LMFDB - Group of Dirichlet characters of modulus 751

Show commands: PariGP / SageMath

sage: H = DirichletGroup(751)

pari: g = idealstar(,751,2)

Character group

sage: G.order() pari: g.no
Order	=	750
sage: H.invariants() pari: g.cyc
Structure	=	$C_{750}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{751}(3,\cdot)$

First 32 of 750 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{751}(1,\cdot)$	751.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{751}(2,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{278}{375}\right)$	$e\left(\frac{208}{375}\right)$	$e\left(\frac{181}{375}\right)$	$e\left(\frac{88}{375}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{41}{375}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{751}(3,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{208}{375}\right)$	$e\left(\frac{1}{750}\right)$	$e\left(\frac{41}{375}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{139}{250}\right)$	$e\left(\frac{217}{250}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{1}{375}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{143}{150}\right)$
$\chi_{751}(4,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{181}{375}\right)$	$e\left(\frac{41}{375}\right)$	$e\left(\frac{362}{375}\right)$	$e\left(\frac{176}{375}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{82}{375}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{751}(5,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{88}{375}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{176}{375}\right)$	$e\left(\frac{98}{375}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{106}{125}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{49}{75}\right)$
$\chi_{751}(6,\cdot)$	751.n	250	yes	$-1$	$1$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{139}{250}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{213}{250}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{751}(7,\cdot)$	751.n	250	yes	$-1$	$1$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{217}{250}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{106}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{751}(8,\cdot)$	751.l	125	yes	$1$	$1$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{751}(9,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{41}{375}\right)$	$e\left(\frac{1}{375}\right)$	$e\left(\frac{82}{375}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{2}{375}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{751}(10,\cdot)$	751.l	125	yes	$1$	$1$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{751}(11,\cdot)$	751.m	150	yes	$-1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{751}(12,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{14}{375}\right)$	$e\left(\frac{83}{750}\right)$	$e\left(\frac{28}{375}\right)$	$e\left(\frac{169}{375}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{83}{375}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{19}{150}\right)$
$\chi_{751}(13,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{289}{375}\right)$	$e\left(\frac{254}{375}\right)$	$e\left(\frac{203}{375}\right)$	$e\left(\frac{194}{375}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{22}{75}\right)$
$\chi_{751}(14,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{311}{375}\right)$	$e\left(\frac{317}{750}\right)$	$e\left(\frac{247}{375}\right)$	$e\left(\frac{31}{375}\right)$	$e\left(\frac{63}{250}\right)$	$e\left(\frac{39}{250}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{317}{375}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{31}{150}\right)$
$\chi_{751}(15,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{296}{375}\right)$	$e\left(\frac{737}{750}\right)$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{91}{375}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{179}{250}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{362}{375}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{91}{150}\right)$
$\chi_{751}(16,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{362}{375}\right)$	$e\left(\frac{82}{375}\right)$	$e\left(\frac{349}{375}\right)$	$e\left(\frac{352}{375}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{44}{125}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{164}{375}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{751}(17,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{329}{750}\right)$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{322}{375}\right)$	$e\left(\frac{231}{250}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{329}{375}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{97}{150}\right)$
$\chi_{751}(18,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{319}{375}\right)$	$e\left(\frac{209}{375}\right)$	$e\left(\frac{263}{375}\right)$	$e\left(\frac{74}{375}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{103}{125}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{43}{375}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{751}(19,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{244}{375}\right)$	$e\left(\frac{134}{375}\right)$	$e\left(\frac{113}{375}\right)$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{751}(20,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{269}{375}\right)$	$e\left(\frac{34}{375}\right)$	$e\left(\frac{163}{375}\right)$	$e\left(\frac{274}{375}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{68}{375}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{751}(21,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{241}{375}\right)$	$e\left(\frac{326}{375}\right)$	$e\left(\frac{107}{375}\right)$	$e\left(\frac{311}{375}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{43}{75}\right)$
$\chi_{751}(22,\cdot)$	751.n	250	yes	$-1$	$1$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{209}{250}\right)$	$e\left(\frac{177}{250}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{751}(23,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{31}{375}\right)$	$e\left(\frac{266}{375}\right)$	$e\left(\frac{62}{375}\right)$	$e\left(\frac{26}{375}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{157}{375}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{751}(24,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{292}{375}\right)$	$e\left(\frac{499}{750}\right)$	$e\left(\frac{209}{375}\right)$	$e\left(\frac{257}{375}\right)$	$e\left(\frac{111}{250}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{124}{375}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{751}(25,\cdot)$	751.o	375	yes	$1$	$1$	$e\left(\frac{176}{375}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{352}{375}\right)$	$e\left(\frac{196}{375}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{347}{375}\right)$	$e\left(\frac{124}{125}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{751}(26,\cdot)$	751.l	125	yes	$1$	$1$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{94}{125}\right)$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{751}(27,\cdot)$	751.n	250	yes	$-1$	$1$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{151}{250}\right)$	$e\left(\frac{124}{125}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{751}(28,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{214}{375}\right)$	$e\left(\frac{733}{750}\right)$	$e\left(\frac{53}{375}\right)$	$e\left(\frac{119}{375}\right)$	$e\left(\frac{137}{250}\right)$	$e\left(\frac{61}{250}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{358}{375}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{119}{150}\right)$
$\chi_{751}(29,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{16}{375}\right)$	$e\left(\frac{577}{750}\right)$	$e\left(\frac{32}{375}\right)$	$e\left(\frac{86}{375}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{209}{250}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{202}{375}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{11}{150}\right)$
$\chi_{751}(30,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{403}{750}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{179}{375}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{201}{250}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{28}{375}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{29}{150}\right)$
$\chi_{751}(31,\cdot)$	751.p	750	yes	$-1$	$1$	$e\left(\frac{116}{375}\right)$	$e\left(\frac{527}{750}\right)$	$e\left(\frac{232}{375}\right)$	$e\left(\frac{61}{375}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{109}{250}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{152}{375}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{61}{150}\right)$
$\chi_{751}(32,\cdot)$	751.k	75	yes	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{14}{15}\right)$

