LMFDB - Dirichlet character orbit 1045.ck

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1045, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([45,18,10])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 1045)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1045.4"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1045$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1045$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$90$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{45})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 90 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{1045}(4,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1045}(9,\cdot)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{1045}(104,\cdot)$	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1045}(119,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{1045}(169,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1045}(214,\cdot)$	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{1045}(234,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{1045}(289,\cdot)$	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{1045}(339,\cdot)$	$1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1045}(389,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1045}(434,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1045}(454,\cdot)$	$1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{1045}(499,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{1045}(614,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{1045}(669,\cdot)$	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{1045}(674,\cdot)$	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1045}(709,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{1045}(719,\cdot)$	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{1045}(764,\cdot)$	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1045}(784,\cdot)$	$1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1045}(834,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{1045}(929,\cdot)$	$1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{1045}(994,\cdot)$	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{1045}(1004,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{43}{45}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{1045}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{1045}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1045}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{1045}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1045}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{1045}(234,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{1045}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{1045}(339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1045}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1045}(434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{1045}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{1045}(614,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{1045}(674,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1045}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{1045}(764,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1045}(784,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1045}(834,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{1045}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{1045}(994,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{1045}(1004,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)

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.ck
Modulus	$1045$
Conductor	$1045$
Order	$90$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1045\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1045\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(90\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);