LMFDB - Dirichlet character orbit 3751.dk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3751, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([228,88])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(20,3751)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3751$
Conductor:	$3751$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$165$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 165 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{3751}(20,\cdot)$	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{41}{165}\right)$
$\chi_{3751}(59,\cdot)$	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{52}{165}\right)$
$\chi_{3751}(71,\cdot)$	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{29}{165}\right)$
$\chi_{3751}(235,\cdot)$	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{32}{165}\right)$
$\chi_{3751}(267,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{103}{165}\right)$
$\chi_{3751}(289,\cdot)$	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{8}{165}\right)$
$\chi_{3751}(317,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{136}{165}\right)$
$\chi_{3751}(324,\cdot)$	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{94}{165}\right)$
$\chi_{3751}(361,\cdot)$	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{146}{165}\right)$
$\chi_{3751}(400,\cdot)$	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{82}{165}\right)$
$\chi_{3751}(412,\cdot)$	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{119}{165}\right)$
$\chi_{3751}(576,\cdot)$	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{3751}(630,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{158}{165}\right)$
$\chi_{3751}(658,\cdot)$	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{76}{165}\right)$
$\chi_{3751}(665,\cdot)$	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{19}{165}\right)$
$\chi_{3751}(702,\cdot)$	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{86}{165}\right)$
$\chi_{3751}(741,\cdot)$	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{112}{165}\right)$
$\chi_{3751}(917,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{92}{165}\right)$
$\chi_{3751}(949,\cdot)$	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{73}{165}\right)$
$\chi_{3751}(999,\cdot)$	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{16}{165}\right)$
$\chi_{3751}(1006,\cdot)$	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{109}{165}\right)$
$\chi_{3751}(1043,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{26}{165}\right)$
$\chi_{3751}(1082,\cdot)$	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{142}{165}\right)$
$\chi_{3751}(1094,\cdot)$	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{134}{165}\right)$
$\chi_{3751}(1258,\cdot)$	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{122}{165}\right)$
$\chi_{3751}(1290,\cdot)$	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{58}{165}\right)$
$\chi_{3751}(1312,\cdot)$	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{128}{165}\right)$
$\chi_{3751}(1347,\cdot)$	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{34}{165}\right)$
$\chi_{3751}(1384,\cdot)$	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{131}{165}\right)$
$\chi_{3751}(1423,\cdot)$	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{7}{165}\right)$
$\chi_{3751}(1435,\cdot)$	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{59}{165}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{3751}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)
\(\chi_{3751}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{52}{165}\right)\)
\(\chi_{3751}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)
\(\chi_{3751}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)
\(\chi_{3751}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)
\(\chi_{3751}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)
\(\chi_{3751}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)
\(\chi_{3751}(324,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)
\(\chi_{3751}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)
\(\chi_{3751}(400,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)
\(\chi_{3751}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)
\(\chi_{3751}(576,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{3751}(630,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)
\(\chi_{3751}(658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)
\(\chi_{3751}(665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)
\(\chi_{3751}(702,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)
\(\chi_{3751}(741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)
\(\chi_{3751}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)
\(\chi_{3751}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)
\(\chi_{3751}(999,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)
\(\chi_{3751}(1006,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)
\(\chi_{3751}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)
\(\chi_{3751}(1082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)
\(\chi_{3751}(1094,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)
\(\chi_{3751}(1258,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)
\(\chi_{3751}(1290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)
\(\chi_{3751}(1312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)
\(\chi_{3751}(1347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{34}{165}\right)\)
\(\chi_{3751}(1384,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)
\(\chi_{3751}(1423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)
\(\chi_{3751}(1435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)

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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	3751.dk
Modulus	$3751$
Conductor	$3751$
Order	$165$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3751\)
Conductor:	\(3751\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(165\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)