from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, base_ring=CyclotomicField(736))
M = H._module
chi = DirichletCharacter(H, M([368,69,320]))
chi.galois_orbit()
[g,chi] = znchar(Mod(3,6016))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6016\) | |
| Conductor: | \(6016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(736\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{736})$ |
| Fixed field: | Number field defined by a degree 736 polynomial (not computed) |
First 31 of 352 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6016}(3,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{351}{736}\right)\) | \(e\left(\frac{389}{736}\right)\) | \(e\left(\frac{129}{368}\right)\) | \(e\left(\frac{351}{368}\right)\) | \(e\left(\frac{377}{736}\right)\) | \(e\left(\frac{139}{736}\right)\) | \(e\left(\frac{1}{184}\right)\) | \(e\left(\frac{107}{184}\right)\) | \(e\left(\frac{163}{736}\right)\) | \(e\left(\frac{609}{736}\right)\) |
| \(\chi_{6016}(27,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{317}{736}\right)\) | \(e\left(\frac{431}{736}\right)\) | \(e\left(\frac{19}{368}\right)\) | \(e\left(\frac{317}{368}\right)\) | \(e\left(\frac{395}{736}\right)\) | \(e\left(\frac{417}{736}\right)\) | \(e\left(\frac{3}{184}\right)\) | \(e\left(\frac{137}{184}\right)\) | \(e\left(\frac{489}{736}\right)\) | \(e\left(\frac{355}{736}\right)\) |
| \(\chi_{6016}(51,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{736}\right)\) | \(e\left(\frac{553}{736}\right)\) | \(e\left(\frac{85}{368}\right)\) | \(e\left(\frac{43}{368}\right)\) | \(e\left(\frac{237}{736}\right)\) | \(e\left(\frac{103}{736}\right)\) | \(e\left(\frac{149}{184}\right)\) | \(e\left(\frac{119}{184}\right)\) | \(e\left(\frac{735}{736}\right)\) | \(e\left(\frac{213}{736}\right)\) |
| \(\chi_{6016}(59,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{325}{736}\right)\) | \(e\left(\frac{551}{736}\right)\) | \(e\left(\frac{283}{368}\right)\) | \(e\left(\frac{325}{368}\right)\) | \(e\left(\frac{131}{736}\right)\) | \(e\left(\frac{265}{736}\right)\) | \(e\left(\frac{35}{184}\right)\) | \(e\left(\frac{65}{184}\right)\) | \(e\left(\frac{369}{736}\right)\) | \(e\left(\frac{155}{736}\right)\) |
| \(\chi_{6016}(75,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{393}{736}\right)\) | \(e\left(\frac{467}{736}\right)\) | \(e\left(\frac{135}{368}\right)\) | \(e\left(\frac{25}{368}\right)\) | \(e\left(\frac{95}{736}\right)\) | \(e\left(\frac{445}{736}\right)\) | \(e\left(\frac{31}{184}\right)\) | \(e\left(\frac{5}{184}\right)\) | \(e\left(\frac{453}{736}\right)\) | \(e\left(\frac{663}{736}\right)\) |
| \(\chi_{6016}(83,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{147}{736}\right)\) | \(e\left(\frac{641}{736}\right)\) | \(e\left(\frac{205}{368}\right)\) | \(e\left(\frac{147}{368}\right)\) | \(e\left(\frac{485}{736}\right)\) | \(e\left(\frac{335}{736}\right)\) | \(e\left(\frac{13}{184}\right)\) | \(e\left(\frac{103}{184}\right)\) | \(e\left(\frac{647}{736}\right)\) | \(e\left(\frac{557}{736}\right)\) |
| \(\chi_{6016}(115,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{379}{736}\right)\) | \(e\left(\frac{441}{736}\right)\) | \(e\left(\frac{133}{368}\right)\) | \(e\left(\frac{11}{368}\right)\) | \(e\left(\frac{189}{736}\right)\) | \(e\left(\frac{343}{736}\right)\) | \(e\left(\frac{21}{184}\right)\) | \(e\left(\frac{39}{184}\right)\) | \(e\left(\frac{111}{736}\right)\) | \(e\left(\frac{645}{736}\right)\) |
