LMFDB - Dirichlet character orbit 497.ba

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(497, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([35,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,497)) 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:	$70$	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:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{497}(6,\cdot)$	$-1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{61}{70}\right)$
$\chi_{497}(27,\cdot)$	$-1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{497}(83,\cdot)$	$-1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{9}{70}\right)$
$\chi_{497}(90,\cdot)$	$-1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{497}(111,\cdot)$	$-1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{497}(146,\cdot)$	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{497}(160,\cdot)$	$-1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{497}(202,\cdot)$	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{23}{70}\right)$
$\chi_{497}(216,\cdot)$	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{497}(223,\cdot)$	$-1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{497}(237,\cdot)$	$-1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{497}(251,\cdot)$	$-1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{497}(286,\cdot)$	$-1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{497}(293,\cdot)$	$-1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{497}(300,\cdot)$	$-1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{497}(342,\cdot)$	$-1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{497}(363,\cdot)$	$-1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{497}(370,\cdot)$	$-1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{497}(384,\cdot)$	$-1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{29}{70}\right)$
$\chi_{497}(391,\cdot)$	$-1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{497}(398,\cdot)$	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{497}(405,\cdot)$	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{11}{70}\right)$
$\chi_{497}(419,\cdot)$	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{70}\right)$
$\chi_{497}(475,\cdot)$	$-1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{41}{70}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{497}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)
\(\chi_{497}(27,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{497}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)
\(\chi_{497}(90,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{497}(111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)
\(\chi_{497}(146,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)
\(\chi_{497}(160,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)
\(\chi_{497}(202,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)
\(\chi_{497}(216,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{497}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{497}(237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{497}(251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{497}(286,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)
\(\chi_{497}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{497}(300,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{497}(342,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)
\(\chi_{497}(363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{497}(370,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{497}(384,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)
\(\chi_{497}(391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)
\(\chi_{497}(398,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)
\(\chi_{497}(405,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)
\(\chi_{497}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)
\(\chi_{497}(475,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)

Introduction

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Properties

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Basic properties

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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.ba
Modulus	$497$
Conductor	$497$
Order	$70$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(497\)
Conductor:	\(497\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(70\)	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)