# Properties

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

# Related objects

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