Click here to search among the remaining 718 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	$751$
Structure	\(C_{750}\)
Order	$750$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{751}(1,\cdot)\)	751.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{751}(2,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{278}{375}\right)\)	\(e\left(\frac{208}{375}\right)\)	\(e\left(\frac{181}{375}\right)\)	\(e\left(\frac{88}{375}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{41}{375}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{751}(3,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{208}{375}\right)\)	\(e\left(\frac{1}{750}\right)\)	\(e\left(\frac{41}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{139}{250}\right)\)	\(e\left(\frac{217}{250}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{1}{375}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{143}{150}\right)\)
\(\chi_{751}(4,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{181}{375}\right)\)	\(e\left(\frac{41}{375}\right)\)	\(e\left(\frac{362}{375}\right)\)	\(e\left(\frac{176}{375}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{82}{375}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{751}(5,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{88}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{176}{375}\right)\)	\(e\left(\frac{98}{375}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{106}{125}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{49}{75}\right)\)
\(\chi_{751}(6,\cdot)\)	751.n	250	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{139}{250}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{213}{250}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{751}(7,\cdot)\)	751.n	250	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{217}{250}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{106}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{751}(8,\cdot)\)	751.l	125	yes	\(1\)	\(1\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{751}(9,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{41}{375}\right)\)	\(e\left(\frac{1}{375}\right)\)	\(e\left(\frac{82}{375}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{2}{375}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{751}(10,\cdot)\)	751.l	125	yes	\(1\)	\(1\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{751}(11,\cdot)\)	751.m	150	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{751}(12,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{375}\right)\)	\(e\left(\frac{83}{750}\right)\)	\(e\left(\frac{28}{375}\right)\)	\(e\left(\frac{169}{375}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{83}{375}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{19}{150}\right)\)
\(\chi_{751}(13,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{289}{375}\right)\)	\(e\left(\frac{254}{375}\right)\)	\(e\left(\frac{203}{375}\right)\)	\(e\left(\frac{194}{375}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{22}{75}\right)\)
\(\chi_{751}(14,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{311}{375}\right)\)	\(e\left(\frac{317}{750}\right)\)	\(e\left(\frac{247}{375}\right)\)	\(e\left(\frac{31}{375}\right)\)	\(e\left(\frac{63}{250}\right)\)	\(e\left(\frac{39}{250}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{317}{375}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{31}{150}\right)\)
\(\chi_{751}(15,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{296}{375}\right)\)	\(e\left(\frac{737}{750}\right)\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{91}{375}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{179}{250}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{362}{375}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{91}{150}\right)\)
\(\chi_{751}(16,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{362}{375}\right)\)	\(e\left(\frac{82}{375}\right)\)	\(e\left(\frac{349}{375}\right)\)	\(e\left(\frac{352}{375}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{44}{125}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{164}{375}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{751}(17,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{329}{750}\right)\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{322}{375}\right)\)	\(e\left(\frac{231}{250}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{329}{375}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{97}{150}\right)\)
