# Properties

 Label 4729.i Modulus $4729$ Conductor $4729$ Order $197$ Real no Primitive yes Minimal yes Parity even

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4729, base_ring=CyclotomicField(394))

M = H._module

chi = DirichletCharacter(H, M([106]))

chi.galois_orbit()

[g,chi] = znchar(Mod(16,4729))

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Basic properties

 Modulus: $$4729$$ Conductor: $$4729$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$197$$ 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: $\Q(\zeta_{197})$ Fixed field: Number field defined by a degree 197 polynomial (not computed)

## First 31 of 196 characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{4729}(16,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{109}{197}\right)$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{21}{197}\right)$$ $$e\left(\frac{174}{197}\right)$$ $$e\left(\frac{57}{197}\right)$$ $$e\left(\frac{26}{197}\right)$$ $$e\left(\frac{130}{197}\right)$$ $$e\left(\frac{93}{197}\right)$$ $$e\left(\frac{86}{197}\right)$$ $$e\left(\frac{143}{197}\right)$$
$$\chi_{4729}(24,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{118}{197}\right)$$ $$e\left(\frac{16}{197}\right)$$ $$e\left(\frac{39}{197}\right)$$ $$e\left(\frac{98}{197}\right)$$ $$e\left(\frac{134}{197}\right)$$ $$e\left(\frac{189}{197}\right)$$ $$e\left(\frac{157}{197}\right)$$ $$e\left(\frac{32}{197}\right)$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{153}{197}\right)$$
$$\chi_{4729}(36,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{127}{197}\right)$$ $$e\left(\frac{84}{197}\right)$$ $$e\left(\frac{57}{197}\right)$$ $$e\left(\frac{22}{197}\right)$$ $$e\left(\frac{14}{197}\right)$$ $$e\left(\frac{155}{197}\right)$$ $$e\left(\frac{184}{197}\right)$$ $$e\left(\frac{168}{197}\right)$$ $$e\left(\frac{149}{197}\right)$$ $$e\left(\frac{163}{197}\right)$$
$$\chi_{4729}(54,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{136}{197}\right)$$ $$e\left(\frac{152}{197}\right)$$ $$e\left(\frac{75}{197}\right)$$ $$e\left(\frac{143}{197}\right)$$ $$e\left(\frac{91}{197}\right)$$ $$e\left(\frac{121}{197}\right)$$ $$e\left(\frac{14}{197}\right)$$ $$e\left(\frac{107}{197}\right)$$ $$e\left(\frac{82}{197}\right)$$ $$e\left(\frac{173}{197}\right)$$
$$\chi_{4729}(81,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{23}{197}\right)$$ $$e\left(\frac{93}{197}\right)$$ $$e\left(\frac{67}{197}\right)$$ $$e\left(\frac{168}{197}\right)$$ $$e\left(\frac{87}{197}\right)$$ $$e\left(\frac{41}{197}\right)$$ $$e\left(\frac{46}{197}\right)$$ $$e\left(\frac{15}{197}\right)$$ $$e\left(\frac{183}{197}\right)$$
$$\chi_{4729}(250,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{197}\right)$$ $$e\left(\frac{185}{197}\right)$$ $$e\left(\frac{20}{197}\right)$$ $$e\left(\frac{25}{197}\right)$$ $$e\left(\frac{195}{197}\right)$$ $$e\left(\frac{6}{197}\right)$$ $$e\left(\frac{30}{197}\right)$$ $$e\left(\frac{173}{197}\right)$$ $$e\left(\frac{35}{197}\right)$$ $$e\left(\frac{33}{197}\right)$$
