LMFDB - Dirichlet character orbit 547.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(547, base_ring=CyclotomicField(182)) M = H._module chi = DirichletCharacter(H, M([60])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(10,547)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$547$
Conductor:	$547$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$91$	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:	$\Q(\zeta_{91})$
Fixed field:	Number field defined by a degree 91 polynomial

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{547}(10,\cdot)$	$1$	$1$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{547}(24,\cdot)$	$1$	$1$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{547}(29,\cdot)$	$1$	$1$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{547}(35,\cdot)$	$1$	$1$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{547}(44,\cdot)$	$1$	$1$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{55}{91}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{36}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{547}(52,\cdot)$	$1$	$1$	$e\left(\frac{48}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{547}(64,\cdot)$	$1$	$1$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{547}(84,\cdot)$	$1$	$1$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{547}(85,\cdot)$	$1$	$1$	$e\left(\frac{55}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{547}(90,\cdot)$	$1$	$1$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{547}(93,\cdot)$	$1$	$1$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{547}(100,\cdot)$	$1$	$1$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{547}(114,\cdot)$	$1$	$1$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{547}(131,\cdot)$	$1$	$1$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{36}{91}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{547}(149,\cdot)$	$1$	$1$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{80}{91}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{547}(154,\cdot)$	$1$	$1$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{547}(161,\cdot)$	$1$	$1$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{79}{91}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{547}(165,\cdot)$	$1$	$1$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{547}(167,\cdot)$	$1$	$1$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{547}(179,\cdot)$	$1$	$1$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{79}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{48}{91}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{547}(185,\cdot)$	$1$	$1$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{547}(195,\cdot)$	$1$	$1$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{547}(204,\cdot)$	$1$	$1$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{79}{91}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{547}(205,\cdot)$	$1$	$1$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{547}(209,\cdot)$	$1$	$1$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{547}(212,\cdot)$	$1$	$1$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{547}(215,\cdot)$	$1$	$1$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{547}(216,\cdot)$	$1$	$1$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{547}(218,\cdot)$	$1$	$1$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{55}{91}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{48}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{547}(224,\cdot)$	$1$	$1$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{36}{91}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{55}{91}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{547}(240,\cdot)$	$1$	$1$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{6}{13}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{547}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{55}{91}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{36}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{547}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{547}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(84,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{547}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(90,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{547}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{36}{91}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{80}{91}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{79}{91}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{547}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{547}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{79}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{48}{91}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{79}{91}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{547}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{547}(215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{547}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(218,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{55}{91}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{48}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{36}{91}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{55}{91}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{547}(240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{6}{13}\right)\)

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First 31 of 72 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	547.m
Modulus	$547$
Conductor	$547$
Order	$91$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(547\)
Conductor:	\(547\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(91\)	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)