from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4729, base_ring=CyclotomicField(1182))
M = H._module
chi = DirichletCharacter(H, M([229]))
chi.galois_orbit()
[g,chi] = znchar(Mod(10,4729))
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: | \(1182\) | 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 1182 polynomial (not computed) |
First 31 of 392 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4729}(10,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{120}{197}\right)\) | \(e\left(\frac{53}{197}\right)\) | \(e\left(\frac{43}{197}\right)\) | \(e\left(\frac{506}{591}\right)\) | \(e\left(\frac{173}{197}\right)\) | \(e\left(\frac{413}{591}\right)\) | \(e\left(\frac{163}{197}\right)\) | \(e\left(\frac{106}{197}\right)\) | \(e\left(\frac{275}{591}\right)\) | \(e\left(\frac{201}{394}\right)\) |
| \(\chi_{4729}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{160}{197}\right)\) | \(e\left(\frac{5}{197}\right)\) | \(e\left(\frac{123}{197}\right)\) | \(e\left(\frac{215}{591}\right)\) | \(e\left(\frac{165}{197}\right)\) | \(e\left(\frac{485}{591}\right)\) | \(e\left(\frac{86}{197}\right)\) | \(e\left(\frac{10}{197}\right)\) | \(e\left(\frac{104}{591}\right)\) | \(e\left(\frac{71}{394}\right)\) |
| \(\chi_{4729}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{197}\right)\) | \(e\left(\frac{121}{197}\right)\) | \(e\left(\frac{61}{197}\right)\) | \(e\left(\frac{278}{591}\right)\) | \(e\left(\frac{53}{197}\right)\) | \(e\left(\frac{311}{591}\right)\) | \(e\left(\frac{190}{197}\right)\) | \(e\left(\frac{45}{197}\right)\) | \(e\left(\frac{74}{591}\right)\) | \(e\left(\frac{221}{394}\right)\) |
| \(\chi_{4729}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{87}{197}\right)\) | \(e\left(\frac{132}{197}\right)\) | \(e\left(\frac{174}{197}\right)\) | \(e\left(\frac{160}{591}\right)\) | \(e\left(\frac{22}{197}\right)\) | \(e\left(\frac{196}{591}\right)\) | \(e\left(\frac{64}{197}\right)\) | \(e\left(\frac{67}{197}\right)\) | \(e\left(\frac{421}{591}\right)\) | \(e\left(\frac{259}{394}\right)\) |
| \(\chi_{4729}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{197}\right)\) | \(e\left(\frac{142}{197}\right)\) | \(e\left(\frac{26}{197}\right)\) | \(e\left(\frac{196}{591}\right)\) | \(e\left(\frac{155}{197}\right)\) | \(e\left(\frac{181}{591}\right)\) | \(e\left(\frac{39}{197}\right)\) | \(e\left(\frac{87}{197}\right)\) | \(e\left(\frac{235}{591}\right)\) | \(e\left(\frac{7}{394}\right)\) |
| \(\chi_{4729}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{197}\right)\) | \(e\left(\frac{32}{197}\right)\) | \(e\left(\frac{78}{197}\right)\) | \(e\left(\frac{194}{591}\right)\) | \(e\left(\frac{71}{197}\right)\) | \(e\left(\frac{149}{591}\right)\) | \(e\left(\frac{117}{197}\right)\) | \(e\left(\frac{64}{197}\right)\) | \(e\left(\frac{311}{591}\right)\) | \(e\left(\frac{21}{394}\right)\) |
| \(\chi_{4729}(76,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{197}\right)\) | \(e\left(\frac{112}{197}\right)\) | \(e\left(\frac{76}{197}\right)\) | \(e\left(\frac{482}{591}\right)\) | \(e\left(\frac{150}{197}\right)\) | \(e\left(\frac{29}{591}\right)\) | \(e\left(\frac{114}{197}\right)\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{5}{591}\right)\) | \(e\left(\frac{369}{394}\right)\) |
