)$	$e\left(\frac{18}{113}\right)$	$e\left(\frac{100}{113}\right)$	$e\left(\frac{72}{113}\right)$	$e\left(\frac{55}{113}\right)$
$\chi_{227}(11,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{14}{113}\right)$	$e\left(\frac{79}{113}\right)$	$e\left(\frac{28}{113}\right)$	$e\left(\frac{41}{113}\right)$	$e\left(\frac{93}{113}\right)$	$e\left(\frac{9}{113}\right)$	$e\left(\frac{42}{113}\right)$	$e\left(\frac{45}{113}\right)$	$e\left(\frac{55}{113}\right)$	$e\left(\frac{53}{113}\right)$
$\chi_{227}(12,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{24}{113}\right)$	$e\left(\frac{87}{113}\right)$	$e\left(\frac{48}{113}\right)$	$e\left(\frac{38}{113}\right)$	$e\left(\frac{111}{113}\right)$	$e\left(\frac{80}{113}\right)$	$e\left(\frac{72}{113}\right)$	$e\left(\frac{61}{113}\right)$	$e\left(\frac{62}{113}\right)$	$e\left(\frac{107}{113}\right)$
$\chi_{227}(13,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{61}{226}\right)$	$e\left(\frac{47}{113}\right)$	$e\left(\frac{61}{113}\right)$	$e\left(\frac{219}{226}\right)$	$e\left(\frac{155}{226}\right)$	$e\left(\frac{64}{113}\right)$	$e\left(\frac{183}{226}\right)$	$e\left(\frac{94}{113}\right)$	$e\left(\frac{27}{113}\right)$	$e\left(\frac{63}{113}\right)$
$\chi_{227}(14,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{155}{226}\right)$	$e\left(\frac{62}{113}\right)$	$e\left(\frac{42}{113}\right)$	$e\left(\frac{123}{226}\right)$	$e\left(\frac{53}{226}\right)$	$e\left(\frac{70}{113}\right)$	$e\left(\frac{13}{226}\right)$	$e\left(\frac{11}{113}\right)$	$e\left(\frac{26}{113}\right)$	$e\left(\frac{23}{113}\right)$
$\chi_{227}(15,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{57}{226}\right)$	$e\left(\frac{68}{113}\right)$	$e\left(\frac{57}{113}\right)$	$e\left(\frac{175}{226}\right)$	$e\left(\frac{193}{226}\right)$	$e\left(\frac{95}{113}\right)$	$e\left(\frac{171}{226}\right)$	$e\left(\frac{23}{113}\right)$	$e\left(\frac{3}{113}\right)$	$e\left(\frac{7}{113}\right)$
$\chi_{227}(16,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{2}{113}\right)$	$e\left(\frac{92}{113}\right)$	$e\left(\frac{4}{113}\right)$	$e\left(\frac{22}{113}\right)$	$e\left(\frac{94}{113}\right)$	$e\left(\frac{82}{113}\right)$	$e\left(\frac{6}{113}\right)$	$e\left(\frac{71}{113}\right)$	$e\left(\frac{24}{113}\right)$	$e\left(\frac{56}{113}\right)$
$\chi_{227}(17,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{99}{226}\right)$	$e\left(\frac{17}{113}\right)$	$e\left(\frac{99}{113}\right)$	$e\left(\frac{185}{226}\right)$	$e\left(\frac{133}{226}\right)$	$e\left(\frac{52}{113}\right)$	$e\left(\frac{71}{226}\right)$	$e\left(\frac{34}{113}\right)$	$e\left(\frac{29}{113}\right)$	$e\left(\frac{30}{113}\right)$
$\chi_{227}(18,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{93}{226}\right)$	$e\left(\frac{105}{113}\right)$	$e\left(\frac{93}{113}\right)$	$e\left(\frac{119}{226}\right)$	$e\left(\frac{77}{226}\right)$	$e\left(\frac{42}{113}\right)$	$e\left(\frac{53}{226}\right)$	$e\left(\frac{97}{113}\right)$	$e\left(\frac{106}{113}\right)$	$e\left(\frac{59}{113}\right)$
