# Properties

 Label 547.o Modulus $547$ Conductor $547$ Order $273$ 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(546))

M = H._module

chi = DirichletCharacter(H, M([2]))

chi.galois_orbit()

[g,chi] = znchar(Mod(4,547))

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: $$273$$ 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: $\Q(\zeta_{273})$ Fixed field: Number field defined by a degree 273 polynomial (not computed)

## First 31 of 144 characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{547}(4,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{273}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{273}\right)$$ $$e\left(\frac{179}{273}\right)$$ $$e\left(\frac{157}{273}\right)$$ $$e\left(\frac{103}{273}\right)$$ $$e\left(\frac{1}{91}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{60}{91}\right)$$ $$e\left(\frac{10}{39}\right)$$
$$\chi_{547}(6,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{215}{273}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{157}{273}\right)$$ $$e\left(\frac{265}{273}\right)$$ $$e\left(\frac{176}{273}\right)$$ $$e\left(\frac{32}{273}\right)$$ $$e\left(\frac{33}{91}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{69}{91}\right)$$ $$e\left(\frac{5}{39}\right)$$
$$\chi_{547}(15,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{62}{273}\right)$$ $$e\left(\frac{89}{273}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{190}{273}\right)$$ $$e\left(\frac{31}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{40}{91}\right)$$ $$e\left(\frac{37}{39}\right)$$
$$\chi_{547}(16,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{273}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{4}{273}\right)$$ $$e\left(\frac{85}{273}\right)$$ $$e\left(\frac{41}{273}\right)$$ $$e\left(\frac{206}{273}\right)$$ $$e\left(\frac{2}{91}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{29}{91}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{547}(19,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{115}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{230}{273}\right)$$ $$e\left(\frac{110}{273}\right)$$ $$e\left(\frac{37}{273}\right)$$ $$e\left(\frac{106}{273}\right)$$ $$e\left(\frac{24}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{19}{39}\right)$$
$$\chi_{547}(25,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{179}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{85}{273}\right)$$ $$e\left(\frac{100}{273}\right)$$ $$e\left(\frac{257}{273}\right)$$ $$e\left(\frac{146}{273}\right)$$ $$e\left(\frac{88}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{91}\right)$$ $$e\left(\frac{35}{39}\right)$$
$$\chi_{547}(34,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{76}{273}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{152}{273}\right)$$ $$e\left(\frac{227}{273}\right)$$ $$e\left(\frac{193}{273}\right)$$ $$e\left(\frac{184}{273}\right)$$ $$e\left(\frac{76}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{10}{91}\right)$$ $$e\left(\frac{19}{39}\right)$$
$$\chi_{547}(36,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{157}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{41}{273}\right)$$ $$e\left(\frac{257}{273}\right)$$ $$e\left(\frac{79}{273}\right)$$ $$e\left(\frac{64}{273}\right)$$ $$e\left(\frac{66}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{47}{91}\right)$$ $$e\left(\frac{10}{39}\right)$$
$$\chi_{547}(49,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{103}{273}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{206}{273}\right)$$ $$e\left(\frac{146}{273}\right)$$ $$e\left(\frac{64}{273}\right)$$ $$e\left(\frac{235}{273}\right)$$ $$e\left(\frac{12}{91}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{83}{91}\right)$$ $$e\left(\frac{16}{39}\right)$$
$$\chi_{547}(51,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{34}{273}\right)$$ $$e\left(\frac{40}{273}\right)$$ $$e\left(\frac{212}{273}\right)$$ $$e\left(\frac{113}{273}\right)$$ $$e\left(\frac{17}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{19}{91}\right)$$ $$e\left(\frac{14}{39}\right)$$
$$\chi_{547}(53,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{122}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{244}{273}\right)$$ $$e\left(\frac{271}{273}\right)$$ $$e\left(\frac{44}{273}\right)$$ $$e\left(\frac{8}{273}\right)$$ $$e\left(\frac{31}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{40}{91}\right)$$ $$e\left(\frac{11}{39}\right)$$
$$\chi_{547}(56,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{106}{273}\right)$$ $$e\left(\frac{205}{273}\right)$$ $$e\left(\frac{131}{273}\right)$$ $$e\left(\frac{272}{273}\right)$$ $$e\left(\frac{53}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{86}{91}\right)$$ $$e\left(\frac{23}{39}\right)$$
$$\chi_{547}(60,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{64}{273}\right)$$ $$e\left(\frac{268}{273}\right)$$ $$e\left(\frac{110}{273}\right)$$ $$e\left(\frac{20}{273}\right)$$ $$e\left(\frac{32}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{91}\right)$$ $$e\left(\frac{8}{39}\right)$$
$$\chi_{547}(62,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{152}{273}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{31}{273}\right)$$ $$e\left(\frac{181}{273}\right)$$ $$e\left(\frac{113}{273}\right)$$ $$e\left(\frac{95}{273}\right)$$ $$e\left(\frac{61}{91}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{20}{91}\right)$$ $$e\left(\frac{38}{39}\right)$$
$$\chi_{547}(66,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{250}{273}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{227}{273}\right)$$ $$e\left(\frac{251}{273}\right)$$ $$e\left(\frac{211}{273}\right)$$ $$e\left(\frac{88}{273}\right)$$ $$e\left(\frac{68}{91}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{76}{91}\right)$$ $$e\left(\frac{4}{39}\right)$$
