LMFDB - Dirichlet character orbit 1502.o

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1502, base_ring=CyclotomicField(750)) M = H._module chi = DirichletCharacter(H, M([736])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,1502)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1502$
Conductor:	$751$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$375$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 751.o	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{375})$
Fixed field:	Number field defined by a degree 375 polynomial (not computed)

First 31 of 200 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1502}(5,\cdot)$	$1$	$1$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{98}{375}\right)$	$e\left(\frac{106}{125}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{194}{375}\right)$	$e\left(\frac{91}{375}\right)$	$e\left(\frac{322}{375}\right)$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{311}{375}\right)$
$\chi_{1502}(9,\cdot)$	$1$	$1$	$e\left(\frac{1}{375}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{2}{375}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{362}{375}\right)$	$e\left(\frac{329}{375}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{277}{375}\right)$
$\chi_{1502}(13,\cdot)$	$1$	$1$	$e\left(\frac{254}{375}\right)$	$e\left(\frac{194}{375}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{32}{375}\right)$	$e\left(\frac{73}{375}\right)$	$e\left(\frac{316}{375}\right)$	$e\left(\frac{197}{375}\right)$	$e\left(\frac{233}{375}\right)$
$\chi_{1502}(19,\cdot)$	$1$	$1$	$e\left(\frac{134}{375}\right)$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{197}{375}\right)$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{211}{375}\right)$	$e\left(\frac{287}{375}\right)$	$e\left(\frac{368}{375}\right)$
$\chi_{1502}(21,\cdot)$	$1$	$1$	$e\left(\frac{326}{375}\right)$	$e\left(\frac{311}{375}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{233}{375}\right)$	$e\left(\frac{262}{375}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{302}{375}\right)$
$\chi_{1502}(23,\cdot)$	$1$	$1$	$e\left(\frac{266}{375}\right)$	$e\left(\frac{26}{375}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{157}{375}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{128}{375}\right)$	$e\left(\frac{292}{375}\right)$	$e\left(\frac{139}{375}\right)$	$e\left(\frac{38}{375}\right)$	$e\left(\frac{182}{375}\right)$
$\chi_{1502}(25,\cdot)$	$1$	$1$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{196}{375}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{347}{375}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{13}{375}\right)$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{269}{375}\right)$	$e\left(\frac{373}{375}\right)$	$e\left(\frac{247}{375}\right)$
$\chi_{1502}(33,\cdot)$	$1$	$1$	$e\left(\frac{358}{375}\right)$	$e\left(\frac{238}{375}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{341}{375}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{221}{375}\right)$	$e\left(\frac{32}{375}\right)$	$e\left(\frac{319}{375}\right)$	$e\left(\frac{166}{375}\right)$
$\chi_{1502}(37,\cdot)$	$1$	$1$	$e\left(\frac{136}{375}\right)$	$e\left(\frac{346}{375}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{272}{375}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{88}{375}\right)$	$e\left(\frac{107}{375}\right)$	$e\left(\frac{119}{375}\right)$	$e\left(\frac{73}{375}\right)$	$e\left(\frac{172}{375}\right)$
$\chi_{1502}(47,\cdot)$	$1$	$1$	$e\left(\frac{293}{375}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{211}{375}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{344}{375}\right)$	$e\left(\frac{316}{375}\right)$	$e\left(\frac{22}{375}\right)$	$e\left(\frac{149}{375}\right)$	$e\left(\frac{161}{375}\right)$
$\chi_{1502}(59,\cdot)$	$1$	$1$	$e\left(\frac{203}{375}\right)$	$e\left(\frac{158}{375}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{31}{375}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{37}{375}\right)$	$e\left(\frac{29}{375}\right)$	$e\left(\frac{356}{375}\right)$
$\chi_{1502}(65,\cdot)$	$1$	$1$	$e\left(\frac{247}{375}\right)$	$e\left(\frac{292}{375}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{119}{375}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{226}{375}\right)$	$e\left(\frac{164}{375}\right)$	$e\left(\frac{263}{375}\right)$	$e\left(\frac{196}{375}\right)$	$e\left(\frac{169}{375}\right)$