$\chi_{227}(19,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{89}{113}\right)$	$e\left(\frac{26}{113}\right)$	$e\left(\frac{65}{113}\right)$	$e\left(\frac{75}{113}\right)$	$e\left(\frac{2}{113}\right)$	$e\left(\frac{33}{113}\right)$	$e\left(\frac{41}{113}\right)$	$e\left(\frac{52}{113}\right)$	$e\left(\frac{51}{113}\right)$	$e\left(\frac{6}{113}\right)$
$\chi_{227}(20,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{13}{226}\right)$	$e\left(\frac{73}{113}\right)$	$e\left(\frac{13}{113}\right)$	$e\left(\frac{143}{226}\right)$	$e\left(\frac{159}{226}\right)$	$e\left(\frac{97}{113}\right)$	$e\left(\frac{39}{226}\right)$	$e\left(\frac{33}{113}\right)$	$e\left(\frac{78}{113}\right)$	$e\left(\frac{69}{113}\right)$
$\chi_{227}(21,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{100}{113}\right)$	$e\left(\frac{80}{113}\right)$	$e\left(\frac{87}{113}\right)$	$e\left(\frac{83}{113}\right)$	$e\left(\frac{67}{113}\right)$	$e\left(\frac{32}{113}\right)$	$e\left(\frac{74}{113}\right)$	$e\left(\frac{47}{113}\right)$	$e\left(\frac{70}{113}\right)$	$e\left(\frac{88}{113}\right)$
$\chi_{227}(22,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{29}{226}\right)$	$e\left(\frac{102}{113}\right)$	$e\left(\frac{29}{113}\right)$	$e\left(\frac{93}{226}\right)$	$e\left(\frac{7}{226}\right)$	$e\left(\frac{86}{113}\right)$	$e\left(\frac{87}{226}\right)$	$e\left(\frac{91}{113}\right)$	$e\left(\frac{61}{113}\right)$	$e\left(\frac{67}{113}\right)$
$\chi_{227}(23,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{17}{113}\right)$	$e\left(\frac{104}{113}\right)$	$e\left(\frac{34}{113}\right)$	$e\left(\frac{74}{113}\right)$	$e\left(\frac{8}{113}\right)$	$e\left(\frac{19}{113}\right)$	$e\left(\frac{51}{113}\right)$	$e\left(\frac{95}{113}\right)$	$e\left(\frac{91}{113}\right)$	$e\left(\frac{24}{113}\right)$
$\chi_{227}(24,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{49}{226}\right)$	$e\left(\frac{110}{113}\right)$	$e\left(\frac{49}{113}\right)$	$e\left(\frac{87}{226}\right)$	$e\left(\frac{43}{226}\right)$	$e\left(\frac{44}{113}\right)$	$e\left(\frac{147}{226}\right)$	$e\left(\frac{107}{113}\right)$	$e\left(\frac{68}{113}\right)$	$e\left(\frac{8}{113}\right)$
$\chi_{227}(25,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{11}{113}\right)$	$e\left(\frac{54}{113}\right)$	$e\left(\frac{22}{113}\right)$	$e\left(\frac{8}{113}\right)$	$e\left(\frac{65}{113}\right)$	$e\left(\frac{112}{113}\right)$	$e\left(\frac{33}{113}\right)$	$e\left(\frac{108}{113}\right)$	$e\left(\frac{19}{113}\right)$	$e\left(\frac{82}{113}\right)$
$\chi_{227}(26,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{31}{113}\right)$	$e\left(\frac{70}{113}\right)$	$e\left(\frac{62}{113}\right)$	$e\left(\frac{2}{113}\right)$	$e\left(\frac{101}{113}\right)$	$e\left(\frac{28}{113}\right)$	$e\left(\frac{93}{113}\right)$	$e\left(\frac{27}{113}\right)$	$e\left(\frac{33}{113}\right)$	$e\left(\frac{77}{113}\right)$
