LMFDB - Dirichlet character orbit 9025.bg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([36,50])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(606,9025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9025$
Conductor:	$475$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$45$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 45 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{9025}(606,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{9025}(821,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{9025}(956,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{9025}(1111,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{9025}(1506,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{9025}(2411,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{9025}(2581,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{9025}(2761,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{9025}(2916,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{9025}(3311,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{9025}(4216,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{9025}(4386,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{9025}(4431,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{9025}(4566,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{9025}(4721,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{9025}(5116,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{9025}(6021,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{9025}(6191,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{9025}(6236,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{9025}(6371,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{9025}(6921,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{9025}(7996,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{9025}(8041,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{9025}(8331,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{45}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{9025}(606,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{9025}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{9025}(956,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{9025}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{9025}(1506,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{9025}(2411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{9025}(2581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{9025}(2761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{9025}(2916,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{9025}(3311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{9025}(4216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{9025}(4386,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{9025}(4431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{9025}(4566,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{9025}(4721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{9025}(5116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{9025}(6021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{9025}(6191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{9025}(6236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{9025}(6371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{9025}(6921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{9025}(7996,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{9025}(8041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{9025}(8331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)

Introduction

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Properties

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Basic properties

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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	9025.bg
Modulus	$9025$
Conductor	$475$
Order	$45$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(9025\)
Conductor:	\(475\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(45\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)