LMFDB - Group of Dirichlet characters of modulus 961

Show commands: PariGP / SageMath

sage: H = DirichletGroup(961)

pari: g = idealstar(,961,2)

Character group

sage: G.order() pari: g.no
Order	=	930
sage: H.invariants() pari: g.cyc
Structure	=	$C_{930}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{961}(3,\cdot)$

First 32 of 930 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{961}(1,\cdot)$	961.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{961}(2,\cdot)$	961.l	155	yes	$1$	$1$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{77}{155}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{141}{155}\right)$	$e\left(\frac{112}{155}\right)$
$\chi_{961}(3,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{1}{930}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{125}{186}\right)$	$e\left(\frac{329}{465}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{1}{465}\right)$	$e\left(\frac{67}{465}\right)$	$e\left(\frac{323}{930}\right)$
$\chi_{961}(4,\cdot)$	961.l	155	yes	$1$	$1$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{154}{155}\right)$	$e\left(\frac{16}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{69}{155}\right)$
$\chi_{961}(5,\cdot)$	961.k	93	yes	$1$	$1$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{76}{93}\right)$
$\chi_{961}(6,\cdot)$	961.m	186	yes	$-1$	$1$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{125}{186}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{5}{186}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{13}{186}\right)$
$\chi_{961}(7,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{77}{155}\right)$	$e\left(\frac{329}{465}\right)$	$e\left(\frac{154}{155}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{257}{465}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{193}{465}\right)$	$e\left(\frac{376}{465}\right)$	$e\left(\frac{247}{465}\right)$
$\chi_{961}(8,\cdot)$	961.l	155	yes	$1$	$1$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{16}{155}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{24}{155}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{26}{155}\right)$
$\chi_{961}(9,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{1}{465}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{193}{465}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{2}{465}\right)$	$e\left(\frac{134}{465}\right)$	$e\left(\frac{323}{465}\right)$
$\chi_{961}(10,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{141}{155}\right)$	$e\left(\frac{67}{465}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{376}{465}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{134}{465}\right)$	$e\left(\frac{143}{465}\right)$	$e\left(\frac{251}{465}\right)$
$\chi_{961}(11,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{112}{155}\right)$	$e\left(\frac{323}{930}\right)$	$e\left(\frac{69}{155}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{247}{465}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{323}{465}\right)$	$e\left(\frac{251}{465}\right)$	$e\left(\frac{169}{930}\right)$
$\chi_{961}(12,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{6}{155}\right)$	$e\left(\frac{319}{930}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{71}{186}\right)$	$e\left(\frac{326}{465}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{319}{465}\right)$	$e\left(\frac{448}{465}\right)$	$e\left(\frac{737}{930}\right)$
$\chi_{961}(13,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{401}{930}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{91}{186}\right)$	$e\left(\frac{334}{465}\right)$	$e\left(\frac{27}{155}\right)$	$e\left(\frac{401}{465}\right)$	$e\left(\frac{362}{465}\right)$	$e\left(\frac{253}{930}\right)$
$\chi_{961}(14,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{28}{155}\right)$	$e\left(\frac{176}{465}\right)$	$e\left(\frac{56}{155}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{23}{465}\right)$	$e\left(\frac{84}{155}\right)$	$e\left(\frac{352}{465}\right)$	$e\left(\frac{334}{465}\right)$	$e\left(\frac{118}{465}\right)$
$\chi_{961}(15,\cdot)$	961.n	310	yes	$-1$	$1$	$e\left(\frac{139}{155}\right)$	$e\left(\frac{147}{310}\right)$	$e\left(\frac{123}{155}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{84}{155}\right)$	$e\left(\frac{51}{310}\right)$
$\chi_{961}(16,\cdot)$	961.l	155	yes	$1$	$1$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{73}{155}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{138}{155}\right)$