$\chi_{227}(27,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{69}{113}\right)$	$e\left(\frac{10}{113}\right)$	$e\left(\frac{25}{113}\right)$	$e\left(\frac{81}{113}\right)$	$e\left(\frac{79}{113}\right)$	$e\left(\frac{4}{113}\right)$	$e\left(\frac{94}{113}\right)$	$e\left(\frac{20}{113}\right)$	$e\left(\frac{37}{113}\right)$	$e\left(\frac{11}{113}\right)$
$\chi_{227}(28,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{78}{113}\right)$	$e\left(\frac{85}{113}\right)$	$e\left(\frac{43}{113}\right)$	$e\left(\frac{67}{113}\right)$	$e\left(\frac{50}{113}\right)$	$e\left(\frac{34}{113}\right)$	$e\left(\frac{8}{113}\right)$	$e\left(\frac{57}{113}\right)$	$e\left(\frac{32}{113}\right)$	$e\left(\frac{37}{113}\right)$
$\chi_{227}(29,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{4}{113}\right)$	$e\left(\frac{71}{113}\right)$	$e\left(\frac{8}{113}\right)$	$e\left(\frac{44}{113}\right)$	$e\left(\frac{75}{113}\right)$	$e\left(\frac{51}{113}\right)$	$e\left(\frac{12}{113}\right)$	$e\left(\frac{29}{113}\right)$	$e\left(\frac{48}{113}\right)$	$e\left(\frac{112}{113}\right)$
$\chi_{227}(30,\cdot)$	227.c	113	yes	$1$	$1$	$e\left(\frac{29}{113}\right)$	$e\left(\frac{91}{113}\right)$	$e\left(\frac{58}{113}\right)$	$e\left(\frac{93}{113}\right)$	$e\left(\frac{7}{113}\right)$	$e\left(\frac{59}{113}\right)$	$e\left(\frac{87}{113}\right)$	$e\left(\frac{69}{113}\right)$	$e\left(\frac{9}{113}\right)$	$e\left(\frac{21}{113}\right)$
$\chi_{227}(31,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{197}{226}\right)$	$e\left(\frac{11}{113}\right)$	$e\left(\frac{84}{113}\right)$	$e\left(\frac{133}{226}\right)$	$e\left(\frac{219}{226}\right)$	$e\left(\frac{27}{113}\right)$	$e\left(\frac{139}{226}\right)$	$e\left(\frac{22}{113}\right)$	$e\left(\frac{52}{113}\right)$	$e\left(\frac{46}{113}\right)$
$\chi_{227}(32,\cdot)$	227.d	226	yes	$-1$	$1$	$e\left(\frac{5}{226}\right)$	$e\left(\frac{2}{113}\right)$	$e\left(\frac{5}{113}\right)$	$e\left(\frac{55}{226}\right)$	$e\left(\frac{9}{226}\right)$	$e\left(\frac{46}{113}\right)$	$e\left(\frac{15}{226}\right)$	$e\left(\frac{4}{113}\right)$	$e\left(\frac{30}{113}\right)$	$e\left(\frac{70}{113}\right)$

Click here to search among the remaining 194 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	$227$
Structure	\(C_{226}\)
Order	$226$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{227}(1,\cdot)\)	227.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{227}(2,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{226}\right)\)	\(e\left(\frac{23}{113}\right)\)	\(e\left(\frac{1}{113}\right)\)	\(e\left(\frac{11}{226}\right)\)	\(e\left(\frac{47}{226}\right)\)	\(e\left(\frac{77}{113}\right)\)	\(e\left(\frac{3}{226}\right)\)	\(e\left(\frac{46}{113}\right)\)	\(e\left(\frac{6}{113}\right)\)	\(e\left(\frac{14}{113}\right)\)
