LMFDB - Dirichlet character orbit 2032.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2032, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([63,63,115])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,2032)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2032$
Conductor:	$1016$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$126$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1016.bt	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
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 126 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2032}(7,\cdot)$	$1$	$1$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{126}\right)$
$\chi_{2032}(23,\cdot)$	$1$	$1$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{113}{126}\right)$
$\chi_{2032}(39,\cdot)$	$1$	$1$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{121}{126}\right)$
$\chi_{2032}(55,\cdot)$	$1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{126}\right)$
$\chi_{2032}(183,\cdot)$	$1$	$1$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{126}\right)$
$\chi_{2032}(311,\cdot)$	$1$	$1$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{95}{126}\right)$
$\chi_{2032}(439,\cdot)$	$1$	$1$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{103}{126}\right)$
$\chi_{2032}(487,\cdot)$	$1$	$1$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{126}\right)$
$\chi_{2032}(551,\cdot)$	$1$	$1$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{2032}(599,\cdot)$	$1$	$1$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{115}{126}\right)$
$\chi_{2032}(647,\cdot)$	$1$	$1$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{125}{126}\right)$
$\chi_{2032}(727,\cdot)$	$1$	$1$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{126}\right)$
$\chi_{2032}(791,\cdot)$	$1$	$1$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{126}\right)$
$\chi_{2032}(807,\cdot)$	$1$	$1$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{126}\right)$
$\chi_{2032}(855,\cdot)$	$1$	$1$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{97}{126}\right)$
$\chi_{2032}(871,\cdot)$	$1$	$1$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{79}{126}\right)$
$\chi_{2032}(903,\cdot)$	$1$	$1$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{83}{126}\right)$
$\chi_{2032}(935,\cdot)$	$1$	$1$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{126}\right)$
$\chi_{2032}(967,\cdot)$	$1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{2032}(999,\cdot)$	$1$	$1$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{126}\right)$
$\chi_{2032}(1191,\cdot)$	$1$	$1$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{126}\right)$
$\chi_{2032}(1239,\cdot)$	$1$	$1$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{107}{126}\right)$
$\chi_{2032}(1255,\cdot)$	$1$	$1$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{65}{126}\right)$
$\chi_{2032}(1335,\cdot)$	$1$	$1$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{126}\right)$
$\chi_{2032}(1367,\cdot)$	$1$	$1$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{101}{126}\right)$
$\chi_{2032}(1511,\cdot)$	$1$	$1$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{126}\right)$
$\chi_{2032}(1527,\cdot)$	$1$	$1$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{126}\right)$
$\chi_{2032}(1591,\cdot)$	$1$	$1$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{126}\right)$
$\chi_{2032}(1607,\cdot)$	$1$	$1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{85}{126}\right)$
$\chi_{2032}(1767,\cdot)$	$1$	$1$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{2032}(1831,\cdot)$	$1$	$1$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{126}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2032}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{126}\right)\)
\(\chi_{2032}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{113}{126}\right)\)
\(\chi_{2032}(39,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{121}{126}\right)\)
\(\chi_{2032}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{126}\right)\)
\(\chi_{2032}(183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{126}\right)\)
\(\chi_{2032}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{95}{126}\right)\)
\(\chi_{2032}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{103}{126}\right)\)
\(\chi_{2032}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{126}\right)\)
\(\chi_{2032}(551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{2032}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{115}{126}\right)\)
\(\chi_{2032}(647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{125}{126}\right)\)
\(\chi_{2032}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{126}\right)\)
\(\chi_{2032}(791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{126}\right)\)
\(\chi_{2032}(807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{126}\right)\)
\(\chi_{2032}(855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{97}{126}\right)\)
\(\chi_{2032}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{79}{126}\right)\)
\(\chi_{2032}(903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{83}{126}\right)\)
\(\chi_{2032}(935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{126}\right)\)
\(\chi_{2032}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{2032}(999,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{126}\right)\)
\(\chi_{2032}(1191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{126}\right)\)
\(\chi_{2032}(1239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{107}{126}\right)\)
\(\chi_{2032}(1255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{65}{126}\right)\)
\(\chi_{2032}(1335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{126}\right)\)
\(\chi_{2032}(1367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{101}{126}\right)\)
\(\chi_{2032}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{126}\right)\)
\(\chi_{2032}(1527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{126}\right)\)
\(\chi_{2032}(1591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{126}\right)\)
\(\chi_{2032}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{85}{126}\right)\)
\(\chi_{2032}(1767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{2032}(1831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{126}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	2032.cn
Modulus	$2032$
Conductor	$1016$
Order	$126$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(2032\)
Conductor:	\(1016\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(126\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1016.bt	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)