LMFDB - Dirichlet character orbit 1045.cj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1045, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([0,81,70])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,1045)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1045$
Conductor:	$209$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$90$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 209.v	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{1045}(6,\cdot)$	$-1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{1045}(61,\cdot)$	$-1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1045}(101,\cdot)$	$-1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{1045}(156,\cdot)$	$-1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{1045}(161,\cdot)$	$-1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1045}(206,\cdot)$	$-1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1045}(226,\cdot)$	$-1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{1045}(271,\cdot)$	$-1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{1045}(321,\cdot)$	$-1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{1045}(446,\cdot)$	$-1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1045}(481,\cdot)$	$-1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{1045}(491,\cdot)$	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{1045}(536,\cdot)$	$-1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{1045}(541,\cdot)$	$-1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{1045}(556,\cdot)$	$-1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{1045}(651,\cdot)$	$-1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{1045}(701,\cdot)$	$-1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{1045}(766,\cdot)$	$-1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{1045}(776,\cdot)$	$-1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1045}(821,\cdot)$	$-1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1045}(871,\cdot)$	$-1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1045}(921,\cdot)$	$-1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1045}(986,\cdot)$	$-1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1045}(1031,\cdot)$	$-1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{28}{45}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{1045}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1045}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(156,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{1045}(161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1045}(206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1045}(226,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{1045}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{1045}(321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{1045}(446,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1045}(481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{1045}(491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{1045}(536,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{1045}(541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{1045}(556,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{1045}(651,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{1045}(701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{1045}(766,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{1045}(776,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1045}(921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1045}(986,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1045}(1031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	1045.cj
Modulus	$1045$
Conductor	$209$
Order	$90$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(1045\)
Conductor:	\(209\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(90\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 209.v	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)