\(\chi_{227}(3,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{23}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)	\(e\left(\frac{46}{113}\right)\)	\(e\left(\frac{27}{113}\right)\)	\(e\left(\frac{64}{113}\right)\)	\(e\left(\frac{39}{113}\right)\)	\(e\left(\frac{69}{113}\right)\)	\(e\left(\frac{82}{113}\right)\)	\(e\left(\frac{50}{113}\right)\)	\(e\left(\frac{79}{113}\right)\)
\(\chi_{227}(4,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{1}{113}\right)\)	\(e\left(\frac{46}{113}\right)\)	\(e\left(\frac{2}{113}\right)\)	\(e\left(\frac{11}{113}\right)\)	\(e\left(\frac{47}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)	\(e\left(\frac{3}{113}\right)\)	\(e\left(\frac{92}{113}\right)\)	\(e\left(\frac{12}{113}\right)\)	\(e\left(\frac{28}{113}\right)\)
\(\chi_{227}(5,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{226}\right)\)	\(e\left(\frac{27}{113}\right)\)	\(e\left(\frac{11}{113}\right)\)	\(e\left(\frac{121}{226}\right)\)	\(e\left(\frac{65}{226}\right)\)	\(e\left(\frac{56}{113}\right)\)	\(e\left(\frac{33}{226}\right)\)	\(e\left(\frac{54}{113}\right)\)	\(e\left(\frac{66}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)
\(\chi_{227}(6,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{226}\right)\)	\(e\left(\frac{64}{113}\right)\)	\(e\left(\frac{47}{113}\right)\)	\(e\left(\frac{65}{226}\right)\)	\(e\left(\frac{175}{226}\right)\)	\(e\left(\frac{3}{113}\right)\)	\(e\left(\frac{141}{226}\right)\)	\(e\left(\frac{15}{113}\right)\)	\(e\left(\frac{56}{113}\right)\)	\(e\left(\frac{93}{113}\right)\)
\(\chi_{227}(7,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{77}{113}\right)\)	\(e\left(\frac{39}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)	\(e\left(\frac{56}{113}\right)\)	\(e\left(\frac{3}{113}\right)\)	\(e\left(\frac{106}{113}\right)\)	\(e\left(\frac{5}{113}\right)\)	\(e\left(\frac{78}{113}\right)\)	\(e\left(\frac{20}{113}\right)\)	\(e\left(\frac{9}{113}\right)\)
\(\chi_{227}(8,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{226}\right)\)	\(e\left(\frac{69}{113}\right)\)	\(e\left(\frac{3}{113}\right)\)	\(e\left(\frac{33}{226}\right)\)	\(e\left(\frac{141}{226}\right)\)	\(e\left(\frac{5}{113}\right)\)	\(e\left(\frac{9}{226}\right)\)	\(e\left(\frac{25}{113}\right)\)	\(e\left(\frac{18}{113}\right)\)	\(e\left(\frac{42}{113}\right)\)
\(\chi_{227}(9,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{46}{113}\right)\)	\(e\left(\frac{82}{113}\right)\)	\(e\left(\frac{92}{113}\right)\)	\(e\left(\frac{54}{113}\right)\)	\(e\left(\frac{15}{113}\right)\)	\(e\left(\frac{78}{113}\right)\)	\(e\left(\frac{25}{113}\right)\)	\(e\left(\frac{51}{113}\right)\)	\(e\left(\frac{100}{113}\right)\)	\(e\left(\frac{45}{113}\right)\)
