LMFDB - Dirichlet character orbit 8415.kh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8415, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([40,60,48,45])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(49,8415)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8415$
Conductor:	$8415$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$120$	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:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$19$	$23$	$26$
$\chi_{8415}(49,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{8415}(229,\cdot)$	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{8415}(994,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8415}(1039,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{8415}(1114,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{8415}(1879,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{8415}(2524,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{8415}(2599,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{8415}(2644,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8415}(3364,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8415}(3589,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{8415}(3919,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{8415}(4129,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{8415}(4174,\cdot)$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{8415}(4354,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8415}(4684,\cdot)$	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{8415}(5074,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{8415}(5119,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{8415}(5404,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{8415}(5449,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8415}(5659,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{8415}(5839,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{8415}(6169,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8415}(6394,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{8415}(6604,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8415}(6649,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{8415}(6934,\cdot)$	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{8415}(6979,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{8415}(7159,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8415}(7879,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{8415}(7924,\cdot)$	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{20}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(19\)	\(23\)	\(26\)
\(\chi_{8415}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{8415}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{8415}(994,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8415}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{8415}(1114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{8415}(1879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{8415}(2524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{8415}(2599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{8415}(2644,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8415}(3364,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8415}(3589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{8415}(3919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{8415}(4129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{8415}(4174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{8415}(4354,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8415}(4684,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{8415}(5074,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{8415}(5119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{8415}(5404,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{8415}(5449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8415}(5659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{8415}(5839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{8415}(6169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8415}(6394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{8415}(6604,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8415}(6649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{8415}(6934,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{8415}(6979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{8415}(7159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8415}(7879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{8415}(7924,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{20}\right)\)

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First 31 of 32 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	8415.kh
Modulus	$8415$
Conductor	$8415$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8415\)
Conductor:	\(8415\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(120\)	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)