$$\chi_{547}(67,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{170}{273}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{67}{273}\right)$$ $$e\left(\frac{127}{273}\right)$$ $$e\left(\frac{209}{273}\right)$$ $$e\left(\frac{38}{273}\right)$$ $$e\left(\frac{79}{91}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{8}{91}\right)$$ $$e\left(\frac{23}{39}\right)$$
$$\chi_{547}(69,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{88}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{176}{273}\right)$$ $$e\left(\frac{191}{273}\right)$$ $$e\left(\frac{166}{273}\right)$$ $$e\left(\frac{55}{273}\right)$$ $$e\left(\frac{88}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{91}\right)$$ $$e\left(\frac{22}{39}\right)$$
$$\chi_{547}(73,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{242}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{211}{273}\right)$$ $$e\left(\frac{184}{273}\right)$$ $$e\left(\frac{47}{273}\right)$$ $$e\left(\frac{83}{273}\right)$$ $$e\left(\frac{60}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{51}{91}\right)$$ $$e\left(\frac{2}{39}\right)$$
$$\chi_{547}(74,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{244}{273}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{215}{273}\right)$$ $$e\left(\frac{269}{273}\right)$$ $$e\left(\frac{88}{273}\right)$$ $$e\left(\frac{16}{273}\right)$$ $$e\left(\frac{62}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{80}{91}\right)$$ $$e\left(\frac{22}{39}\right)$$
$$\chi_{547}(76,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{116}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{232}{273}\right)$$ $$e\left(\frac{16}{273}\right)$$ $$e\left(\frac{194}{273}\right)$$ $$e\left(\frac{209}{273}\right)$$ $$e\left(\frac{25}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{44}{91}\right)$$ $$e\left(\frac{29}{39}\right)$$
$$\chi_{547}(78,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{85}{273}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{170}{273}\right)$$ $$e\left(\frac{200}{273}\right)$$ $$e\left(\frac{241}{273}\right)$$ $$e\left(\frac{19}{273}\right)$$ $$e\left(\frac{85}{91}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{4}{91}\right)$$ $$e\left(\frac{31}{39}\right)$$
$$\chi_{547}(82,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{46}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{92}{273}\right)$$ $$e\left(\frac{44}{273}\right)$$ $$e\left(\frac{124}{273}\right)$$ $$e\left(\frac{97}{273}\right)$$ $$e\left(\frac{46}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{30}{91}\right)$$ $$e\left(\frac{31}{39}\right)$$
$$\chi_{547}(86,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{73}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{146}{273}\right)$$ $$e\left(\frac{236}{273}\right)$$ $$e\left(\frac{268}{273}\right)$$ $$e\left(\frac{148}{273}\right)$$ $$e\left(\frac{73}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{12}{91}\right)$$ $$e\left(\frac{28}{39}\right)$$
$$\chi_{547}(97,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{199}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{125}{273}\right)$$ $$e\left(\frac{131}{273}\right)$$ $$e\left(\frac{121}{273}\right)$$ $$e\left(\frac{22}{273}\right)$$ $$e\left(\frac{17}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{19}{91}\right)$$ $$e\left(\frac{1}{39}\right)$$
$$\chi_{547}(99,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{191}{273}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{109}{273}\right)$$ $$e\left(\frac{64}{273}\right)$$ $$e\left(\frac{230}{273}\right)$$ $$e\left(\frac{17}{273}\right)$$ $$e\left(\frac{9}{91}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{85}{91}\right)$$ $$e\left(\frac{38}{39}\right)$$
$$\chi_{547}(110,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{125}{273}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{250}{273}\right)$$ $$e\left(\frac{262}{273}\right)$$ $$e\left(\frac{242}{273}\right)$$ $$e\left(\frac{44}{273}\right)$$ $$e\left(\frac{34}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{38}{91}\right)$$ $$e\left(\frac{2}{39}\right)$$
$$\chi_{547}(111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{185}{273}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{97}{273}\right)$$ $$e\left(\frac{82}{273}\right)$$ $$e\left(\frac{107}{273}\right)$$ $$e\left(\frac{218}{273}\right)$$ $$e\left(\frac{3}{91}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{89}{91}\right)$$ $$e\left(\frac{17}{39}\right)$$
$$\chi_{547}(113,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{67}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{134}{273}\right)$$ $$e\left(\frac{254}{273}\right)$$ $$e\left(\frac{145}{273}\right)$$ $$e\left(\frac{76}{273}\right)$$ $$e\left(\frac{67}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{16}{91}\right)$$ $$e\left(\frac{7}{39}\right)$$
$$\chi_{547}(115,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{236}{273}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{199}{273}\right)$$ $$e\left(\frac{202}{273}\right)$$ $$e\left(\frac{197}{273}\right)$$ $$e\left(\frac{11}{273}\right)$$ $$e\left(\frac{54}{91}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{55}{91}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{547}(116,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{160}{273}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{47}{273}\right)$$ $$e\left(\frac{248}{273}\right)$$ $$e\left(\frac{4}{273}\right)$$ $$e\left(\frac{100}{273}\right)$$ $$e\left(\frac{69}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{45}{91}\right)$$ $$e\left(\frac{1}{39}\right)$$
$$\chi_{547}(118,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{256}{273}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{239}{273}\right)$$ $$e\left(\frac{233}{273}\right)$$ $$e\left(\frac{61}{273}\right)$$ $$e\left(\frac{160}{273}\right)$$ $$e\left(\frac{74}{91}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{72}{91}\right)$$ $$e\left(\frac{25}{39}\right)$$