\(\chi_{227}(10,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{6}{113}\right)\)	\(e\left(\frac{50}{113}\right)\)	\(e\left(\frac{12}{113}\right)\)	\(e\left(\frac{66}{113}\right)\)	\(e\left(\frac{56}{113}\right)\)	\(e\left(\frac{20}{113}\right)\)	\(e\left(\frac{18}{113}\right)\)	\(e\left(\frac{100}{113}\right)\)	\(e\left(\frac{72}{113}\right)\)	\(e\left(\frac{55}{113}\right)\)
\(\chi_{227}(11,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{14}{113}\right)\)	\(e\left(\frac{79}{113}\right)\)	\(e\left(\frac{28}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)	\(e\left(\frac{93}{113}\right)\)	\(e\left(\frac{9}{113}\right)\)	\(e\left(\frac{42}{113}\right)\)	\(e\left(\frac{45}{113}\right)\)	\(e\left(\frac{55}{113}\right)\)	\(e\left(\frac{53}{113}\right)\)
\(\chi_{227}(12,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{24}{113}\right)\)	\(e\left(\frac{87}{113}\right)\)	\(e\left(\frac{48}{113}\right)\)	\(e\left(\frac{38}{113}\right)\)	\(e\left(\frac{111}{113}\right)\)	\(e\left(\frac{80}{113}\right)\)	\(e\left(\frac{72}{113}\right)\)	\(e\left(\frac{61}{113}\right)\)	\(e\left(\frac{62}{113}\right)\)	\(e\left(\frac{107}{113}\right)\)
\(\chi_{227}(13,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{226}\right)\)	\(e\left(\frac{47}{113}\right)\)	\(e\left(\frac{61}{113}\right)\)	\(e\left(\frac{219}{226}\right)\)	\(e\left(\frac{155}{226}\right)\)	\(e\left(\frac{64}{113}\right)\)	\(e\left(\frac{183}{226}\right)\)	\(e\left(\frac{94}{113}\right)\)	\(e\left(\frac{27}{113}\right)\)	\(e\left(\frac{63}{113}\right)\)
\(\chi_{227}(14,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{226}\right)\)	\(e\left(\frac{62}{113}\right)\)	\(e\left(\frac{42}{113}\right)\)	\(e\left(\frac{123}{226}\right)\)	\(e\left(\frac{53}{226}\right)\)	\(e\left(\frac{70}{113}\right)\)	\(e\left(\frac{13}{226}\right)\)	\(e\left(\frac{11}{113}\right)\)	\(e\left(\frac{26}{113}\right)\)	\(e\left(\frac{23}{113}\right)\)
\(\chi_{227}(15,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{226}\right)\)	\(e\left(\frac{68}{113}\right)\)	\(e\left(\frac{57}{113}\right)\)	\(e\left(\frac{175}{226}\right)\)	\(e\left(\frac{193}{226}\right)\)	\(e\left(\frac{95}{113}\right)\)	\(e\left(\frac{171}{226}\right)\)	\(e\left(\frac{23}{113}\right)\)	\(e\left(\frac{3}{113}\right)\)	\(e\left(\frac{7}{113}\right)\)
\(\chi_{227}(16,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{2}{113}\right)\)	\(e\left(\frac{92}{113}\right)\)	\(e\left(\frac{4}{113}\right)\)	\(e\left(\frac{22}{113}\right)\)	\(e\left(\frac{94}{113}\right)\)	\(e\left(\frac{82}{113}\right)\)	\(e\left(\frac{6}{113}\right)\)	\(e\left(\frac{71}{113}\right)\)	\(e\left(\frac{24}{113}\right)\)	\(e\left(\frac{56}{113}\right)\)
\(\chi_{227}(17,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{226}\right)\)	\(e\left(\frac{17}{113}\right)\)	\(e\left(\frac{99}{113}\right)\)	\(e\left(\frac{185}{226}\right)\)	\(e\left(\frac{133}{226}\right)\)	\(e\left(\frac{52}{113}\right)\)	\(e\left(\frac{71}{226}\right)\)	\(e\left(\frac{34}{113}\right)\)	\(e\left(\frac{29}{113}\right)\)	\(e\left(\frac{30}{113}\right)\)