$\chi_{961}(17,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{123}{155}\right)$	$e\left(\frac{727}{930}\right)$	$e\left(\frac{91}{155}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{107}{186}\right)$	$e\left(\frac{173}{465}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{262}{465}\right)$	$e\left(\frac{349}{465}\right)$	$e\left(\frac{461}{930}\right)$
$\chi_{961}(18,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{313}{465}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{424}{465}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{161}{465}\right)$	$e\left(\frac{92}{465}\right)$	$e\left(\frac{194}{465}\right)$
$\chi_{961}(19,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{91}{155}\right)$	$e\left(\frac{107}{465}\right)$	$e\left(\frac{27}{155}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{214}{465}\right)$	$e\left(\frac{388}{465}\right)$	$e\left(\frac{151}{465}\right)$
$\chi_{961}(20,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{92}{155}\right)$	$e\left(\frac{379}{465}\right)$	$e\left(\frac{29}{155}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{142}{465}\right)$	$e\left(\frac{121}{155}\right)$	$e\left(\frac{293}{465}\right)$	$e\left(\frac{101}{465}\right)$	$e\left(\frac{122}{465}\right)$
$\chi_{961}(21,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{659}{930}\right)$	$e\left(\frac{52}{155}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{163}{186}\right)$	$e\left(\frac{121}{465}\right)$	$e\left(\frac{78}{155}\right)$	$e\left(\frac{194}{465}\right)$	$e\left(\frac{443}{465}\right)$	$e\left(\frac{817}{930}\right)$
$\chi_{961}(22,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{63}{155}\right)$	$e\left(\frac{17}{930}\right)$	$e\left(\frac{126}{155}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{79}{186}\right)$	$e\left(\frac{13}{465}\right)$	$e\left(\frac{34}{155}\right)$	$e\left(\frac{17}{465}\right)$	$e\left(\frac{209}{465}\right)$	$e\left(\frac{841}{930}\right)$
$\chi_{961}(23,\cdot)$	961.n	310	yes	$-1$	$1$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{29}{310}\right)$	$e\left(\frac{116}{155}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{29}{62}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{29}{155}\right)$	$e\left(\frac{83}{155}\right)$	$e\left(\frac{67}{310}\right)$
$\chi_{961}(24,\cdot)$	961.p	930	yes	$-1$	$1$	$e\left(\frac{112}{155}\right)$	$e\left(\frac{13}{930}\right)$	$e\left(\frac{69}{155}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{137}{186}\right)$	$e\left(\frac{92}{465}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{13}{465}\right)$	$e\left(\frac{406}{465}\right)$	$e\left(\frac{479}{930}\right)$
$\chi_{961}(25,\cdot)$	961.k	93	yes	$1$	$1$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{59}{93}\right)$
$\chi_{961}(26,\cdot)$	961.m	186	yes	$-1$	$1$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{19}{186}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{157}{186}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{185}{186}\right)$
$\chi_{961}(27,\cdot)$	961.n	310	yes	$-1$	$1$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{1}{310}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{6}{155}\right)$	$e\left(\frac{1}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{13}{310}\right)$
$\chi_{961}(28,\cdot)$	961.o	465	yes	$1$	$1$	$e\left(\frac{134}{155}\right)$	$e\left(\frac{23}{465}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{254}{465}\right)$	$e\left(\frac{92}{155}\right)$	$e\left(\frac{46}{465}\right)$	$e\left(\frac{292}{465}\right)$	$e\left(\frac{454}{465}\right)$
$\chi_{961}(29,\cdot)$	961.n	310	yes	$-1$	$1$	$e\left(\frac{151}{155}\right)$	$e\left(\frac{153}{310}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{29}{62}\right)$	$e\left(\frac{117}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{21}{155}\right)$	$e\left(\frac{129}{310}\right)$
$\chi_{961}(30,\cdot)$	961.j	62	yes	$-1$	$1$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{55}{62}\right)$
$\chi_{961}(32,\cdot)$	961.i	31	yes	$1$	$1$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{19}{31}\right)$
$\chi_{961}(33,\cdot)$	961.l	155	yes	$1$	$1$	$e\left(\frac{61}{155}\right)$	$e\left(\frac{54}{155}\right)$	$e\left(\frac{122}{155}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{37}{155}\right)$	$e\left(\frac{28}{155}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{82}{155}\right)$

