Properties

Label 547.m
Modulus $547$
Conductor $547$
Order $91$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(182))
 
M = H._module
 
chi = DirichletCharacter(H, M([60]))
 
chi.galois_orbit()
 
[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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{547}(10,\cdot)\) \(1\) \(1\) \(e\left(\frac{30}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{60}{91}\right)\) \(e\left(\frac{1}{91}\right)\) \(e\left(\frac{69}{91}\right)\) \(e\left(\frac{87}{91}\right)\) \(e\left(\frac{90}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{31}{91}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(24,\cdot)\) \(1\) \(1\) \(e\left(\frac{72}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{53}{91}\right)\) \(e\left(\frac{57}{91}\right)\) \(e\left(\frac{20}{91}\right)\) \(e\left(\frac{45}{91}\right)\) \(e\left(\frac{34}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{38}{91}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{15}{91}\right)\) \(e\left(\frac{23}{91}\right)\) \(e\left(\frac{40}{91}\right)\) \(e\left(\frac{90}{91}\right)\) \(e\left(\frac{68}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{76}{91}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(35,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{91}\right)\) \(e\left(\frac{41}{91}\right)\) \(e\left(\frac{8}{91}\right)\) \(e\left(\frac{18}{91}\right)\) \(e\left(\frac{50}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{88}{91}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{24}{91}\right)\) \(e\left(\frac{55}{91}\right)\) \(e\left(\frac{64}{91}\right)\) \(e\left(\frac{53}{91}\right)\) \(e\left(\frac{36}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{67}{91}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{547}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{48}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{91}\right)\) \(e\left(\frac{38}{91}\right)\) \(e\left(\frac{74}{91}\right)\) \(e\left(\frac{30}{91}\right)\) \(e\left(\frac{53}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{86}{91}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{547}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{91}\right)\) \(e\left(\frac{88}{91}\right)\) \(e\left(\frac{66}{91}\right)\) \(e\left(\frac{12}{91}\right)\) \(e\left(\frac{3}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{89}{91}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(84,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{87}{91}\right)\) \(e\left(\frac{6}{91}\right)\) \(e\left(\frac{50}{91}\right)\) \(e\left(\frac{67}{91}\right)\) \(e\left(\frac{85}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{91}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{547}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{91}\right)\) \(e\left(\frac{17}{91}\right)\) \(e\left(\frac{81}{91}\right)\) \(e\left(\frac{23}{91}\right)\) \(e\left(\frac{74}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{72}{91}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(90,\cdot)\) \(1\) \(1\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{73}{91}\right)\) \(e\left(\frac{27}{91}\right)\) \(e\left(\frac{43}{91}\right)\) \(e\left(\frac{74}{91}\right)\) \(e\left(\frac{64}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{18}{91}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(93,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{62}{91}\right)\) \(e\left(\frac{89}{91}\right)\) \(e\left(\frac{44}{91}\right)\) \(e\left(\frac{8}{91}\right)\) \(e\left(\frac{2}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{91}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{547}(100,\cdot)\) \(1\) \(1\) \(e\left(\frac{60}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{29}{91}\right)\) \(e\left(\frac{2}{91}\right)\) \(e\left(\frac{47}{91}\right)\) \(e\left(\frac{83}{91}\right)\) \(e\left(\frac{89}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{62}{91}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(114,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{38}{91}\right)\) \(e\left(\frac{34}{91}\right)\) \(e\left(\frac{71}{91}\right)\) \(e\left(\frac{46}{91}\right)\) \(e\left(\frac{57}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{53}{91}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(131,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{91}\right)\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{16}{91}\right)\) \(e\left(\frac{36}{91}\right)\) \(e\left(\frac{9}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{85}{91}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(149,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{68}{91}\right)\) \(e\left(\frac{80}{91}\right)\) \(e\left(\frac{60}{91}\right)\) \(e\left(\frac{44}{91}\right)\) \(e\left(\frac{11}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{23}{91}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{547}(154,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{4}{91}\right)\) \(e\left(\frac{3}{91}\right)\) \(e\left(\frac{75