LMFDB - Dirichlet character orbit 1359.cg

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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([125,112])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 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("1359.5"); 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1359}(5,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(47,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(74,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(95,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(137,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(173,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(200,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(239,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(248,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(272,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(290,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(320,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(344,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(347,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(401,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(446,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(464,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(515,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(533,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(569,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(614,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(635,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(644,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(659,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(662,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1359}(707,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(794,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1359}(824,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(893,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1359}(923,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1359}(1082,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{4}{5}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1359}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(74,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(200,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(248,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(272,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(290,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(320,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(344,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(446,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(464,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(569,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(635,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(644,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(662,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1359}(707,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(794,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1359}(824,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1359}(923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1359}(1082,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)

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Basic properties

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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.cg
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);