$$\chi_{4729}(251,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{191}{197}\right)$$ $$e\left(\frac{86}{197}\right)$$ $$e\left(\frac{185}{197}\right)$$ $$e\left(\frac{182}{197}\right)$$ $$e\left(\frac{80}{197}\right)$$ $$e\left(\frac{154}{197}\right)$$ $$e\left(\frac{179}{197}\right)$$ $$e\left(\frac{172}{197}\right)$$ $$e\left(\frac{176}{197}\right)$$ $$e\left(\frac{59}{197}\right)$$
$$\chi_{4729}(253,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{43}{197}\right)$$ $$e\left(\frac{106}{197}\right)$$ $$e\left(\frac{86}{197}\right)$$ $$e\left(\frac{9}{197}\right)$$ $$e\left(\frac{149}{197}\right)$$ $$e\left(\frac{144}{197}\right)$$ $$e\left(\frac{129}{197}\right)$$ $$e\left(\frac{15}{197}\right)$$ $$e\left(\frac{52}{197}\right)$$ $$e\left(\frac{4}{197}\right)$$
$$\chi_{4729}(256,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{197}\right)$$ $$e\left(\frac{93}{197}\right)$$ $$e\left(\frac{42}{197}\right)$$ $$e\left(\frac{151}{197}\right)$$ $$e\left(\frac{114}{197}\right)$$ $$e\left(\frac{52}{197}\right)$$ $$e\left(\frac{63}{197}\right)$$ $$e\left(\frac{186}{197}\right)$$ $$e\left(\frac{172}{197}\right)$$ $$e\left(\frac{89}{197}\right)$$
$$\chi_{4729}(295,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{62}{197}\right)$$ $$e\left(\frac{162}{197}\right)$$ $$e\left(\frac{124}{197}\right)$$ $$e\left(\frac{155}{197}\right)$$ $$e\left(\frac{27}{197}\right)$$ $$e\left(\frac{116}{197}\right)$$ $$e\left(\frac{186}{197}\right)$$ $$e\left(\frac{127}{197}\right)$$ $$e\left(\frac{20}{197}\right)$$ $$e\left(\frac{47}{197}\right)$$
$$\chi_{4729}(314,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{150}{197}\right)$$ $$e\left(\frac{17}{197}\right)$$ $$e\left(\frac{103}{197}\right)$$ $$e\left(\frac{178}{197}\right)$$ $$e\left(\frac{167}{197}\right)$$ $$e\left(\frac{90}{197}\right)$$ $$e\left(\frac{56}{197}\right)$$ $$e\left(\frac{34}{197}\right)$$ $$e\left(\frac{131}{197}\right)$$ $$e\left(\frac{101}{197}\right)$$
$$\chi_{4729}(319,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{107}{197}\right)$$ $$e\left(\frac{108}{197}\right)$$ $$e\left(\frac{17}{197}\right)$$ $$e\left(\frac{169}{197}\right)$$ $$e\left(\frac{18}{197}\right)$$ $$e\left(\frac{143}{197}\right)$$ $$e\left(\frac{124}{197}\right)$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{79}{197}\right)$$ $$e\left(\frac{97}{197}\right)$$
$$\chi_{4729}(325,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{50}{197}\right)$$ $$e\left(\frac{137}{197}\right)$$ $$e\left(\frac{100}{197}\right)$$ $$e\left(\frac{125}{197}\right)$$ $$e\left(\frac{187}{197}\right)$$ $$e\left(\frac{30}{197}\right)$$ $$e\left(\frac{150}{197}\right)$$ $$e\left(\frac{77}{197}\right)$$ $$e\left(\frac{175}{197}\right)$$ $$e\left(\frac{165}{197}\right)$$
$$\chi_{4729}(375,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{56}{197}\right)$$ $$e\left(\frac{38}{197}\right)$$ $$e\left(\frac{146}{197}\right)$$ $$e\left(\frac{75}{197}\right)$$ $$e\left(\frac{169}{197}\right)$$ $$e\left(\frac{57}{197}\right)$$ $$e\left(\frac{112}{197}\right)$$ $$e\left(\frac{165}{197}\right)$$ $$e\left(\frac{43}{197}\right)$$
$$\chi_{4729}(384,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{30}{197}\right)$$ $$e\left(\frac{161}{197}\right)$$ $$e\left(\frac{60}{197}\right)$$ $$e\left(\frac{75}{197}\right)$$ $$e\left(\frac{191}{197}\right)$$ $$e\left(\frac{18}{197}\right)$$ $$e\left(\frac{90}{197}\right)$$ $$e\left(\frac{125}{197}\right)$$ $$e\left(\frac{105}{197}\right)$$ $$e\left(\frac{99}{197}\right)$$