| \(\chi_{6016}(131,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{736}\right)\) | \(e\left(\frac{5}{736}\right)\) | \(e\left(\frac{241}{368}\right)\) | \(e\left(\frac{31}{368}\right)\) | \(e\left(\frac{633}{736}\right)\) | \(e\left(\frac{331}{736}\right)\) | \(e\left(\frac{9}{184}\right)\) | \(e\left(\frac{43}{184}\right)\) | \(e\left(\frac{547}{736}\right)\) | \(e\left(\frac{513}{736}\right)\) |
| \(\chi_{6016}(147,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{736}\right)\) | \(e\left(\frac{401}{736}\right)\) | \(e\left(\frac{45}{368}\right)\) | \(e\left(\frac{131}{368}\right)\) | \(e\left(\frac{277}{736}\right)\) | \(e\left(\frac{639}{736}\right)\) | \(e\left(\frac{133}{184}\right)\) | \(e\left(\frac{63}{184}\right)\) | \(e\left(\frac{151}{736}\right)\) | \(e\left(\frac{221}{736}\right)\) |
| \(\chi_{6016}(155,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{736}\right)\) | \(e\left(\frac{271}{736}\right)\) | \(e\left(\frac{35}{368}\right)\) | \(e\left(\frac{61}{368}\right)\) | \(e\left(\frac{11}{736}\right)\) | \(e\left(\frac{129}{736}\right)\) | \(e\left(\frac{83}{184}\right)\) | \(e\left(\frac{49}{184}\right)\) | \(e\left(\frac{649}{736}\right)\) | \(e\left(\frac{131}{736}\right)\) |
| \(\chi_{6016}(195,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{143}{736}\right)\) | \(e\left(\frac{213}{736}\right)\) | \(e\left(\frac{257}{368}\right)\) | \(e\left(\frac{143}{368}\right)\) | \(e\left(\frac{617}{736}\right)\) | \(e\left(\frac{411}{736}\right)\) | \(e\left(\frac{89}{184}\right)\) | \(e\left(\frac{139}{184}\right)\) | \(e\left(\frac{339}{736}\right)\) | \(e\left(\frac{657}{736}\right)\) |
| \(\chi_{6016}(243,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{736}\right)\) | \(e\left(\frac{473}{736}\right)\) | \(e\left(\frac{277}{368}\right)\) | \(e\left(\frac{283}{368}\right)\) | \(e\left(\frac{413}{736}\right)\) | \(e\left(\frac{695}{736}\right)\) | \(e\left(\frac{5}{184}\right)\) | \(e\left(\frac{167}{184}\right)\) | \(e\left(\frac{79}{736}\right)\) | \(e\left(\frac{101}{736}\right)\) |
| \(\chi_{6016}(251,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{661}{736}\right)\) | \(e\left(\frac{439}{736}\right)\) | \(e\left(\frac{331}{368}\right)\) | \(e\left(\frac{293}{368}\right)\) | \(e\left(\frac{83}{736}\right)\) | \(e\left(\frac{505}{736}\right)\) | \(e\left(\frac{91}{184}\right)\) | \(e\left(\frac{169}{184}\right)\) | \(e\left(\frac{481}{736}\right)\) | \(e\left(\frac{587}{736}\right)\) |
| \(\chi_{6016}(259,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{703}{736}\right)\) | \(e\left(\frac{517}{736}\right)\) | \(e\left(\frac{337}{368}\right)\) | \(e\left(\frac{335}{368}\right)\) | \(e\left(\frac{537}{736}\right)\) | \(e\left(\frac{75}{736}\right)\) | \(e\left(\frac{121}{184}\right)\) | \(e\left(\frac{67}{184}\right)\) | \(e\left(\frac{35}{736}\right)\) | \(e\left(\frac{641}{736}\right)\) |
| \(\chi_{6016}(267,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{441}{736}\right)\) | \(e\left(\frac{451}{736}\right)\) | \(e\left(\frac{247}{368}\right)\) | \(e\left(\frac{73}{368}\right)\) | \(e\left(\frac{719}{736}\right)\) | \(e\left(\frac{269}{736}\right)\) | \(e\left(\frac{39}{184}\right)\) | \(e\left(\frac{125}{184}\right)\) | \(e\left(\frac{469}{736}\right)\) | \(e\left(\frac{199}{736}\right)\) |