$\chi_{1502}(77,\cdot)$	$1$	$1$	$e\left(\frac{308}{375}\right)$	$e\left(\frac{188}{375}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{241}{375}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{89}{375}\right)$	$e\left(\frac{121}{375}\right)$	$e\left(\frac{82}{375}\right)$	$e\left(\frac{44}{375}\right)$	$e\left(\frac{191}{375}\right)$
$\chi_{1502}(81,\cdot)$	$1$	$1$	$e\left(\frac{2}{375}\right)$	$e\left(\frac{347}{375}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{266}{375}\right)$	$e\left(\frac{349}{375}\right)$	$e\left(\frac{283}{375}\right)$	$e\left(\frac{161}{375}\right)$	$e\left(\frac{179}{375}\right)$
$\chi_{1502}(87,\cdot)$	$1$	$1$	$e\left(\frac{289}{375}\right)$	$e\left(\frac{79}{375}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{203}{375}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{187}{375}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{206}{375}\right)$	$e\left(\frac{202}{375}\right)$	$e\left(\frac{178}{375}\right)$
$\chi_{1502}(89,\cdot)$	$1$	$1$	$e\left(\frac{193}{375}\right)$	$e\left(\frac{298}{375}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{169}{375}\right)$	$e\left(\frac{116}{375}\right)$	$e\left(\frac{122}{375}\right)$	$e\left(\frac{349}{375}\right)$	$e\left(\frac{211}{375}\right)$
$\chi_{1502}(95,\cdot)$	$1$	$1$	$e\left(\frac{127}{375}\right)$	$e\left(\frac{97}{375}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{254}{375}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{16}{375}\right)$	$e\left(\frac{224}{375}\right)$	$e\left(\frac{158}{375}\right)$	$e\left(\frac{286}{375}\right)$	$e\left(\frac{304}{375}\right)$
$\chi_{1502}(97,\cdot)$	$1$	$1$	$e\left(\frac{112}{375}\right)$	$e\left(\frac{307}{375}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{224}{375}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{271}{375}\right)$	$e\left(\frac{44}{375}\right)$	$e\left(\frac{98}{375}\right)$	$e\left(\frac{16}{375}\right)$	$e\left(\frac{274}{375}\right)$
$\chi_{1502}(105,\cdot)$	$1$	$1$	$e\left(\frac{319}{375}\right)$	$e\left(\frac{34}{375}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{263}{375}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{52}{375}\right)$	$e\left(\frac{353}{375}\right)$	$e\left(\frac{326}{375}\right)$	$e\left(\frac{367}{375}\right)$	$e\left(\frac{238}{375}\right)$
$\chi_{1502}(109,\cdot)$	$1$	$1$	$e\left(\frac{91}{375}\right)$	$e\left(\frac{226}{375}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{103}{375}\right)$	$e\left(\frac{317}{375}\right)$	$e\left(\frac{314}{375}\right)$	$e\left(\frac{13}{375}\right)$	$e\left(\frac{82}{375}\right)$
$\chi_{1502}(115,\cdot)$	$1$	$1$	$e\left(\frac{259}{375}\right)$	$e\left(\frac{124}{375}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{143}{375}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{322}{375}\right)$	$e\left(\frac{8}{375}\right)$	$e\left(\frac{86}{375}\right)$	$e\left(\frac{37}{375}\right)$	$e\left(\frac{118}{375}\right)$
$\chi_{1502}(123,\cdot)$	$1$	$1$	$e\left(\frac{233}{375}\right)$	$e\left(\frac{113}{375}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{91}{375}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{239}{375}\right)$	$e\left(\frac{346}{375}\right)$	$e\left(\frac{157}{375}\right)$	$e\left(\frac{194}{375}\right)$	$e\left(\frac{41}{375}\right)$
$\chi_{1502}(127,\cdot)$	$1$	$1$	$e\left(\frac{149}{375}\right)$	$e\left(\frac{164}{375}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{298}{375}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{317}{375}\right)$	$e\left(\frac{313}{375}\right)$	$e\left(\frac{271}{375}\right)$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{23}{375}\right)$
$\chi_{1502}(139,\cdot)$	$1$	$1$	$e\left(\frac{19}{375}\right)$	$e\left(\frac{109}{375}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{38}{375}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{128}{375}\right)$	$e\left(\frac{251}{375}\right)$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{13}{375}\right)$
$\chi_{1502}(149,\cdot)$	$1$	$1$	$e\left(\frac{28}{375}\right)$	$e\left(\frac{358}{375}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{56}{375}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{349}{375}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{212}{375}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{256}{375}\right)$
