LMFDB - Dirichlet character orbit 8925.kj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8925, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([60,6,40,105])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,8925)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8925$
Conductor:	$8925$	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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{8925}(2,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(128,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(263,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(767,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(1052,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(1283,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(1787,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(1817,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(1913,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(2048,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(2552,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(2678,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(2837,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(3572,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(3602,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(3698,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(3833,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(4337,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(4463,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(4622,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(4853,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(5387,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(5483,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(6122,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(6248,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(6638,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{8925}(7142,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8925}(7172,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8925}(7403,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(8033,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8925}(8192,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{11}{12}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{8925}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(1052,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(1787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(1817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(1913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(2048,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(2552,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(2678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(2837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(3572,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(3602,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(3698,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(3833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(4337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(4463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(4622,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(4853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(5387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(5483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(6122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(6248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(6638,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{8925}(7142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8925}(7172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8925}(7403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(8033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8925}(8192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)

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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	8925.kj
Modulus	$8925$
Conductor	$8925$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8925\)
Conductor:	\(8925\)	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)