LMFDB - Dirichlet character orbit 1323.ca

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([70,48])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,1323)) 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:	$63$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	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 63 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1323}(25,\cdot)$	$1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(58,\cdot)$	$1$	$1$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(88,\cdot)$	$1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{1323}(121,\cdot)$	$1$	$1$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(151,\cdot)$	$1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(184,\cdot)$	$1$	$1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{1323}(247,\cdot)$	$1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{1}{7}\right)$	$1$
$\chi_{1323}(277,\cdot)$	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{1323}(310,\cdot)$	$1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{1323}(340,\cdot)$	$1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{1323}(403,\cdot)$	$1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{7}\right)$	$1$
$\chi_{1323}(436,\cdot)$	$1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{1323}(466,\cdot)$	$1$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(499,\cdot)$	$1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(529,\cdot)$	$1$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{1323}(562,\cdot)$	$1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(592,\cdot)$	$1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(625,\cdot)$	$1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{1323}(688,\cdot)$	$1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{7}\right)$	$1$
$\chi_{1323}(718,\cdot)$	$1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{1323}(751,\cdot)$	$1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{1323}(781,\cdot)$	$1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{1323}(844,\cdot)$	$1$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{7}\right)$	$1$
$\chi_{1323}(877,\cdot)$	$1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{1323}(907,\cdot)$	$1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(940,\cdot)$	$1$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(970,\cdot)$	$1$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{1323}(1003,\cdot)$	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(1033,\cdot)$	$1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{1323}(1066,\cdot)$	$1$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{1323}(1129,\cdot)$	$1$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{1}{7}\right)$	$1$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1323}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{1323}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{1323}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)
\(\chi_{1323}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{1323}(310,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{1323}(340,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{1323}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)
\(\chi_{1323}(436,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{1323}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{1323}(562,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{1323}(688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)
\(\chi_{1323}(718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{1323}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{1323}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{1323}(844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)
\(\chi_{1323}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{1323}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(940,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(970,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{1323}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{1323}(1066,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{1323}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)

Introduction

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Basic properties

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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.ca
Modulus	$1323$
Conductor	$1323$
Order	$63$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1323\)
Conductor:	\(1323\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(63\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)