\(\chi_{227}(18,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{226}\right)\)	\(e\left(\frac{105}{113}\right)\)	\(e\left(\frac{93}{113}\right)\)	\(e\left(\frac{119}{226}\right)\)	\(e\left(\frac{77}{226}\right)\)	\(e\left(\frac{42}{113}\right)\)	\(e\left(\frac{53}{226}\right)\)	\(e\left(\frac{97}{113}\right)\)	\(e\left(\frac{106}{113}\right)\)	\(e\left(\frac{59}{113}\right)\)
\(\chi_{227}(19,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{89}{113}\right)\)	\(e\left(\frac{26}{113}\right)\)	\(e\left(\frac{65}{113}\right)\)	\(e\left(\frac{75}{113}\right)\)	\(e\left(\frac{2}{113}\right)\)	\(e\left(\frac{33}{113}\right)\)	\(e\left(\frac{41}{113}\right)\)	\(e\left(\frac{52}{113}\right)\)	\(e\left(\frac{51}{113}\right)\)	\(e\left(\frac{6}{113}\right)\)
\(\chi_{227}(20,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{226}\right)\)	\(e\left(\frac{73}{113}\right)\)	\(e\left(\frac{13}{113}\right)\)	\(e\left(\frac{143}{226}\right)\)	\(e\left(\frac{159}{226}\right)\)	\(e\left(\frac{97}{113}\right)\)	\(e\left(\frac{39}{226}\right)\)	\(e\left(\frac{33}{113}\right)\)	\(e\left(\frac{78}{113}\right)\)	\(e\left(\frac{69}{113}\right)\)
\(\chi_{227}(21,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{100}{113}\right)\)	\(e\left(\frac{80}{113}\right)\)	\(e\left(\frac{87}{113}\right)\)	\(e\left(\frac{83}{113}\right)\)	\(e\left(\frac{67}{113}\right)\)	\(e\left(\frac{32}{113}\right)\)	\(e\left(\frac{74}{113}\right)\)	\(e\left(\frac{47}{113}\right)\)	\(e\left(\frac{70}{113}\right)\)	\(e\left(\frac{88}{113}\right)\)
\(\chi_{227}(22,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{226}\right)\)	\(e\left(\frac{102}{113}\right)\)	\(e\left(\frac{29}{113}\right)\)	\(e\left(\frac{93}{226}\right)\)	\(e\left(\frac{7}{226}\right)\)	\(e\left(\frac{86}{113}\right)\)	\(e\left(\frac{87}{226}\right)\)	\(e\left(\frac{91}{113}\right)\)	\(e\left(\frac{61}{113}\right)\)	\(e\left(\frac{67}{113}\right)\)
\(\chi_{227}(23,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{17}{113}\right)\)	\(e\left(\frac{104}{113}\right)\)	\(e\left(\frac{34}{113}\right)\)	\(e\left(\frac{74}{113}\right)\)	\(e\left(\frac{8}{113}\right)\)	\(e\left(\frac{19}{113}\right)\)	\(e\left(\frac{51}{113}\right)\)	\(e\left(\frac{95}{113}\right)\)	\(e\left(\frac{91}{113}\right)\)	\(e\left(\frac{24}{113}\right)\)
\(\chi_{227}(24,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{226}\right)\)	\(e\left(\frac{110}{113}\right)\)	\(e\left(\frac{49}{113}\right)\)	\(e\left(\frac{87}{226}\right)\)	\(e\left(\frac{43}{226}\right)\)	\(e\left(\frac{44}{113}\right)\)	\(e\left(\frac{147}{226}\right)\)	\(e\left(\frac{107}{113}\right)\)	\(e\left(\frac{68}{113}\right)\)	\(e\left(\frac{8}{113}\right)\)
\(\chi_{227}(25,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{11}{113}\right)\)	\(e\left(\frac{54}{113}\right)\)	\(e\left(\frac{22}{113}\right)\)	\(e\left(\frac{8}{113}\right)\)	\(e\left(\frac{65}{113}\right)\)	\(e\left(\frac{112}{113}\right)\)	\(e\left(\frac{33}{113}\right)\)	\(e\left(\frac{108}{113}\right)\)	\(e\left(\frac{19}{113}\right)\)	\(e\left(\frac{82}{113}\right)\)