$\chi_{1502}(167,\cdot)$	$1$	$1$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{14}{375}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{373}{375}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{242}{375}\right)$	$e\left(\frac{13}{375}\right)$	$e\left(\frac{46}{375}\right)$	$e\left(\frac{107}{375}\right)$	$e\left(\frac{98}{375}\right)$
$\chi_{1502}(169,\cdot)$	$1$	$1$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{13}{375}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{266}{375}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{64}{375}\right)$	$e\left(\frac{146}{375}\right)$	$e\left(\frac{257}{375}\right)$	$e\left(\frac{19}{375}\right)$	$e\left(\frac{91}{375}\right)$
$\chi_{1502}(181,\cdot)$	$1$	$1$	$e\left(\frac{148}{375}\right)$	$e\left(\frac{178}{375}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{296}{375}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{184}{375}\right)$	$e\left(\frac{326}{375}\right)$	$e\left(\frac{317}{375}\right)$	$e\left(\frac{289}{375}\right)$	$e\left(\frac{121}{375}\right)$
$\chi_{1502}(199,\cdot)$	$1$	$1$	$e\left(\frac{328}{375}\right)$	$e\left(\frac{283}{375}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{281}{375}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{124}{375}\right)$	$e\left(\frac{236}{375}\right)$	$e\left(\frac{287}{375}\right)$	$e\left(\frac{154}{375}\right)$	$e\left(\frac{106}{375}\right)$
$\chi_{1502}(201,\cdot)$	$1$	$1$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{154}{375}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{353}{375}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{37}{375}\right)$	$e\left(\frac{143}{375}\right)$	$e\left(\frac{131}{375}\right)$	$e\left(\frac{52}{375}\right)$	$e\left(\frac{328}{375}\right)$
$\chi_{1502}(203,\cdot)$	$1$	$1$	$e\left(\frac{239}{375}\right)$	$e\left(\frac{29}{375}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{103}{375}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{287}{375}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{256}{375}\right)$	$e\left(\frac{302}{375}\right)$	$e\left(\frac{203}{375}\right)$

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

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1502}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{98}{375}\right)\)	\(e\left(\frac{106}{125}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{194}{375}\right)\)	\(e\left(\frac{91}{375}\right)\)	\(e\left(\frac{322}{375}\right)\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{311}{375}\right)\)
\(\chi_{1502}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{375}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{2}{375}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{362}{375}\right)\)	\(e\left(\frac{329}{375}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{277}{375}\right)\)
\(\chi_{1502}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{254}{375}\right)\)	\(e\left(\frac{194}{375}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{32}{375}\right)\)	\(e\left(\frac{73}{375}\right)\)	\(e\left(\frac{316}{375}\right)\)	\(e\left(\frac{197}{375}\right)\)	\(e\left(\frac{233}{375}\right)\)
\(\chi_{1502}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{375}\right)\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{197}{375}\right)\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{211}{375}\right)\)	\(e\left(\frac{287}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)
\(\chi_{1502}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{326}{375}\right)\)	\(e\left(\frac{311}{375}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{233}{375}\right)\)	\(e\left(\frac{262}{375}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{302}{375}\right)\)
\(\chi_{1502}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{266}{375}\right)\)	\(e\left(\frac{26}{375}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{157}{375}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{128}{375}\right)\)	\(e\left(\frac{292}{375}\right)\)	\(e\left(\frac{139}{375}\right)\)	\(e\left(\frac{38}{375}\right)\)	\(e\left(\frac{182}{375}\right)\)
\(\chi_{1502}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{196}{375}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{347}{375}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{13}{375}\right)\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{269}{375}\right)\)	\(e\left(\frac{373}{375}\right)\)	\(e\left(\frac{247}{375}\right)\)
