LMFDB - Dirichlet character orbit 5225.jm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5225, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([153,144,80])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(47, 5225)) 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("5225.47"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5225$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$5225$	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:	odd	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{5225}(47,\cdot)$	$-1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{5225}(92,\cdot)$	$-1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{5225}(158,\cdot)$	$-1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{5225}(302,\cdot)$	$-1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{5225}(367,\cdot)$	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{5225}(423,\cdot)$	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(537,\cdot)$	$-1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(708,\cdot)$	$-1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(852,\cdot)$	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{5225}(872,\cdot)$	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{5225}(917,\cdot)$	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(973,\cdot)$	$-1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(1087,\cdot)$	$-1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(1127,\cdot)$	$-1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{5225}(1258,\cdot)$	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(1263,\cdot)$	$-1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{5225}(1422,\cdot)$	$-1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{5225}(1467,\cdot)$	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(1677,\cdot)$	$-1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(1697,\cdot)$	$-1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{5225}(1928,\cdot)$	$-1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{5225}(2088,\cdot)$	$-1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{5225}(2227,\cdot)$	$-1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(2247,\cdot)$	$-1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(2638,\cdot)$	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{5225}(2753,\cdot)$	$-1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{5225}(2797,\cdot)$	$-1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5225}(2913,\cdot)$	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{5225}(3303,\cdot)$	$-1$	$1$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{5225}(3448,\cdot)$	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{5225}(3463,\cdot)$	$-1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{13}{18}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{5225}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{5225}(92,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{5225}(158,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{5225}(302,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{5225}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{5225}(423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(708,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(852,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{5225}(872,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{5225}(917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(973,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(1087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(1127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{5225}(1258,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(1263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{5225}(1422,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{5225}(1467,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(1677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(1697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{5225}(1928,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{5225}(2088,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{5225}(2227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(2247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(2638,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{5225}(2753,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{5225}(2797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5225}(2913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{5225}(3303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{5225}(3448,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{5225}(3463,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)

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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	5225.jm
Modulus	$5225$
Conductor	$5225$
Order	$180$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(5225\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(5225\)	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);