Click here to search among the remaining 898 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	$961$
Structure	\(C_{930}\)
Order	$930$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{961}(1,\cdot)\)	961.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{961}(2,\cdot)\)	961.l	155	yes	\(1\)	\(1\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{77}{155}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{141}{155}\right)\)	\(e\left(\frac{112}{155}\right)\)
\(\chi_{961}(3,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{1}{930}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{125}{186}\right)\)	\(e\left(\frac{329}{465}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{1}{465}\right)\)	\(e\left(\frac{67}{465}\right)\)	\(e\left(\frac{323}{930}\right)\)
\(\chi_{961}(4,\cdot)\)	961.l	155	yes	\(1\)	\(1\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{154}{155}\right)\)	\(e\left(\frac{16}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{69}{155}\right)\)
\(\chi_{961}(5,\cdot)\)	961.k	93	yes	\(1\)	\(1\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)
\(\chi_{961}(6,\cdot)\)	961.m	186	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{125}{186}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{5}{186}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{13}{186}\right)\)
\(\chi_{961}(7,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{77}{155}\right)\)	\(e\left(\frac{329}{465}\right)\)	\(e\left(\frac{154}{155}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{257}{465}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{193}{465}\right)\)	\(e\left(\frac{376}{465}\right)\)	\(e\left(\frac{247}{465}\right)\)
\(\chi_{961}(8,\cdot)\)	961.l	155	yes	\(1\)	\(1\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{16}{155}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{26}{155}\right)\)
\(\chi_{961}(9,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{1}{465}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{193}{465}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{2}{465}\right)\)	\(e\left(\frac{134}{465}\right)\)	\(e\left(\frac{323}{465}\right)\)
\(\chi_{961}(10,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{141}{155}\right)\)	\(e\left(\frac{67}{465}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{376}{465}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{134}{465}\right)\)	\(e\left(\frac{143}{465}\right)\)	\(e\left(\frac{251}{465}\right)\)
\(\chi_{961}(11,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{112}{155}\right)\)	\(e\left(\frac{323}{930}\right)\)	\(e\left(\frac{69}{155}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{247}{465}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{323}{465}\right)\)	\(e\left(\frac{251}{465}\right)\)	\(e\left(\frac{169}{930}\right)\)
\(\chi_{961}(12,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{155}\right)\)	\(e\left(\frac{319}{930}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{71}{186}\right)\)	\(e\left(\frac{326}{465}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{319}{465}\right)\)	\(e\left(\frac{448}{465}\right)\)	\(e\left(\frac{737}{930}\right)\)
\(\chi_{961}(13,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{401}{930}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{91}{186}\right)\)	\(e\left(\frac{334}{465}\right)\)	\(e\left(\frac{27}{155}\right)\)	\(e\left(\frac{401}{465}\right)\)	\(e\left(\frac{362}{465}\right)\)	\(e\left(\frac{253}{930}\right)\)
\(\chi_{961}(14,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{28}{155}\right)\)	\(e\left(\frac{176}{465}\right)\)	\(e\left(\frac{56}{155}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{23}{465}\right)\)	\(e\left(\frac{84}{155}\right)\)	\(e\left(\frac{352}{465}\right)\)	\(e\left(\frac{334}{465}\right)\)	\(e\left(\frac{118}{465}\right)\)
\(\chi_{961}(15,\cdot)\)	961.n	310	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{155}\right)\)	\(e\left(\frac{147}{310}\right)\)	\(e\left(\frac{123}{155}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{84}{155}\right)\)	\(e\left(\frac{51}{310}\right)\)
\(\chi_{961}(16,\cdot)\)	961.l	155	yes	\(1\)	\(1\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{73}{155}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{138}{155}\right)\)