\(\chi_{1502}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{358}{375}\right)\)	\(e\left(\frac{238}{375}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{341}{375}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{221}{375}\right)\)	\(e\left(\frac{32}{375}\right)\)	\(e\left(\frac{319}{375}\right)\)	\(e\left(\frac{166}{375}\right)\)
\(\chi_{1502}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{136}{375}\right)\)	\(e\left(\frac{346}{375}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{272}{375}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{88}{375}\right)\)	\(e\left(\frac{107}{375}\right)\)	\(e\left(\frac{119}{375}\right)\)	\(e\left(\frac{73}{375}\right)\)	\(e\left(\frac{172}{375}\right)\)
\(\chi_{1502}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{375}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{211}{375}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{344}{375}\right)\)	\(e\left(\frac{316}{375}\right)\)	\(e\left(\frac{22}{375}\right)\)	\(e\left(\frac{149}{375}\right)\)	\(e\left(\frac{161}{375}\right)\)
\(\chi_{1502}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{375}\right)\)	\(e\left(\frac{158}{375}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{31}{375}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{37}{375}\right)\)	\(e\left(\frac{29}{375}\right)\)	\(e\left(\frac{356}{375}\right)\)
\(\chi_{1502}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{375}\right)\)	\(e\left(\frac{292}{375}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{119}{375}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{226}{375}\right)\)	\(e\left(\frac{164}{375}\right)\)	\(e\left(\frac{263}{375}\right)\)	\(e\left(\frac{196}{375}\right)\)	\(e\left(\frac{169}{375}\right)\)
\(\chi_{1502}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{308}{375}\right)\)	\(e\left(\frac{188}{375}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{241}{375}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{89}{375}\right)\)	\(e\left(\frac{121}{375}\right)\)	\(e\left(\frac{82}{375}\right)\)	\(e\left(\frac{44}{375}\right)\)	\(e\left(\frac{191}{375}\right)\)
\(\chi_{1502}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{375}\right)\)	\(e\left(\frac{347}{375}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{266}{375}\right)\)	\(e\left(\frac{349}{375}\right)\)	\(e\left(\frac{283}{375}\right)\)	\(e\left(\frac{161}{375}\right)\)	\(e\left(\frac{179}{375}\right)\)
\(\chi_{1502}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{375}\right)\)	\(e\left(\frac{79}{375}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{203}{375}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{187}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{206}{375}\right)\)	\(e\left(\frac{202}{375}\right)\)	\(e\left(\frac{178}{375}\right)\)
\(\chi_{1502}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{375}\right)\)	\(e\left(\frac{298}{375}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{169}{375}\right)\)	\(e\left(\frac{116}{375}\right)\)	\(e\left(\frac{122}{375}\right)\)	\(e\left(\frac{349}{375}\right)\)	\(e\left(\frac{211}{375}\right)\)
\(\chi_{1502}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{375}\right)\)	\(e\left(\frac{97}{375}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{254}{375}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{16}{375}\right)\)	\(e\left(\frac{224}{375}\right)\)	\(e\left(\frac{158}{375}\right)\)	\(e\left(\frac{286}{375}\right)\)	\(e\left(\frac{304}{375}\right)\)
\(\chi_{1502}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{112}{375}\right)\)	\(e\left(\frac{307}{375}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{224}{375}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{271}{375}\right)\)	\(e\left(\frac{44}{375}\right)\)	\(e\left(\frac{98}{375}\right)\)	\(e\left(\frac{16}{375}\right)\)	\(e\left(\frac{274}{375}\right)\)
\(\chi_{1502}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{375}\right)\)	\(e\left(\frac{34}{375}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{263}{375}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{52}{375}\right)\)	\(e\left(\frac{353}{375}\right)\)	\(e\left(\frac{326}{375}\right)\)	\(e\left(\frac{367}{375}\right)\)	\(e\left(\frac{238}{375}\right)\)
\(\chi_{1502}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{375}\right)\)	\(e\left(\frac{226}{375}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{103}{375}\right)\)	\(e\left(\frac{317}{375}\right)\)	\(e\left(\frac{314}{375}\right)\)	\(e\left(\frac{13}{375}\right)\)	\(e\left(\frac{82}{375}\right)\)
