from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4729, base_ring=CyclotomicField(1182))
M = H._module
chi = DirichletCharacter(H, M([994]))
chi.galois_orbit()
[g,chi] = znchar(Mod(14,4729))
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: | \(591\) | 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: | $\Q(\zeta_{591})$ |
| Fixed field: | Number field defined by a degree 591 polynomial (not computed) |
First 31 of 392 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4729}(14,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{197}\right)\) | \(e\left(\frac{58}{197}\right)\) | \(e\left(\frac{166}{197}\right)\) | \(e\left(\frac{524}{591}\right)\) | \(e\left(\frac{141}{197}\right)\) | \(e\left(\frac{110}{591}\right)\) | \(e\left(\frac{52}{197}\right)\) | \(e\left(\frac{116}{197}\right)\) | \(e\left(\frac{182}{591}\right)\) | \(e\left(\frac{136}{197}\right)\) |
| \(\chi_{4729}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{197}\right)\) | \(e\left(\frac{138}{197}\right)\) | \(e\left(\frac{164}{197}\right)\) | \(e\left(\frac{221}{591}\right)\) | \(e\left(\frac{23}{197}\right)\) | \(e\left(\frac{581}{591}\right)\) | \(e\left(\frac{49}{197}\right)\) | \(e\left(\frac{79}{197}\right)\) | \(e\left(\frac{467}{591}\right)\) | \(e\left(\frac{113}{197}\right)\) |
| \(\chi_{4729}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{92}{197}\right)\) | \(e\left(\frac{126}{197}\right)\) | \(e\left(\frac{184}{197}\right)\) | \(e\left(\frac{296}{591}\right)\) | \(e\left(\frac{21}{197}\right)\) | \(e\left(\frac{8}{591}\right)\) | \(e\left(\frac{79}{197}\right)\) | \(e\left(\frac{55}{197}\right)\) | \(e\left(\frac{572}{591}\right)\) | \(e\left(\frac{146}{197}\right)\) |
| \(\chi_{4729}(35,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{197}\right)\) | \(e\left(\frac{137}{197}\right)\) | \(e\left(\frac{100}{197}\right)\) | \(e\left(\frac{178}{591}\right)\) | \(e\left(\frac{187}{197}\right)\) | \(e\left(\frac{484}{591}\right)\) | \(e\left(\frac{150}{197}\right)\) | \(e\left(\frac{77}{197}\right)\) | \(e\left(\frac{328}{591}\right)\) | \(e\left(\frac{165}{197}\right)\) |
| \(\chi_{4729}(37,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{197}\right)\) | \(e\left(\frac{162}{197}\right)\) | \(e\left(\frac{124}{197}\right)\) | \(e\left(\frac{71}{591}\right)\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{545}{591}\right)\) | \(e\left(\frac{186}{197}\right)\) | \(e\left(\frac{127}{197}\right)\) | \(e\left(\frac{257}{591}\right)\) | \(e\left(\frac{47}{197}\right)\) |
| \(\chi_{4729}(40,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{197}\right)\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{152}{197}\right)\) | \(e\left(\frac{176}{591}\right)\) | \(e\left(\frac{103}{197}\right)\) | \(e\left(\frac{452}{591}\right)\) | \(e\left(\frac{31}{197}\right)\) | \(e\left(\frac{54}{197}\right)\) | \(e\left(\frac{404}{591}\right)\) | \(e\left(\frac{172}{197}\right)\) |
| \(\chi_{4729}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{116}{197}\right)\) | \(e\left(\frac{176}{197}\right)\) | \(e\left(\frac{35}{197}\right)\) | \(e\left(\frac{476}{591}\right)\) | \(e\left(\frac{95}{197}\right)\) | \(e\left(\frac{524}{591}\right)\) | \(e\left(\frac{151}{197}\right)\) | \(e\left(\frac{155}{197}\right)\) | \(e\left(\frac{233}{591}\right)\) | \(e\left(\frac{107}{197}\right)\) |
