LMFDB - Dirichlet character orbit 497.bc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(497, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([70,18])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,497)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$497$
Conductor:	$497$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$105$	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 105 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{497}(2,\cdot)$	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{97}{105}\right)$
$\chi_{497}(4,\cdot)$	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{497}(9,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{497}(16,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{73}{105}\right)$
$\chi_{497}(18,\cdot)$	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{497}(58,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{497}(60,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{497}(74,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{497}(79,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{46}{105}\right)$
$\chi_{497}(81,\cdot)$	$1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{497}(86,\cdot)$	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{497}(95,\cdot)$	$1$	$1$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{23}{105}\right)$
$\chi_{497}(100,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{497}(107,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{497}(109,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{29}{105}\right)$
$\chi_{497}(114,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{497}(121,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{497}(135,\cdot)$	$1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{497}(144,\cdot)$	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{62}{105}\right)$
$\chi_{497}(151,\cdot)$	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{105}\right)$
$\chi_{497}(158,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{38}{105}\right)$
$\chi_{497}(191,\cdot)$	$1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{497}(200,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{497}(219,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{497}(221,\cdot)$	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{497}(228,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{68}{105}\right)$
$\chi_{497}(240,\cdot)$	$1$	$1$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{497}(242,\cdot)$	$1$	$1$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{497}(249,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{8}{105}\right)$
$\chi_{497}(256,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{497}(263,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{104}{105}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{497}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)
\(\chi_{497}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{497}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{497}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)
\(\chi_{497}(18,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{497}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{497}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{497}(74,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{497}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)
\(\chi_{497}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{497}(86,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{497}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)
\(\chi_{497}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{497}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{497}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)
\(\chi_{497}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{497}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{497}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{497}(144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)
\(\chi_{497}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)
\(\chi_{497}(158,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)
\(\chi_{497}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{497}(200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{497}(219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{497}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{497}(228,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)
\(\chi_{497}(240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{497}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{497}(249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)
\(\chi_{497}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{497}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)

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First 31 of 48 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	497.bc
Modulus	$497$
Conductor	$497$
Order	$105$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(497\)
Conductor:	\(497\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(105\)	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)