\(\chi_{227}(26,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{31}{113}\right)\)	\(e\left(\frac{70}{113}\right)\)	\(e\left(\frac{62}{113}\right)\)	\(e\left(\frac{2}{113}\right)\)	\(e\left(\frac{101}{113}\right)\)	\(e\left(\frac{28}{113}\right)\)	\(e\left(\frac{93}{113}\right)\)	\(e\left(\frac{27}{113}\right)\)	\(e\left(\frac{33}{113}\right)\)	\(e\left(\frac{77}{113}\right)\)
\(\chi_{227}(27,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{69}{113}\right)\)	\(e\left(\frac{10}{113}\right)\)	\(e\left(\frac{25}{113}\right)\)	\(e\left(\frac{81}{113}\right)\)	\(e\left(\frac{79}{113}\right)\)	\(e\left(\frac{4}{113}\right)\)	\(e\left(\frac{94}{113}\right)\)	\(e\left(\frac{20}{113}\right)\)	\(e\left(\frac{37}{113}\right)\)	\(e\left(\frac{11}{113}\right)\)
\(\chi_{227}(28,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{78}{113}\right)\)	\(e\left(\frac{85}{113}\right)\)	\(e\left(\frac{43}{113}\right)\)	\(e\left(\frac{67}{113}\right)\)	\(e\left(\frac{50}{113}\right)\)	\(e\left(\frac{34}{113}\right)\)	\(e\left(\frac{8}{113}\right)\)	\(e\left(\frac{57}{113}\right)\)	\(e\left(\frac{32}{113}\right)\)	\(e\left(\frac{37}{113}\right)\)
\(\chi_{227}(29,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{4}{113}\right)\)	\(e\left(\frac{71}{113}\right)\)	\(e\left(\frac{8}{113}\right)\)	\(e\left(\frac{44}{113}\right)\)	\(e\left(\frac{75}{113}\right)\)	\(e\left(\frac{51}{113}\right)\)	\(e\left(\frac{12}{113}\right)\)	\(e\left(\frac{29}{113}\right)\)	\(e\left(\frac{48}{113}\right)\)	\(e\left(\frac{112}{113}\right)\)
\(\chi_{227}(30,\cdot)\)	227.c	113	yes	\(1\)	\(1\)	\(e\left(\frac{29}{113}\right)\)	\(e\left(\frac{91}{113}\right)\)	\(e\left(\frac{58}{113}\right)\)	\(e\left(\frac{93}{113}\right)\)	\(e\left(\frac{7}{113}\right)\)	\(e\left(\frac{59}{113}\right)\)	\(e\left(\frac{87}{113}\right)\)	\(e\left(\frac{69}{113}\right)\)	\(e\left(\frac{9}{113}\right)\)	\(e\left(\frac{21}{113}\right)\)
\(\chi_{227}(31,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{226}\right)\)	\(e\left(\frac{11}{113}\right)\)	\(e\left(\frac{84}{113}\right)\)	\(e\left(\frac{133}{226}\right)\)	\(e\left(\frac{219}{226}\right)\)	\(e\left(\frac{27}{113}\right)\)	\(e\left(\frac{139}{226}\right)\)	\(e\left(\frac{22}{113}\right)\)	\(e\left(\frac{52}{113}\right)\)	\(e\left(\frac{46}{113}\right)\)
\(\chi_{227}(32,\cdot)\)	227.d	226	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{226}\right)\)	\(e\left(\frac{2}{113}\right)\)	\(e\left(\frac{5}{113}\right)\)	\(e\left(\frac{55}{226}\right)\)	\(e\left(\frac{9}{226}\right)\)	\(e\left(\frac{46}{113}\right)\)	\(e\left(\frac{15}{226}\right)\)	\(e\left(\frac{4}{113}\right)\)	\(e\left(\frac{30}{113}\right)\)	\(e\left(\frac{70}{113}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 226 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.