| \(\chi_{4729}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{197}\right)\) | \(e\left(\frac{95}{197}\right)\) | \(e\left(\frac{170}{197}\right)\) | \(e\left(\frac{539}{591}\right)\) | \(e\left(\frac{180}{197}\right)\) | \(e\left(\frac{350}{591}\right)\) | \(e\left(\frac{58}{197}\right)\) | \(e\left(\frac{190}{197}\right)\) | \(e\left(\frac{203}{591}\right)\) | \(e\left(\frac{182}{197}\right)\) |
| \(\chi_{4729}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{197}\right)\) | \(e\left(\frac{133}{197}\right)\) | \(e\left(\frac{41}{197}\right)\) | \(e\left(\frac{400}{591}\right)\) | \(e\left(\frac{55}{197}\right)\) | \(e\left(\frac{490}{591}\right)\) | \(e\left(\frac{160}{197}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{166}{591}\right)\) | \(e\left(\frac{176}{197}\right)\) |
| \(\chi_{4729}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{197}\right)\) | \(e\left(\frac{47}{197}\right)\) | \(e\left(\frac{53}{197}\right)\) | \(e\left(\frac{248}{591}\right)\) | \(e\left(\frac{172}{197}\right)\) | \(e\left(\frac{422}{591}\right)\) | \(e\left(\frac{178}{197}\right)\) | \(e\left(\frac{94}{197}\right)\) | \(e\left(\frac{32}{591}\right)\) | \(e\left(\frac{117}{197}\right)\) |
| \(\chi_{4729}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{106}{197}\right)\) | \(e\left(\frac{188}{197}\right)\) | \(e\left(\frac{15}{197}\right)\) | \(e\left(\frac{7}{591}\right)\) | \(e\left(\frac{97}{197}\right)\) | \(e\left(\frac{112}{591}\right)\) | \(e\left(\frac{121}{197}\right)\) | \(e\left(\frac{179}{197}\right)\) | \(e\left(\frac{325}{591}\right)\) | \(e\left(\frac{74}{197}\right)\) |
| \(\chi_{4729}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{197}\right)\) | \(e\left(\frac{163}{197}\right)\) | \(e\left(\frac{188}{197}\right)\) | \(e\left(\frac{311}{591}\right)\) | \(e\left(\frac{60}{197}\right)\) | \(e\left(\frac{248}{591}\right)\) | \(e\left(\frac{85}{197}\right)\) | \(e\left(\frac{129}{197}\right)\) | \(e\left(\frac{2}{591}\right)\) | \(e\left(\frac{192}{197}\right)\) |
| \(\chi_{4729}(100,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{197}\right)\) | \(e\left(\frac{106}{197}\right)\) | \(e\left(\frac{86}{197}\right)\) | \(e\left(\frac{421}{591}\right)\) | \(e\left(\frac{149}{197}\right)\) | \(e\left(\frac{235}{591}\right)\) | \(e\left(\frac{129}{197}\right)\) | \(e\left(\frac{15}{197}\right)\) | \(e\left(\frac{550}{591}\right)\) | \(e\left(\frac{4}{197}\right)\) |
| \(\chi_{4729}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{197}\right)\) | \(e\left(\frac{115}{197}\right)\) | \(e\left(\frac{71}{197}\right)\) | \(e\left(\frac{20}{591}\right)\) | \(e\left(\frac{52}{197}\right)\) | \(e\left(\frac{320}{591}\right)\) | \(e\left(\frac{8}{197}\right)\) | \(e\left(\frac{33}{197}\right)\) | \(e\left(\frac{422}{591}\right)\) | \(e\left(\frac{127}{197}\right)\) |
| \(\chi_{4729}(118,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{197}\right)\) | \(e\left(\frac{83}{197}\right)\) | \(e\left(\frac{190}{197}\right)\) | \(e\left(\frac{220}{591}\right)\) | \(e\left(\frac{178}{197}\right)\) | \(e\left(\frac{565}{591}\right)\) | \(e\left(\frac{88}{197}\right)\) | \(e\left(\frac{166}{197}\right)\) | \(e\left(\frac{505}{591}\right)\) | \(e\left(\frac{18}{197}\right)\) |