$$\chi_{4729}(471,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{159}{197}\right)$$ $$e\left(\frac{85}{197}\right)$$ $$e\left(\frac{121}{197}\right)$$ $$e\left(\frac{102}{197}\right)$$ $$e\left(\frac{47}{197}\right)$$ $$e\left(\frac{56}{197}\right)$$ $$e\left(\frac{83}{197}\right)$$ $$e\left(\frac{170}{197}\right)$$ $$e\left(\frac{64}{197}\right)$$ $$e\left(\frac{111}{197}\right)$$
$$\chi_{4729}(490,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{133}{197}\right)$$ $$e\left(\frac{195}{197}\right)$$ $$e\left(\frac{69}{197}\right)$$ $$e\left(\frac{37}{197}\right)$$ $$e\left(\frac{131}{197}\right)$$ $$e\left(\frac{1}{197}\right)$$ $$e\left(\frac{5}{197}\right)$$ $$e\left(\frac{193}{197}\right)$$ $$e\left(\frac{170}{197}\right)$$ $$e\left(\frac{104}{197}\right)$$
$$\chi_{4729}(497,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{47}{197}\right)$$ $$e\left(\frac{180}{197}\right)$$ $$e\left(\frac{94}{197}\right)$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{30}{197}\right)$$ $$e\left(\frac{107}{197}\right)$$ $$e\left(\frac{141}{197}\right)$$ $$e\left(\frac{163}{197}\right)$$ $$e\left(\frac{66}{197}\right)$$ $$e\left(\frac{96}{197}\right)$$
$$\chi_{4729}(576,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{39}{197}\right)$$ $$e\left(\frac{32}{197}\right)$$ $$e\left(\frac{78}{197}\right)$$ $$e\left(\frac{196}{197}\right)$$ $$e\left(\frac{71}{197}\right)$$ $$e\left(\frac{181}{197}\right)$$ $$e\left(\frac{117}{197}\right)$$ $$e\left(\frac{64}{197}\right)$$ $$e\left(\frac{38}{197}\right)$$ $$e\left(\frac{109}{197}\right)$$
$$\chi_{4729}(637,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{173}{197}\right)$$ $$e\left(\frac{147}{197}\right)$$ $$e\left(\frac{149}{197}\right)$$ $$e\left(\frac{137}{197}\right)$$ $$e\left(\frac{123}{197}\right)$$ $$e\left(\frac{25}{197}\right)$$ $$e\left(\frac{125}{197}\right)$$ $$e\left(\frac{97}{197}\right)$$ $$e\left(\frac{113}{197}\right)$$ $$e\left(\frac{39}{197}\right)$$
$$\chi_{4729}(665,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{132}{197}\right)$$ $$e\left(\frac{78}{197}\right)$$ $$e\left(\frac{67}{197}\right)$$ $$e\left(\frac{133}{197}\right)$$ $$e\left(\frac{13}{197}\right)$$ $$e\left(\frac{158}{197}\right)$$ $$e\left(\frac{2}{197}\right)$$ $$e\left(\frac{156}{197}\right)$$ $$e\left(\frac{68}{197}\right)$$ $$e\left(\frac{81}{197}\right)$$
$$\chi_{4729}(682,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{197}\right)$$ $$e\left(\frac{105}{197}\right)$$ $$e\left(\frac{22}{197}\right)$$ $$e\left(\frac{126}{197}\right)$$ $$e\left(\frac{116}{197}\right)$$ $$e\left(\frac{46}{197}\right)$$ $$e\left(\frac{33}{197}\right)$$ $$e\left(\frac{13}{197}\right)$$ $$e\left(\frac{137}{197}\right)$$ $$e\left(\frac{56}{197}\right)$$
$$\chi_{4729}(734,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{85}{197}\right)$$ $$e\left(\frac{95}{197}\right)$$ $$e\left(\frac{170}{197}\right)$$ $$e\left(\frac{114}{197}\right)$$ $$e\left(\frac{180}{197}\right)$$ $$e\left(\frac{51}{197}\right)$$ $$e\left(\frac{58}{197}\right)$$ $$e\left(\frac{190}{197}\right)$$ $$e\left(\frac{2}{197}\right)$$ $$e\left(\frac{182}{197}\right)$$
