LMFDB - Dirichlet character orbit 9450.gw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9450, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([35,9,15])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(479,9450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9450$
Conductor:	$4725$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$90$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4725.gw	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:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{9450}(479,\cdot)$	$1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{9450}(509,\cdot)$	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{9450}(1109,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{9450}(1139,\cdot)$	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{9450}(1739,\cdot)$	$1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{9450}(1769,\cdot)$	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{9450}(2369,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{9450}(3029,\cdot)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{9450}(3629,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{9450}(3659,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{9450}(4259,\cdot)$	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{9450}(4289,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{9450}(4889,\cdot)$	$1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{9450}(4919,\cdot)$	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{9450}(5519,\cdot)$	$1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{9450}(6179,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{9450}(6779,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{9450}(6809,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{9450}(7409,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{9450}(7439,\cdot)$	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{9450}(8039,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{9450}(8069,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{9450}(8669,\cdot)$	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{9450}(9329,\cdot)$	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{5}{18}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{9450}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{9450}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{9450}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(1139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{9450}(1739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{9450}(1769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{9450}(2369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{9450}(3029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{9450}(3629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{9450}(3659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{9450}(4259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{9450}(4289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{9450}(4889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(4919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{9450}(5519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{9450}(6179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{9450}(6779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(6809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{9450}(7409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{9450}(7439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{9450}(8039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{9450}(8069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{9450}(8669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(9329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

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	9450.gw
Modulus	$9450$
Conductor	$4725$
Order	$90$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9450\)
Conductor:	\(4725\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(90\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4725.gw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)