| \(\chi_{4729}(130,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{197}\right)\) | \(e\left(\frac{58}{197}\right)\) | \(e\left(\frac{166}{197}\right)\) | \(e\left(\frac{130}{591}\right)\) | \(e\left(\frac{141}{197}\right)\) | \(e\left(\frac{307}{591}\right)\) | \(e\left(\frac{52}{197}\right)\) | \(e\left(\frac{116}{197}\right)\) | \(e\left(\frac{379}{591}\right)\) | \(e\left(\frac{136}{197}\right)\) |
| \(\chi_{4729}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{197}\right)\) | \(e\left(\frac{118}{197}\right)\) | \(e\left(\frac{66}{197}\right)\) | \(e\left(\frac{149}{591}\right)\) | \(e\left(\frac{151}{197}\right)\) | \(e\left(\frac{20}{591}\right)\) | \(e\left(\frac{99}{197}\right)\) | \(e\left(\frac{39}{197}\right)\) | \(e\left(\frac{248}{591}\right)\) | \(e\left(\frac{168}{197}\right)\) |
| \(\chi_{4729}(135,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{197}\right)\) | \(e\left(\frac{34}{197}\right)\) | \(e\left(\frac{9}{197}\right)\) | \(e\left(\frac{83}{591}\right)\) | \(e\left(\frac{137}{197}\right)\) | \(e\left(\frac{146}{591}\right)\) | \(e\left(\frac{112}{197}\right)\) | \(e\left(\frac{68}{197}\right)\) | \(e\left(\frac{392}{591}\right)\) | \(e\left(\frac{5}{197}\right)\) |
| \(\chi_{4729}(150,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{52}{197}\right)\) | \(e\left(\frac{174}{197}\right)\) | \(e\left(\frac{104}{197}\right)\) | \(e\left(\frac{193}{591}\right)\) | \(e\left(\frac{29}{197}\right)\) | \(e\left(\frac{133}{591}\right)\) | \(e\left(\frac{156}{197}\right)\) | \(e\left(\frac{151}{197}\right)\) | \(e\left(\frac{349}{591}\right)\) | \(e\left(\frac{14}{197}\right)\) |
| \(\chi_{4729}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{197}\right)\) | \(e\left(\frac{10}{197}\right)\) | \(e\left(\frac{49}{197}\right)\) | \(e\left(\frac{430}{591}\right)\) | \(e\left(\frac{133}{197}\right)\) | \(e\left(\frac{379}{591}\right)\) | \(e\left(\frac{172}{197}\right)\) | \(e\left(\frac{20}{197}\right)\) | \(e\left(\frac{208}{591}\right)\) | \(e\left(\frac{71}{197}\right)\) |
| \(\chi_{4729}(177,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{104}{197}\right)\) | \(e\left(\frac{151}{197}\right)\) | \(e\left(\frac{11}{197}\right)\) | \(e\left(\frac{583}{591}\right)\) | \(e\left(\frac{58}{197}\right)\) | \(e\left(\frac{463}{591}\right)\) | \(e\left(\frac{115}{197}\right)\) | \(e\left(\frac{105}{197}\right)\) | \(e\left(\frac{304}{591}\right)\) | \(e\left(\frac{28}{197}\right)\) |
| \(\chi_{4729}(187,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{197}\right)\) | \(e\left(\frac{20}{197}\right)\) | \(e\left(\frac{98}{197}\right)\) | \(e\left(\frac{269}{591}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{167}{591}\right)\) | \(e\left(\frac{147}{197}\right)\) | \(e\left(\frac{40}{197}\right)\) | \(e\left(\frac{416}{591}\right)\) | \(e\left(\frac{142}{197}\right)\) |
| \(\chi_{4729}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{184}{197}\right)\) | \(e\left(\frac{55}{197}\right)\) | \(e\left(\frac{171}{197}\right)\) | \(e\left(\frac{395}{591}\right)\) | \(e\left(\frac{42}{197}\right)\) | \(e\left(\frac{410}{591}\right)\) | \(e\left(\frac{158}{197}\right)\) | \(e\left(\frac{110}{197}\right)\) | \(e\left(\frac{356}{591}\right)\) | \(e\left(\frac{95}{197}\right)\) |