| \(\chi_{4729}(84,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{197}\right)\) | \(e\left(\frac{100}{197}\right)\) | \(e\left(\frac{96}{197}\right)\) | \(e\left(\frac{557}{591}\right)\) | \(e\left(\frac{148}{197}\right)\) | \(e\left(\frac{47}{591}\right)\) | \(e\left(\frac{144}{197}\right)\) | \(e\left(\frac{3}{197}\right)\) | \(e\left(\frac{110}{591}\right)\) | \(e\left(\frac{41}{394}\right)\) |
| \(\chi_{4729}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{105}{197}\right)\) | \(e\left(\frac{71}{197}\right)\) | \(e\left(\frac{13}{197}\right)\) | \(e\left(\frac{98}{591}\right)\) | \(e\left(\frac{176}{197}\right)\) | \(e\left(\frac{386}{591}\right)\) | \(e\left(\frac{118}{197}\right)\) | \(e\left(\frac{142}{197}\right)\) | \(e\left(\frac{413}{591}\right)\) | \(e\left(\frac{299}{394}\right)\) |
| \(\chi_{4729}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{197}\right)\) | \(e\left(\frac{180}{197}\right)\) | \(e\left(\frac{94}{197}\right)\) | \(e\left(\frac{254}{591}\right)\) | \(e\left(\frac{30}{197}\right)\) | \(e\left(\frac{518}{591}\right)\) | \(e\left(\frac{141}{197}\right)\) | \(e\left(\frac{163}{197}\right)\) | \(e\left(\frac{395}{591}\right)\) | \(e\left(\frac{389}{394}\right)\) |
| \(\chi_{4729}(126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{197}\right)\) | \(e\left(\frac{168}{197}\right)\) | \(e\left(\frac{114}{197}\right)\) | \(e\left(\frac{329}{591}\right)\) | \(e\left(\frac{28}{197}\right)\) | \(e\left(\frac{536}{591}\right)\) | \(e\left(\frac{171}{197}\right)\) | \(e\left(\frac{139}{197}\right)\) | \(e\left(\frac{500}{591}\right)\) | \(e\left(\frac{61}{394}\right)\) |
| \(\chi_{4729}(140,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{197}\right)\) | \(e\left(\frac{111}{197}\right)\) | \(e\left(\frac{12}{197}\right)\) | \(e\left(\frac{439}{591}\right)\) | \(e\left(\frac{117}{197}\right)\) | \(e\left(\frac{523}{591}\right)\) | \(e\left(\frac{18}{197}\right)\) | \(e\left(\frac{25}{197}\right)\) | \(e\left(\frac{457}{591}\right)\) | \(e\left(\frac{79}{394}\right)\) |
| \(\chi_{4729}(142,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{117}{197}\right)\) | \(e\left(\frac{96}{197}\right)\) | \(e\left(\frac{37}{197}\right)\) | \(e\left(\frac{385}{591}\right)\) | \(e\left(\frac{16}{197}\right)\) | \(e\left(\frac{250}{591}\right)\) | \(e\left(\frac{154}{197}\right)\) | \(e\left(\frac{192}{197}\right)\) | \(e\left(\frac{145}{591}\right)\) | \(e\left(\frac{63}{394}\right)\) |
| \(\chi_{4729}(146,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{197}\right)\) | \(e\left(\frac{61}{197}\right)\) | \(e\left(\frac{161}{197}\right)\) | \(e\left(\frac{62}{591}\right)\) | \(e\left(\frac{43}{197}\right)\) | \(e\left(\frac{401}{591}\right)\) | \(e\left(\frac{143}{197}\right)\) | \(e\left(\frac{122}{197}\right)\) | \(e\left(\frac{8}{591}\right)\) | \(e\left(\frac{157}{394}\right)\) |
| \(\chi_{4729}(148,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{197}\right)\) | \(e\left(\frac{136}{197}\right)\) | \(e\left(\frac{36}{197}\right)\) | \(e\left(\frac{332}{591}\right)\) | \(e\left(\frac{154}{197}\right)\) | \(e\left(\frac{584}{591}\right)\) | \(e\left(\frac{54}{197}\right)\) | \(e\left(\frac{75}{197}\right)\) | \(e\left(\frac{386}{591}\right)\) | \(e\left(\frac{237}{394}\right)\) |
