LMFDB - Dirichlet character orbit 1323.cj

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([112,33])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(61, 1323)) 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("1323.61"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1323$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1323$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$126$	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:	$\Q(\zeta_{63})$	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 126 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1323}(61,\cdot)$	$-1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(94,\cdot)$	$-1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(124,\cdot)$	$-1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(157,\cdot)$	$-1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(187,\cdot)$	$-1$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(220,\cdot)$	$-1$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(250,\cdot)$	$-1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(283,\cdot)$	$-1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(346,\cdot)$	$-1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(376,\cdot)$	$-1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(409,\cdot)$	$-1$	$1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(439,\cdot)$	$-1$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(502,\cdot)$	$-1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(535,\cdot)$	$-1$	$1$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(565,\cdot)$	$-1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(598,\cdot)$	$-1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(628,\cdot)$	$-1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(661,\cdot)$	$-1$	$1$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(691,\cdot)$	$-1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(724,\cdot)$	$-1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(787,\cdot)$	$-1$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(817,\cdot)$	$-1$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(850,\cdot)$	$-1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(880,\cdot)$	$-1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(943,\cdot)$	$-1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(976,\cdot)$	$-1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(1006,\cdot)$	$-1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(1039,\cdot)$	$-1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(1069,\cdot)$	$-1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(1102,\cdot)$	$-1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(1132,\cdot)$	$-1$	$1$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1323}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(94,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(220,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(250,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(346,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(376,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(409,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(502,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(535,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(598,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(628,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(724,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(787,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(850,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(880,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(943,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(976,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(1006,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(1039,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(1069,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(1102,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(1132,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)

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First 31 of 36 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	1323.cj
Modulus	$1323$
Conductor	$1323$
Order	$126$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1323\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1323\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(126\)	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);