}{91}\right)\) \(e\left(\frac{87}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{33}{91}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(161,\cdot)\) \(1\) \(1\) \(e\left(\frac{66}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{41}{91}\right)\) \(e\left(\frac{75}{91}\right)\) \(e\left(\frac{79}{91}\right)\) \(e\left(\frac{64}{91}\right)\) \(e\left(\frac{16}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{50}{91}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(165,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{44}{91}\right)\) \(e\left(\frac{25}{91}\right)\) \(e\left(\frac{87}{91}\right)\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{66}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{47}{91}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{547}(167,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{46}{91}\right)\) \(e\left(\frac{22}{91}\right)\) \(e\left(\frac{62}{91}\right)\) \(e\left(\frac{3}{91}\right)\) \(e\left(\frac{69}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{45}{91}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{547}(179,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{8}{91}\right)\) \(e\left(\frac{79}{91}\right)\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{48}{91}\right)\) \(e\left(\frac{12}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{83}{91}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(185,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{40}{91}\right)\) \(e\left(\frac{31}{91}\right)\) \(e\left(\frac{46}{91}\right)\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{60}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{51}{91}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(195,\cdot)\) \(1\) \(1\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{25}{91}\right)\) \(e\left(\frac{8}{91}\right)\) \(e\left(\frac{6}{91}\right)\) \(e\left(\frac{59}{91}\right)\) \(e\left(\frac{83}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{66}{91}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(204,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{12}{91}\right)\) \(e\left(\frac{73}{91}\right)\) \(e\left(\frac{32}{91}\right)\) \(e\left(\frac{72}{91}\right)\) \(e\left(\frac{18}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{79}{91}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(205,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{90}{91}\right)\) \(e\left(\frac{47}{91}\right)\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{85}{91}\right)\) \(e\left(\frac{44}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{91}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{547}(209,\cdot)\) \(1\) \(1\) \(e\left(\frac{50}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{91}\right)\) \(e\left(\frac{32}{91}\right)\) \(e\left(\frac{24}{91}\right)\) \(e\left(\frac{54}{91}\right)\) \(e\left(\frac{59}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{547}(212,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{91}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{82}{91}\right)\) \(e\left(\frac{59}{91}\right)\) \(e\left(\frac{67}{91}\right)\) \(e\left(\frac{37}{91}\right)\) \(e\left(\frac{32}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{91}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{547}(215,\cdot)\) \(1\) \(1\) \(e\left(\frac{54}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{91}\right)\) \(e\left(\frac{20}{91}\right)\) \(e\left(\frac{15}{91}\right)\) \(e\left(\frac{11}{91}\right)\) \(e\left(\frac{71}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{74}{91}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{547}(216,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{91}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{66}{91}\right)\) \(e\left(\frac{83}{91}\right)\) \(e\left(\frac{85}{91}\right)\) \(e\left(\frac{32}{91}\right)\) \(e\left(\frac{8}{91}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{91}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(218,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{91}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{32}{91}\right)\) \(e\left(\frac{43}{91}\right)\) \(e\left(\frac{55}{91}\right)\) \(e\left(\frac{10}{91}\right)\) \(e\left(\frac{48}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{59}{91}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{547}(224,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{36}{91}\right)\) \(e\left(\frac{37}{91}\right)\) \(e\left(\frac{5}{91}\right)\) \(e\left(\frac{34}{91}\right)\) \(e\left(\frac{54}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{55}{91}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{547}(240,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{91}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{22}{91}\right)\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{89}{91}\right)\) \(e\left(\frac{41}{91}\right)\) \(e\left(\frac{33}{91}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{69}{91}\right)\) \(e\left(\frac{6}{13}\right)\)