LMFDB - Dirichlet character orbit 1359.by

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1359, base_ring=CyclotomicField(150)) M = H._module chi = DirichletCharacter(H, M([25,102])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(20, 1359)) 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("1359.20"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1359$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1359$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$150$	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:	$\Q(\zeta_{75})$	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 150 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1359}(20,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1359}(29,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1359}(50,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1359}(68,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1359}(86,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1359}(110,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1359}(245,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1359}(275,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1359}(299,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1359}(311,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1359}(374,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1359}(380,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1359}(383,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1359}(425,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1359}(473,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1359}(482,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1359}(497,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1359}(551,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1359}(563,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1359}(578,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1359}(695,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1359}(698,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1359}(731,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1359}(752,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1359}(833,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1359}(839,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1359}(878,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1359}(950,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1359}(956,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1359}(974,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1359}(992,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{4}{15}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1359}(20,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1359}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1359}(50,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1359}(68,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1359}(86,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1359}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1359}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1359}(275,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1359}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1359}(311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1359}(374,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1359}(380,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1359}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1359}(425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1359}(473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1359}(482,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1359}(497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1359}(551,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1359}(563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1359}(578,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1359}(695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1359}(698,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1359}(731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1359}(752,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1359}(833,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1359}(839,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1359}(878,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1359}(950,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1359}(956,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1359}(974,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1359}(992,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 40 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	1359.by
Modulus	$1359$
Conductor	$1359$
Order	$150$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1359\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1359\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(150\)	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);