| \(\chi_{4729}(149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{60}{197}\right)\) | \(e\left(\frac{125}{197}\right)\) | \(e\left(\frac{120}{197}\right)\) | \(e\left(\frac{56}{591}\right)\) | \(e\left(\frac{185}{197}\right)\) | \(e\left(\frac{305}{591}\right)\) | \(e\left(\frac{180}{197}\right)\) | \(e\left(\frac{53}{197}\right)\) | \(e\left(\frac{236}{591}\right)\) | \(e\left(\frac{199}{394}\right)\) |
| \(\chi_{4729}(160,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{197}\right)\) | \(e\left(\frac{1}{197}\right)\) | \(e\left(\frac{64}{197}\right)\) | \(e\left(\frac{437}{591}\right)\) | \(e\left(\frac{33}{197}\right)\) | \(e\left(\frac{491}{591}\right)\) | \(e\left(\frac{96}{197}\right)\) | \(e\left(\frac{2}{197}\right)\) | \(e\left(\frac{533}{591}\right)\) | \(e\left(\frac{93}{394}\right)\) |
| \(\chi_{4729}(171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{197}\right)\) | \(e\left(\frac{51}{197}\right)\) | \(e\left(\frac{112}{197}\right)\) | \(e\left(\frac{26}{591}\right)\) | \(e\left(\frac{107}{197}\right)\) | \(e\left(\frac{416}{591}\right)\) | \(e\left(\frac{168}{197}\right)\) | \(e\left(\frac{102}{197}\right)\) | \(e\left(\frac{194}{591}\right)\) | \(e\left(\frac{15}{394}\right)\) |
| \(\chi_{4729}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{197}\right)\) | \(e\left(\frac{195}{197}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{308}{591}\right)\) | \(e\left(\frac{131}{197}\right)\) | \(e\left(\frac{200}{591}\right)\) | \(e\left(\frac{5}{197}\right)\) | \(e\left(\frac{193}{197}\right)\) | \(e\left(\frac{116}{591}\right)\) | \(e\left(\frac{11}{394}\right)\) |
| \(\chi_{4729}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{197}\right)\) | \(e\left(\frac{63}{197}\right)\) | \(e\left(\frac{92}{197}\right)\) | \(e\left(\frac{148}{591}\right)\) | \(e\left(\frac{109}{197}\right)\) | \(e\left(\frac{4}{591}\right)\) | \(e\left(\frac{138}{197}\right)\) | \(e\left(\frac{126}{197}\right)\) | \(e\left(\frac{286}{591}\right)\) | \(e\left(\frac{343}{394}\right)\) |
| \(\chi_{4729}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{66}{197}\right)\) | \(e\left(\frac{39}{197}\right)\) | \(e\left(\frac{132}{197}\right)\) | \(e\left(\frac{101}{591}\right)\) | \(e\left(\frac{105}{197}\right)\) | \(e\left(\frac{434}{591}\right)\) | \(e\left(\frac{1}{197}\right)\) | \(e\left(\frac{78}{197}\right)\) | \(e\left(\frac{299}{591}\right)\) | \(e\left(\frac{81}{394}\right)\) |
| \(\chi_{4729}(190,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{197}\right)\) | \(e\left(\frac{191}{197}\right)\) | \(e\left(\frac{10}{197}\right)\) | \(e\left(\frac{136}{591}\right)\) | \(e\left(\frac{196}{197}\right)\) | \(e\left(\frac{403}{591}\right)\) | \(e\left(\frac{15}{197}\right)\) | \(e\left(\frac{185}{197}\right)\) | \(e\left(\frac{151}{591}\right)\) | \(e\left(\frac{33}{394}\right)\) |
| \(\chi_{4729}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{72}{197}\right)\) | \(e\left(\frac{150}{197}\right)\) | \(e\left(\frac{144}{197}\right)\) | \(e\left(\frac{146}{591}\right)\) | \(e\left(\frac{25}{197}\right)\) | \(e\left(\frac{563}{591}\right)\) | \(e\left(\frac{19}{197}\right)\) | \(e\left(\frac{103}{197}\right)\) | \(e\left(\frac{362}{591}\right)\) | \(e\left(\frac{357}{394}\right)\) |