\(\chi_{1502}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{375}\right)\)	\(e\left(\frac{124}{375}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{143}{375}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{322}{375}\right)\)	\(e\left(\frac{8}{375}\right)\)	\(e\left(\frac{86}{375}\right)\)	\(e\left(\frac{37}{375}\right)\)	\(e\left(\frac{118}{375}\right)\)
\(\chi_{1502}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{375}\right)\)	\(e\left(\frac{113}{375}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{91}{375}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{239}{375}\right)\)	\(e\left(\frac{346}{375}\right)\)	\(e\left(\frac{157}{375}\right)\)	\(e\left(\frac{194}{375}\right)\)	\(e\left(\frac{41}{375}\right)\)
\(\chi_{1502}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{375}\right)\)	\(e\left(\frac{164}{375}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{298}{375}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{317}{375}\right)\)	\(e\left(\frac{313}{375}\right)\)	\(e\left(\frac{271}{375}\right)\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{23}{375}\right)\)
\(\chi_{1502}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{375}\right)\)	\(e\left(\frac{109}{375}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{38}{375}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{128}{375}\right)\)	\(e\left(\frac{251}{375}\right)\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{13}{375}\right)\)
\(\chi_{1502}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{375}\right)\)	\(e\left(\frac{358}{375}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{56}{375}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{349}{375}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{212}{375}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{256}{375}\right)\)
\(\chi_{1502}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{14}{375}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{373}{375}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{242}{375}\right)\)	\(e\left(\frac{13}{375}\right)\)	\(e\left(\frac{46}{375}\right)\)	\(e\left(\frac{107}{375}\right)\)	\(e\left(\frac{98}{375}\right)\)
\(\chi_{1502}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{13}{375}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{266}{375}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{64}{375}\right)\)	\(e\left(\frac{146}{375}\right)\)	\(e\left(\frac{257}{375}\right)\)	\(e\left(\frac{19}{375}\right)\)	\(e\left(\frac{91}{375}\right)\)
\(\chi_{1502}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{375}\right)\)	\(e\left(\frac{178}{375}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{296}{375}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{184}{375}\right)\)	\(e\left(\frac{326}{375}\right)\)	\(e\left(\frac{317}{375}\right)\)	\(e\left(\frac{289}{375}\right)\)	\(e\left(\frac{121}{375}\right)\)
\(\chi_{1502}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{328}{375}\right)\)	\(e\left(\frac{283}{375}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{281}{375}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{124}{375}\right)\)	\(e\left(\frac{236}{375}\right)\)	\(e\left(\frac{287}{375}\right)\)	\(e\left(\frac{154}{375}\right)\)	\(e\left(\frac{106}{375}\right)\)
\(\chi_{1502}(201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{154}{375}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{353}{375}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{37}{375}\right)\)	\(e\left(\frac{143}{375}\right)\)	\(e\left(\frac{131}{375}\right)\)	\(e\left(\frac{52}{375}\right)\)	\(e\left(\frac{328}{375}\right)\)
\(\chi_{1502}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{375}\right)\)	\(e\left(\frac{29}{375}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{103}{375}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{287}{375}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{256}{375}\right)\)	\(e\left(\frac{302}{375}\right)\)	\(e\left(\frac{203}{375}\right)\)

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First 31 of 200 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1502.o
Modulus	$1502$
Conductor	$751$
Order	$375$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1502\)
Conductor:	\(751\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(375\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 751.o	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)