$$\chi_{4729}(735,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{142}{197}\right)$$ $$e\left(\frac{66}{197}\right)$$ $$e\left(\frac{87}{197}\right)$$ $$e\left(\frac{158}{197}\right)$$ $$e\left(\frac{11}{197}\right)$$ $$e\left(\frac{164}{197}\right)$$ $$e\left(\frac{32}{197}\right)$$ $$e\left(\frac{132}{197}\right)$$ $$e\left(\frac{103}{197}\right)$$ $$e\left(\frac{114}{197}\right)$$
$$\chi_{4729}(739,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{97}{197}\right)$$ $$e\left(\frac{120}{197}\right)$$ $$e\left(\frac{194}{197}\right)$$ $$e\left(\frac{144}{197}\right)$$ $$e\left(\frac{20}{197}\right)$$ $$e\left(\frac{137}{197}\right)$$ $$e\left(\frac{94}{197}\right)$$ $$e\left(\frac{43}{197}\right)$$ $$e\left(\frac{44}{197}\right)$$ $$e\left(\frac{64}{197}\right)$$
$$\chi_{4729}(746,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{78}{197}\right)$$ $$e\left(\frac{64}{197}\right)$$ $$e\left(\frac{156}{197}\right)$$ $$e\left(\frac{195}{197}\right)$$ $$e\left(\frac{142}{197}\right)$$ $$e\left(\frac{165}{197}\right)$$ $$e\left(\frac{37}{197}\right)$$ $$e\left(\frac{128}{197}\right)$$ $$e\left(\frac{76}{197}\right)$$ $$e\left(\frac{21}{197}\right)$$
$$\chi_{4729}(788,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{197}\right)$$ $$e\left(\frac{155}{197}\right)$$ $$e\left(\frac{70}{197}\right)$$ $$e\left(\frac{186}{197}\right)$$ $$e\left(\frac{190}{197}\right)$$ $$e\left(\frac{21}{197}\right)$$ $$e\left(\frac{105}{197}\right)$$ $$e\left(\frac{113}{197}\right)$$ $$e\left(\frac{24}{197}\right)$$ $$e\left(\frac{17}{197}\right)$$
$$\chi_{4729}(821,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{114}{197}\right)$$ $$e\left(\frac{139}{197}\right)$$ $$e\left(\frac{31}{197}\right)$$ $$e\left(\frac{88}{197}\right)$$ $$e\left(\frac{56}{197}\right)$$ $$e\left(\frac{29}{197}\right)$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{81}{197}\right)$$ $$e\left(\frac{5}{197}\right)$$ $$e\left(\frac{61}{197}\right)$$
$$\chi_{4729}(857,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{60}{197}\right)$$ $$e\left(\frac{125}{197}\right)$$ $$e\left(\frac{120}{197}\right)$$ $$e\left(\frac{150}{197}\right)$$ $$e\left(\frac{185}{197}\right)$$ $$e\left(\frac{36}{197}\right)$$ $$e\left(\frac{180}{197}\right)$$ $$e\left(\frac{53}{197}\right)$$ $$e\left(\frac{13}{197}\right)$$ $$e\left(\frac{1}{197}\right)$$
$$\chi_{4729}(864,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{48}{197}\right)$$ $$e\left(\frac{100}{197}\right)$$ $$e\left(\frac{96}{197}\right)$$ $$e\left(\frac{120}{197}\right)$$ $$e\left(\frac{148}{197}\right)$$ $$e\left(\frac{147}{197}\right)$$ $$e\left(\frac{144}{197}\right)$$ $$e\left(\frac{3}{197}\right)$$ $$e\left(\frac{168}{197}\right)$$ $$e\left(\frac{119}{197}\right)$$
$$\chi_{4729}(907,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{138}{197}\right)$$ $$e\left(\frac{189}{197}\right)$$ $$e\left(\frac{79}{197}\right)$$ $$e\left(\frac{148}{197}\right)$$ $$e\left(\frac{130}{197}\right)$$ $$e\left(\frac{4}{197}\right)$$ $$e\left(\frac{20}{197}\right)$$ $$e\left(\frac{181}{197}\right)$$ $$e\left(\frac{89}{197}\right)$$ $$e\left(\frac{22}{197}\right)$$