LMFDB - Dirichlet character orbit 1045.cs

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1045, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([45,162,100])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 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("1045.17"); 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:	$180$	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:	$\Q(\zeta_{180})$	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 180 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{1045}(17,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{1045}(28,\cdot)$	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{1045}(62,\cdot)$	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{1045}(63,\cdot)$	$1$	$1$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1045}(73,\cdot)$	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{1045}(112,\cdot)$	$1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{1045}(118,\cdot)$	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{1045}(123,\cdot)$	$1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{1045}(138,\cdot)$	$1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{1045}(233,\cdot)$	$1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{1045}(237,\cdot)$	$1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{1045}(272,\cdot)$	$1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1045}(282,\cdot)$	$1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{1045}(283,\cdot)$	$1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{1045}(327,\cdot)$	$1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{1045}(332,\cdot)$	$1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{1045}(347,\cdot)$	$1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{1045}(348,\cdot)$	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{1045}(358,\cdot)$	$1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{1045}(403,\cdot)$	$1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{1045}(442,\cdot)$	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{1045}(453,\cdot)$	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{1045}(492,\cdot)$	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{1045}(503,\cdot)$	$1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{1045}(557,\cdot)$	$1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{1045}(567,\cdot)$	$1$	$1$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{1045}(568,\cdot)$	$1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{1045}(612,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{1045}(613,\cdot)$	$1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{1045}(633,\cdot)$	$1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{1045}(662,\cdot)$	$1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{77}{90}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{1045}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{1045}(28,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{1045}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{1045}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1045}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)
\(\chi_{1045}(112,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)
\(\chi_{1045}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{1045}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{1045}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{1045}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{1045}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{1045}(272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1045}(282,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)
\(\chi_{1045}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)
\(\chi_{1045}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{1045}(332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{1045}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{1045}(348,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{1045}(358,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{1045}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{1045}(442,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{1045}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{1045}(492,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)
\(\chi_{1045}(503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{1045}(557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{1045}(567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{1045}(568,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{1045}(612,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{1045}(613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{1045}(633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{1045}(662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)

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First 31 of 48 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.cs
Modulus	$1045$
Conductor	$1045$
Order	$180$
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:	\(180\)	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);