LMFDB - Dirichlet character orbit 497.bd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(497, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([140,93])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,497)) 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:	$210$	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{497}(11,\cdot)$	$-1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{497}(44,\cdot)$	$-1$	$1$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{497}(53,\cdot)$	$-1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{497}(65,\cdot)$	$-1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{497}(67,\cdot)$	$-1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{497}(93,\cdot)$	$-1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{497}(102,\cdot)$	$-1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{32}{105}\right)$
$\chi_{497}(123,\cdot)$	$-1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{497}(130,\cdot)$	$-1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{101}{105}\right)$
$\chi_{497}(149,\cdot)$	$-1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{497}(163,\cdot)$	$-1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{497}(170,\cdot)$	$-1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{497}(177,\cdot)$	$-1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{497}(184,\cdot)$	$-1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{497}(186,\cdot)$	$-1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{497}(198,\cdot)$	$-1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{497}(205,\cdot)$	$-1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{46}{105}\right)$
$\chi_{497}(207,\cdot)$	$-1$	$1$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{497}(226,\cdot)$	$-1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{497}(235,\cdot)$	$-1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{497}(268,\cdot)$	$-1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{73}{105}\right)$
$\chi_{497}(275,\cdot)$	$-1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{497}(282,\cdot)$	$-1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{97}{105}\right)$
$\chi_{497}(291,\cdot)$	$-1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{497}(305,\cdot)$	$-1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{104}{105}\right)$
$\chi_{497}(312,\cdot)$	$-1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{497}(317,\cdot)$	$-1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{497}(319,\cdot)$	$-1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{8}{105}\right)$
$\chi_{497}(326,\cdot)$	$-1$	$1$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{497}(331,\cdot)$	$-1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{497}(340,\cdot)$	$-1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{68}{105}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{497}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{497}(44,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{497}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{497}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{497}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{497}(93,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{497}(102,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{32}{105}\right)\)
\(\chi_{497}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{497}(130,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)
\(\chi_{497}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{497}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{497}(170,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{497}(177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{497}(184,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{497}(186,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{497}(198,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{497}(205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)
\(\chi_{497}(207,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{497}(226,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{497}(235,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{497}(268,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)
\(\chi_{497}(275,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{497}(282,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)
\(\chi_{497}(291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{497}(305,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)
\(\chi_{497}(312,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{497}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{497}(319,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)
\(\chi_{497}(326,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{497}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{497}(340,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{68}{105}\right)\)

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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.bd
Modulus	$497$
Conductor	$497$
Order	$210$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(497\)
Conductor:	\(497\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(210\)	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)