| \(\chi_{4729}(195,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{92}{197}\right)\) | \(e\left(\frac{126}{197}\right)\) | \(e\left(\frac{184}{197}\right)\) | \(e\left(\frac{493}{591}\right)\) | \(e\left(\frac{21}{197}\right)\) | \(e\left(\frac{205}{591}\right)\) | \(e\left(\frac{79}{197}\right)\) | \(e\left(\frac{55}{197}\right)\) | \(e\left(\frac{178}{591}\right)\) | \(e\left(\frac{146}{197}\right)\) |
| \(\chi_{4729}(196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{166}{197}\right)\) | \(e\left(\frac{116}{197}\right)\) | \(e\left(\frac{135}{197}\right)\) | \(e\left(\frac{457}{591}\right)\) | \(e\left(\frac{85}{197}\right)\) | \(e\left(\frac{220}{591}\right)\) | \(e\left(\frac{104}{197}\right)\) | \(e\left(\frac{35}{197}\right)\) | \(e\left(\frac{364}{591}\right)\) | \(e\left(\frac{75}{197}\right)\) |
| \(\chi_{4729}(224,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{192}{197}\right)\) | \(e\left(\frac{6}{197}\right)\) | \(e\left(\frac{187}{197}\right)\) | \(e\left(\frac{455}{591}\right)\) | \(e\left(\frac{1}{197}\right)\) | \(e\left(\frac{188}{591}\right)\) | \(e\left(\frac{182}{197}\right)\) | \(e\left(\frac{12}{197}\right)\) | \(e\left(\frac{440}{591}\right)\) | \(e\left(\frac{82}{197}\right)\) |
| \(\chi_{4729}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{197}\right)\) | \(e\left(\frac{45}{197}\right)\) | \(e\left(\frac{122}{197}\right)\) | \(e\left(\frac{556}{591}\right)\) | \(e\left(\frac{106}{197}\right)\) | \(e\left(\frac{31}{591}\right)\) | \(e\left(\frac{183}{197}\right)\) | \(e\left(\frac{90}{197}\right)\) | \(e\left(\frac{148}{591}\right)\) | \(e\left(\frac{24}{197}\right)\) |
| \(\chi_{4729}(266,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{165}{197}\right)\) | \(e\left(\frac{196}{197}\right)\) | \(e\left(\frac{133}{197}\right)\) | \(e\left(\frac{154}{591}\right)\) | \(e\left(\frac{164}{197}\right)\) | \(e\left(\frac{100}{591}\right)\) | \(e\left(\frac{101}{197}\right)\) | \(e\left(\frac{195}{197}\right)\) | \(e\left(\frac{58}{591}\right)\) | \(e\left(\frac{52}{197}\right)\) |
| \(\chi_{4729}(294,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{197}\right)\) | \(e\left(\frac{184}{197}\right)\) | \(e\left(\frac{153}{197}\right)\) | \(e\left(\frac{229}{591}\right)\) | \(e\left(\frac{162}{197}\right)\) | \(e\left(\frac{118}{591}\right)\) | \(e\left(\frac{131}{197}\right)\) | \(e\left(\frac{171}{197}\right)\) | \(e\left(\frac{163}{591}\right)\) | \(e\left(\frac{85}{197}\right)\) |
| \(\chi_{4729}(304,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{197}\right)\) | \(e\left(\frac{86}{197}\right)\) | \(e\left(\frac{185}{197}\right)\) | \(e\left(\frac{152}{591}\right)\) | \(e\left(\frac{80}{197}\right)\) | \(e\left(\frac{68}{591}\right)\) | \(e\left(\frac{179}{197}\right)\) | \(e\left(\frac{172}{197}\right)\) | \(e\left(\frac{134}{591}\right)\) | \(e\left(\frac{59}{197}\right)\) |
| \(\chi_{4729}(336,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{197}\right)\) | \(e\left(\frac{74}{197}\right)\) | \(e\left(\frac{8}{197}\right)\) | \(e\left(\frac{227}{591}\right)\) | \(e\left(\frac{78}{197}\right)\) | \(e\left(\frac{86}{591}\right)\) | \(e\left(\frac{12}{197}\right)\) | \(e\left(\frac{148}{197}\right)\) | \(e\left(\frac{239}{591}\right)\) | \(e\left(\frac{92}{197}\right)\) |