\(\chi_{751}(18,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{319}{375}\right)\)	\(e\left(\frac{209}{375}\right)\)	\(e\left(\frac{263}{375}\right)\)	\(e\left(\frac{74}{375}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{103}{125}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{43}{375}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{751}(19,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{244}{375}\right)\)	\(e\left(\frac{134}{375}\right)\)	\(e\left(\frac{113}{375}\right)\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{751}(20,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{269}{375}\right)\)	\(e\left(\frac{34}{375}\right)\)	\(e\left(\frac{163}{375}\right)\)	\(e\left(\frac{274}{375}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{68}{375}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{751}(21,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{241}{375}\right)\)	\(e\left(\frac{326}{375}\right)\)	\(e\left(\frac{107}{375}\right)\)	\(e\left(\frac{311}{375}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{43}{75}\right)\)
\(\chi_{751}(22,\cdot)\)	751.n	250	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{209}{250}\right)\)	\(e\left(\frac{177}{250}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{751}(23,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{31}{375}\right)\)	\(e\left(\frac{266}{375}\right)\)	\(e\left(\frac{62}{375}\right)\)	\(e\left(\frac{26}{375}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{157}{375}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{751}(24,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{292}{375}\right)\)	\(e\left(\frac{499}{750}\right)\)	\(e\left(\frac{209}{375}\right)\)	\(e\left(\frac{257}{375}\right)\)	\(e\left(\frac{111}{250}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{124}{375}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{751}(25,\cdot)\)	751.o	375	yes	\(1\)	\(1\)	\(e\left(\frac{176}{375}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{352}{375}\right)\)	\(e\left(\frac{196}{375}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{347}{375}\right)\)	\(e\left(\frac{124}{125}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{751}(26,\cdot)\)	751.l	125	yes	\(1\)	\(1\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{94}{125}\right)\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{22}{25}\right)\)
\(\chi_{751}(27,\cdot)\)	751.n	250	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{151}{250}\right)\)	\(e\left(\frac{124}{125}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{751}(28,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{214}{375}\right)\)	\(e\left(\frac{733}{750}\right)\)	\(e\left(\frac{53}{375}\right)\)	\(e\left(\frac{119}{375}\right)\)	\(e\left(\frac{137}{250}\right)\)	\(e\left(\frac{61}{250}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{358}{375}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{119}{150}\right)\)
\(\chi_{751}(29,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{375}\right)\)	\(e\left(\frac{577}{750}\right)\)	\(e\left(\frac{32}{375}\right)\)	\(e\left(\frac{86}{375}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{209}{250}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{202}{375}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{11}{150}\right)\)
\(\chi_{751}(30,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{403}{750}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{179}{375}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{201}{250}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{28}{375}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{29}{150}\right)\)
\(\chi_{751}(31,\cdot)\)	751.p	750	yes	\(-1\)	\(1\)	\(e\left(\frac{116}{375}\right)\)	\(e\left(\frac{527}{750}\right)\)	\(e\left(\frac{232}{375}\right)\)	\(e\left(\frac{61}{375}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{109}{250}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{152}{375}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{61}{150}\right)\)
\(\chi_{751}(32,\cdot)\)	751.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{14}{15}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 750 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.