LMFDB - Dirichlet character orbit 1323.cl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([56,69])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(40,1323)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1323$
Conductor:	$1323$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$126$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1323}(40,\cdot)$	$-1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(52,\cdot)$	$-1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(103,\cdot)$	$-1$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(115,\cdot)$	$-1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{1323}(229,\cdot)$	$-1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{1323}(241,\cdot)$	$-1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{1323}(292,\cdot)$	$-1$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{1323}(304,\cdot)$	$-1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{1323}(355,\cdot)$	$-1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{1323}(367,\cdot)$	$-1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(418,\cdot)$	$-1$	$1$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{1323}(430,\cdot)$	$-1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{1323}(481,\cdot)$	$-1$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(493,\cdot)$	$-1$	$1$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(544,\cdot)$	$-1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(556,\cdot)$	$-1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{1323}(670,\cdot)$	$-1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{1323}(682,\cdot)$	$-1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{1323}(733,\cdot)$	$-1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{1323}(745,\cdot)$	$-1$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{1323}(796,\cdot)$	$-1$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{1323}(808,\cdot)$	$-1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(859,\cdot)$	$-1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{1323}(871,\cdot)$	$-1$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{1323}(922,\cdot)$	$-1$	$1$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(934,\cdot)$	$-1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(985,\cdot)$	$-1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(997,\cdot)$	$-1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{1323}(1111,\cdot)$	$-1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{1323}(1123,\cdot)$	$-1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{11}{14}\right)$	$-1$
$\chi_{1323}(1174,\cdot)$	$-1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{9}{14}\right)$	$-1$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1323}(40,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(52,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{1323}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{1323}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{1323}(292,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{1323}(304,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{1323}(355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{1323}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(418,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{1323}(430,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{1323}(481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(544,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(556,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{1323}(670,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{1323}(682,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{1323}(733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{1323}(745,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{1323}(796,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{1323}(808,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(859,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{1323}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{1323}(922,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(934,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(985,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{1323}(1111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{1323}(1123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)
\(\chi_{1323}(1174,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)

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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.cl
Modulus	$1323$
Conductor	$1323$
Order	$126$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1323\)
Conductor:	\(1323\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(126\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)