LMFDB - Dirichlet character orbit 875.bf

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(150)) M = H._module chi = DirichletCharacter(H, M([27,125])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(19,875)) 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:	$150$	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:	$\Q(\zeta_{75})$
Fixed field:	Number field defined by a degree 150 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{875}(19,\cdot)$	$-1$	$1$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{875}(54,\cdot)$	$-1$	$1$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{41}{75}\right)$
$\chi_{875}(59,\cdot)$	$-1$	$1$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{875}(89,\cdot)$	$-1$	$1$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{875}(94,\cdot)$	$-1$	$1$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{19}{75}\right)$
$\chi_{875}(129,\cdot)$	$-1$	$1$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{31}{75}\right)$
$\chi_{875}(159,\cdot)$	$-1$	$1$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{875}(164,\cdot)$	$-1$	$1$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{875}(194,\cdot)$	$-1$	$1$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{14}{75}\right)$
$\chi_{875}(229,\cdot)$	$-1$	$1$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{875}(234,\cdot)$	$-1$	$1$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{875}(264,\cdot)$	$-1$	$1$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{8}{75}\right)$
$\chi_{875}(269,\cdot)$	$-1$	$1$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{4}{75}\right)$
$\chi_{875}(304,\cdot)$	$-1$	$1$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{16}{75}\right)$
$\chi_{875}(334,\cdot)$	$-1$	$1$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{32}{75}\right)$
$\chi_{875}(339,\cdot)$	$-1$	$1$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{73}{75}\right)$
$\chi_{875}(369,\cdot)$	$-1$	$1$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{74}{75}\right)$
$\chi_{875}(404,\cdot)$	$-1$	$1$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{11}{75}\right)$
$\chi_{875}(409,\cdot)$	$-1$	$1$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{22}{75}\right)$
$\chi_{875}(439,\cdot)$	$-1$	$1$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{875}(444,\cdot)$	$-1$	$1$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{64}{75}\right)$
$\chi_{875}(479,\cdot)$	$-1$	$1$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{75}\right)$
$\chi_{875}(509,\cdot)$	$-1$	$1$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{17}{75}\right)$
$\chi_{875}(514,\cdot)$	$-1$	$1$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{875}(544,\cdot)$	$-1$	$1$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{59}{75}\right)$
$\chi_{875}(579,\cdot)$	$-1$	$1$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{71}{75}\right)$
$\chi_{875}(584,\cdot)$	$-1$	$1$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{7}{75}\right)$
$\chi_{875}(614,\cdot)$	$-1$	$1$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{53}{75}\right)$
$\chi_{875}(619,\cdot)$	$-1$	$1$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{49}{75}\right)$
$\chi_{875}(654,\cdot)$	$-1$	$1$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{61}{75}\right)$
$\chi_{875}(684,\cdot)$	$-1$	$1$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{2}{75}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{875}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{875}(54,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{41}{75}\right)\)
\(\chi_{875}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{875}(89,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{875}(94,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{19}{75}\right)\)
\(\chi_{875}(129,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{31}{75}\right)\)
\(\chi_{875}(159,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{875}(164,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{875}(194,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{14}{75}\right)\)
\(\chi_{875}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{875}(234,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{875}(264,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)
\(\chi_{875}(269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)
\(\chi_{875}(304,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{16}{75}\right)\)
\(\chi_{875}(334,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{32}{75}\right)\)
\(\chi_{875}(339,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{73}{75}\right)\)
\(\chi_{875}(369,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)
\(\chi_{875}(404,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{11}{75}\right)\)
\(\chi_{875}(409,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{22}{75}\right)\)
\(\chi_{875}(439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{875}(444,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{64}{75}\right)\)
\(\chi_{875}(479,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{75}\right)\)
\(\chi_{875}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{17}{75}\right)\)
\(\chi_{875}(514,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{875}(544,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{59}{75}\right)\)
\(\chi_{875}(579,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{71}{75}\right)\)
\(\chi_{875}(584,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{7}{75}\right)\)
\(\chi_{875}(614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{53}{75}\right)\)
\(\chi_{875}(619,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{49}{75}\right)\)
\(\chi_{875}(654,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)
\(\chi_{875}(684,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)

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First 31 of 40 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.bf
Modulus	$875$
Conductor	$875$
Order	$150$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(875\)
Conductor:	\(875\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(150\)	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)