LMFDB - Dirichlet character orbit 3636.ck

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3636, base_ring=CyclotomicField(150)) M = H._module chi = DirichletCharacter(H, M([75,100,63])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(43, 3636)) 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("3636.43"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3636$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3636$	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:	$\Q(\zeta_{75})$
Fixed field:	Number field defined by a degree 150 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{3636}(43,\cdot)$	$-1$	$1$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{17}{150}\right)$
$\chi_{3636}(211,\cdot)$	$-1$	$1$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{13}{150}\right)$
$\chi_{3636}(223,\cdot)$	$-1$	$1$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{3636}(247,\cdot)$	$-1$	$1$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{37}{150}\right)$
$\chi_{3636}(367,\cdot)$	$-1$	$1$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{131}{150}\right)$
$\chi_{3636}(427,\cdot)$	$-1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{61}{150}\right)$
$\chi_{3636}(535,\cdot)$	$-1$	$1$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{19}{150}\right)$
$\chi_{3636}(619,\cdot)$	$-1$	$1$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{41}{150}\right)$
$\chi_{3636}(655,\cdot)$	$-1$	$1$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{143}{150}\right)$
$\chi_{3636}(691,\cdot)$	$-1$	$1$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{29}{150}\right)$
$\chi_{3636}(727,\cdot)$	$-1$	$1$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{3636}(931,\cdot)$	$-1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{139}{150}\right)$
$\chi_{3636}(979,\cdot)$	$-1$	$1$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{59}{150}\right)$
$\chi_{3636}(1087,\cdot)$	$-1$	$1$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{47}{150}\right)$
$\chi_{3636}(1255,\cdot)$	$-1$	$1$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{67}{150}\right)$
$\chi_{3636}(1435,\cdot)$	$-1$	$1$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{103}{150}\right)$
$\chi_{3636}(1447,\cdot)$	$-1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{3636}(1519,\cdot)$	$-1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{77}{150}\right)$
$\chi_{3636}(1579,\cdot)$	$-1$	$1$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{31}{150}\right)$
$\chi_{3636}(1591,\cdot)$	$-1$	$1$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{23}{150}\right)$
$\chi_{3636}(1663,\cdot)$	$-1$	$1$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{83}{150}\right)$
$\chi_{3636}(1831,\cdot)$	$-1$	$1$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{91}{150}\right)$
$\chi_{3636}(1867,\cdot)$	$-1$	$1$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{43}{150}\right)$
$\chi_{3636}(1903,\cdot)$	$-1$	$1$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{79}{150}\right)$
$\chi_{3636}(1939,\cdot)$	$-1$	$1$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{1}{150}\right)$
$\chi_{3636}(2191,\cdot)$	$-1$	$1$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{109}{150}\right)$
$\chi_{3636}(2203,\cdot)$	$-1$	$1$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{71}{150}\right)$
$\chi_{3636}(2299,\cdot)$	$-1$	$1$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{97}{150}\right)$
$\chi_{3636}(2419,\cdot)$	$-1$	$1$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{149}{150}\right)$
$\chi_{3636}(2635,\cdot)$	$-1$	$1$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{113}{150}\right)$
$\chi_{3636}(2659,\cdot)$	$-1$	$1$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{7}{150}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{3636}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{17}{150}\right)\)
\(\chi_{3636}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{13}{150}\right)\)
\(\chi_{3636}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{3636}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{37}{150}\right)\)
\(\chi_{3636}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{131}{150}\right)\)
\(\chi_{3636}(427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{61}{150}\right)\)
\(\chi_{3636}(535,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{19}{150}\right)\)
\(\chi_{3636}(619,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{41}{150}\right)\)
\(\chi_{3636}(655,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{143}{150}\right)\)
\(\chi_{3636}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{29}{150}\right)\)
\(\chi_{3636}(727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{3636}(931,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{139}{150}\right)\)
\(\chi_{3636}(979,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{59}{150}\right)\)
\(\chi_{3636}(1087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)
\(\chi_{3636}(1255,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{67}{150}\right)\)
\(\chi_{3636}(1435,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{103}{150}\right)\)
\(\chi_{3636}(1447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{3636}(1519,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{77}{150}\right)\)
\(\chi_{3636}(1579,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{31}{150}\right)\)
\(\chi_{3636}(1591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{23}{150}\right)\)
\(\chi_{3636}(1663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{83}{150}\right)\)
\(\chi_{3636}(1831,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{91}{150}\right)\)
\(\chi_{3636}(1867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{43}{150}\right)\)
\(\chi_{3636}(1903,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{79}{150}\right)\)
\(\chi_{3636}(1939,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{1}{150}\right)\)
\(\chi_{3636}(2191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{109}{150}\right)\)
\(\chi_{3636}(2203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{71}{150}\right)\)
\(\chi_{3636}(2299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)
\(\chi_{3636}(2419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{149}{150}\right)\)
\(\chi_{3636}(2635,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{113}{150}\right)\)
\(\chi_{3636}(2659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{7}{150}\right)\)

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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	3636.ck
Modulus	$3636$
Conductor	$3636$
Order	$150$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(3636\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3636\)	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);