| \(\chi_{4729}(210,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{197}\right)\) | \(e\left(\frac{179}{197}\right)\) | \(e\left(\frac{30}{197}\right)\) | \(e\left(\frac{211}{591}\right)\) | \(e\left(\frac{194}{197}\right)\) | \(e\left(\frac{421}{591}\right)\) | \(e\left(\frac{45}{197}\right)\) | \(e\left(\frac{161}{197}\right)\) | \(e\left(\frac{256}{591}\right)\) | \(e\left(\frac{99}{394}\right)\) |
| \(\chi_{4729}(213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{126}{197}\right)\) | \(e\left(\frac{164}{197}\right)\) | \(e\left(\frac{55}{197}\right)\) | \(e\left(\frac{157}{591}\right)\) | \(e\left(\frac{93}{197}\right)\) | \(e\left(\frac{148}{591}\right)\) | \(e\left(\frac{181}{197}\right)\) | \(e\left(\frac{131}{197}\right)\) | \(e\left(\frac{535}{591}\right)\) | \(e\left(\frac{83}{394}\right)\) |
| \(\chi_{4729}(219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{188}{197}\right)\) | \(e\left(\frac{129}{197}\right)\) | \(e\left(\frac{179}{197}\right)\) | \(e\left(\frac{425}{591}\right)\) | \(e\left(\frac{120}{197}\right)\) | \(e\left(\frac{299}{591}\right)\) | \(e\left(\frac{170}{197}\right)\) | \(e\left(\frac{61}{197}\right)\) | \(e\left(\frac{398}{591}\right)\) | \(e\left(\frac{177}{394}\right)\) |
| \(\chi_{4729}(222,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{7}{197}\right)\) | \(e\left(\frac{54}{197}\right)\) | \(e\left(\frac{104}{591}\right)\) | \(e\left(\frac{34}{197}\right)\) | \(e\left(\frac{482}{591}\right)\) | \(e\left(\frac{81}{197}\right)\) | \(e\left(\frac{14}{197}\right)\) | \(e\left(\frac{185}{591}\right)\) | \(e\left(\frac{257}{394}\right)\) |
| \(\chi_{4729}(240,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{197}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{82}{197}\right)\) | \(e\left(\frac{209}{591}\right)\) | \(e\left(\frac{110}{197}\right)\) | \(e\left(\frac{389}{591}\right)\) | \(e\left(\frac{123}{197}\right)\) | \(e\left(\frac{138}{197}\right)\) | \(e\left(\frac{332}{591}\right)\) | \(e\left(\frac{113}{394}\right)\) |
| \(\chi_{4729}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{197}\right)\) | \(e\left(\frac{36}{197}\right)\) | \(e\left(\frac{137}{197}\right)\) | \(e\left(\frac{563}{591}\right)\) | \(e\left(\frac{6}{197}\right)\) | \(e\left(\frac{143}{591}\right)\) | \(e\left(\frac{107}{197}\right)\) | \(e\left(\frac{72}{197}\right)\) | \(e\left(\frac{473}{591}\right)\) | \(e\left(\frac{393}{394}\right)\) |
| \(\chi_{4729}(247,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{197}\right)\) | \(e\left(\frac{143}{197}\right)\) | \(e\left(\frac{90}{197}\right)\) | \(e\left(\frac{436}{591}\right)\) | \(e\left(\frac{188}{197}\right)\) | \(e\left(\frac{475}{591}\right)\) | \(e\left(\frac{135}{197}\right)\) | \(e\left(\frac{89}{197}\right)\) | \(e\left(\frac{571}{591}\right)\) | \(e\left(\frac{297}{394}\right)\) |
| \(\chi_{4729}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{190}{197}\right)\) | \(e\left(\frac{166}{197}\right)\) | \(e\left(\frac{183}{197}\right)\) | \(e\left(\frac{440}{591}\right)\) | \(e\left(\frac{159}{197}\right)\) | \(e\left(\frac{539}{591}\right)\) | \(e\left(\frac{176}{197}\right)\) | \(e\left(\frac{135}{197}\right)\) | \(e\left(\frac{419}{591}\right)\) | \(e\left(\frac{269}{394}\right)\) |