\(\chi_{961}(17,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{123}{155}\right)\)	\(e\left(\frac{727}{930}\right)\)	\(e\left(\frac{91}{155}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{107}{186}\right)\)	\(e\left(\frac{173}{465}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{262}{465}\right)\)	\(e\left(\frac{349}{465}\right)\)	\(e\left(\frac{461}{930}\right)\)
\(\chi_{961}(18,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{313}{465}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{424}{465}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{161}{465}\right)\)	\(e\left(\frac{92}{465}\right)\)	\(e\left(\frac{194}{465}\right)\)
\(\chi_{961}(19,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{91}{155}\right)\)	\(e\left(\frac{107}{465}\right)\)	\(e\left(\frac{27}{155}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{214}{465}\right)\)	\(e\left(\frac{388}{465}\right)\)	\(e\left(\frac{151}{465}\right)\)
\(\chi_{961}(20,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{92}{155}\right)\)	\(e\left(\frac{379}{465}\right)\)	\(e\left(\frac{29}{155}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{142}{465}\right)\)	\(e\left(\frac{121}{155}\right)\)	\(e\left(\frac{293}{465}\right)\)	\(e\left(\frac{101}{465}\right)\)	\(e\left(\frac{122}{465}\right)\)
\(\chi_{961}(21,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{659}{930}\right)\)	\(e\left(\frac{52}{155}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{163}{186}\right)\)	\(e\left(\frac{121}{465}\right)\)	\(e\left(\frac{78}{155}\right)\)	\(e\left(\frac{194}{465}\right)\)	\(e\left(\frac{443}{465}\right)\)	\(e\left(\frac{817}{930}\right)\)
\(\chi_{961}(22,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{155}\right)\)	\(e\left(\frac{17}{930}\right)\)	\(e\left(\frac{126}{155}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{79}{186}\right)\)	\(e\left(\frac{13}{465}\right)\)	\(e\left(\frac{34}{155}\right)\)	\(e\left(\frac{17}{465}\right)\)	\(e\left(\frac{209}{465}\right)\)	\(e\left(\frac{841}{930}\right)\)
\(\chi_{961}(23,\cdot)\)	961.n	310	yes	\(-1\)	\(1\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{29}{310}\right)\)	\(e\left(\frac{116}{155}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{29}{62}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{29}{155}\right)\)	\(e\left(\frac{83}{155}\right)\)	\(e\left(\frac{67}{310}\right)\)
\(\chi_{961}(24,\cdot)\)	961.p	930	yes	\(-1\)	\(1\)	\(e\left(\frac{112}{155}\right)\)	\(e\left(\frac{13}{930}\right)\)	\(e\left(\frac{69}{155}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{137}{186}\right)\)	\(e\left(\frac{92}{465}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{13}{465}\right)\)	\(e\left(\frac{406}{465}\right)\)	\(e\left(\frac{479}{930}\right)\)
\(\chi_{961}(25,\cdot)\)	961.k	93	yes	\(1\)	\(1\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)
\(\chi_{961}(26,\cdot)\)	961.m	186	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{19}{186}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{157}{186}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{185}{186}\right)\)
\(\chi_{961}(27,\cdot)\)	961.n	310	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{1}{310}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{6}{155}\right)\)	\(e\left(\frac{1}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{13}{310}\right)\)
\(\chi_{961}(28,\cdot)\)	961.o	465	yes	\(1\)	\(1\)	\(e\left(\frac{134}{155}\right)\)	\(e\left(\frac{23}{465}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{254}{465}\right)\)	\(e\left(\frac{92}{155}\right)\)	\(e\left(\frac{46}{465}\right)\)	\(e\left(\frac{292}{465}\right)\)	\(e\left(\frac{454}{465}\right)\)
\(\chi_{961}(29,\cdot)\)	961.n	310	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{155}\right)\)	\(e\left(\frac{153}{310}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{29}{62}\right)\)	\(e\left(\frac{117}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{21}{155}\right)\)	\(e\left(\frac{129}{310}\right)\)
\(\chi_{961}(30,\cdot)\)	961.j	62	yes	\(-1\)	\(1\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{55}{62}\right)\)
\(\chi_{961}(32,\cdot)\)	961.i	31	yes	\(1\)	\(1\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)
\(\chi_{961}(33,\cdot)\)	961.l	155	yes	\(1\)	\(1\)	\(e\left(\frac{61}{155}\right)\)	\(e\left(\frac{54}{155}\right)\)	\(e\left(\frac{122}{155}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{37}{155}\right)\)	\(e\left(\frac{28}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{82}{155}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 930 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.