LMFDB - Dirichlet character orbit 875.bi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(300)) M = H._module chi = DirichletCharacter(H, M([3,100])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,875)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$875$
Conductor:	$875$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$300$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{300})$
Fixed field:	Number field defined by a degree 300 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{875}(2,\cdot)$	$-1$	$1$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{53}{75}\right)$
$\chi_{875}(23,\cdot)$	$-1$	$1$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{875}(37,\cdot)$	$-1$	$1$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{875}(53,\cdot)$	$-1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{1}{75}\right)$
$\chi_{875}(58,\cdot)$	$-1$	$1$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{14}{75}\right)$
$\chi_{875}(67,\cdot)$	$-1$	$1$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{64}{75}\right)$
$\chi_{875}(72,\cdot)$	$-1$	$1$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{875}(88,\cdot)$	$-1$	$1$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{875}(102,\cdot)$	$-1$	$1$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{43}{75}\right)$
$\chi_{875}(123,\cdot)$	$-1$	$1$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{28}{75}\right)$
$\chi_{875}(128,\cdot)$	$-1$	$1$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{71}{75}\right)$
$\chi_{875}(137,\cdot)$	$-1$	$1$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{875}(142,\cdot)$	$-1$	$1$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{875}(158,\cdot)$	$-1$	$1$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{49}{75}\right)$
$\chi_{875}(163,\cdot)$	$-1$	$1$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{32}{75}\right)$
$\chi_{875}(172,\cdot)$	$-1$	$1$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{16}{75}\right)$
$\chi_{875}(177,\cdot)$	$-1$	$1$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{875}(198,\cdot)$	$-1$	$1$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{875}(212,\cdot)$	$-1$	$1$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{32}{75}\right)$
$\chi_{875}(228,\cdot)$	$-1$	$1$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{31}{75}\right)$
$\chi_{875}(233,\cdot)$	$-1$	$1$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{875}(242,\cdot)$	$-1$	$1$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{34}{75}\right)$
$\chi_{875}(247,\cdot)$	$-1$	$1$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{71}{75}\right)$
$\chi_{875}(263,\cdot)$	$-1$	$1$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{67}{75}\right)$
$\chi_{875}(277,\cdot)$	$-1$	$1$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{875}(298,\cdot)$	$-1$	$1$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{875}(303,\cdot)$	$-1$	$1$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{875}(312,\cdot)$	$-1$	$1$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{22}{75}\right)$
$\chi_{875}(317,\cdot)$	$-1$	$1$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{14}{75}\right)$
$\chi_{875}(333,\cdot)$	$-1$	$1$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{4}{75}\right)$
$\chi_{875}(338,\cdot)$	$-1$	$1$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{62}{75}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{875}(2,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{53}{75}\right)\)
\(\chi_{875}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{875}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{875}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{1}{75}\right)\)
\(\chi_{875}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{14}{75}\right)\)
\(\chi_{875}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{64}{75}\right)\)
\(\chi_{875}(72,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{875}(88,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{875}(102,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{43}{75}\right)\)
\(\chi_{875}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{28}{75}\right)\)
\(\chi_{875}(128,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{71}{75}\right)\)
\(\chi_{875}(137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{875}(142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{875}(158,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{49}{75}\right)\)
\(\chi_{875}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{32}{75}\right)\)
\(\chi_{875}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{16}{75}\right)\)
\(\chi_{875}(177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{875}(198,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{875}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{32}{75}\right)\)
\(\chi_{875}(228,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{31}{75}\right)\)
\(\chi_{875}(233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{875}(242,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{34}{75}\right)\)
\(\chi_{875}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{71}{75}\right)\)
\(\chi_{875}(263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{67}{75}\right)\)
\(\chi_{875}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{875}(298,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{875}(303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{875}(312,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{22}{75}\right)\)
\(\chi_{875}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{14}{75}\right)\)
\(\chi_{875}(333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{4}{75}\right)\)
\(\chi_{875}(338,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{62}{75}\right)\)

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First 31 of 80 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	875.bi
Modulus	$875$
Conductor	$875$
Order	$300$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(875\)
Conductor:	\(875\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(300\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)