| \(\chi_{6016}(291,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{679}{736}\right)\) | \(e\left(\frac{157}{736}\right)\) | \(e\left(\frac{281}{368}\right)\) | \(e\left(\frac{311}{368}\right)\) | \(e\left(\frac{593}{736}\right)\) | \(e\left(\frac{531}{736}\right)\) | \(e\left(\frac{25}{184}\right)\) | \(e\left(\frac{99}{184}\right)\) | \(e\left(\frac{395}{736}\right)\) | \(e\left(\frac{505}{736}\right)\) |
| \(\chi_{6016}(299,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{129}{736}\right)\) | \(e\left(\frac{187}{736}\right)\) | \(e\left(\frac{255}{368}\right)\) | \(e\left(\frac{129}{368}\right)\) | \(e\left(\frac{711}{736}\right)\) | \(e\left(\frac{309}{736}\right)\) | \(e\left(\frac{79}{184}\right)\) | \(e\left(\frac{173}{184}\right)\) | \(e\left(\frac{733}{736}\right)\) | \(e\left(\frac{639}{736}\right)\) |
| \(\chi_{6016}(307,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{203}{736}\right)\) | \(e\left(\frac{9}{736}\right)\) | \(e\left(\frac{213}{368}\right)\) | \(e\left(\frac{203}{368}\right)\) | \(e\left(\frac{109}{736}\right)\) | \(e\left(\frac{7}{736}\right)\) | \(e\left(\frac{53}{184}\right)\) | \(e\left(\frac{151}{184}\right)\) | \(e\left(\frac{543}{736}\right)\) | \(e\left(\frac{629}{736}\right)\) |
| \(\chi_{6016}(331,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{585}{736}\right)\) | \(e\left(\frac{403}{736}\right)\) | \(e\left(\frac{215}{368}\right)\) | \(e\left(\frac{217}{368}\right)\) | \(e\left(\frac{383}{736}\right)\) | \(e\left(\frac{477}{736}\right)\) | \(e\left(\frac{63}{184}\right)\) | \(e\left(\frac{117}{184}\right)\) | \(e\left(\frac{517}{736}\right)\) | \(e\left(\frac{279}{736}\right)\) |
| \(\chi_{6016}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{45}{736}\right)\) | \(e\left(\frac{31}{736}\right)\) | \(e\left(\frac{243}{368}\right)\) | \(e\left(\frac{45}{368}\right)\) | \(e\left(\frac{539}{736}\right)\) | \(e\left(\frac{433}{736}\right)\) | \(e\left(\frac{19}{184}\right)\) | \(e\left(\frac{9}{184}\right)\) | \(e\left(\frac{153}{736}\right)\) | \(e\left(\frac{531}{736}\right)\) |
| \(\chi_{6016}(363,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{369}{736}\right)\) | \(e\left(\frac{107}{736}\right)\) | \(e\left(\frac{79}{368}\right)\) | \(e\left(\frac{1}{368}\right)\) | \(e\left(\frac{151}{736}\right)\) | \(e\left(\frac{165}{736}\right)\) | \(e\left(\frac{119}{184}\right)\) | \(e\left(\frac{37}{184}\right)\) | \(e\left(\frac{77}{736}\right)\) | \(e\left(\frac{527}{736}\right)\) |
| \(\chi_{6016}(371,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{251}{736}\right)\) | \(e\left(\frac{729}{736}\right)\) | \(e\left(\frac{325}{368}\right)\) | \(e\left(\frac{251}{368}\right)\) | \(e\left(\frac{733}{736}\right)\) | \(e\left(\frac{567}{736}\right)\) | \(e\left(\frac{61}{184}\right)\) | \(e\left(\frac{87}{184}\right)\) | \(e\left(\frac{559}{736}\right)\) | \(e\left(\frac{165}{736}\right)\) |
| \(\chi_{6016}(379,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{213}{736}\right)\) | \(e\left(\frac{343}{736}\right)\) | \(e\left(\frac{267}{368}\right)\) | \(e\left(\frac{213}{368}\right)\) | \(e\left(\frac{147}{736}\right)\) | \(e\left(\frac{185}{736}\right)\) | \(e\left(\frac{139}{184}\right)\) | \(e\left(\frac{153}{184}\right)\) | \(e\left(\frac{577}{736}\right)\) | \(e\left(\frac{11}{736}\right)\) |
| \(\chi_{6016}(403,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{547}{736}\right)\) | \(e\left(\frac{17}{736}\right)\) | \(e\left(\frac{157}{368}\right)\) | \(e\left(\frac{179}{368}\right)\) | \(e\left(\frac{533}{736}\right)\) | \(e\left(\frac{95}{736}\right)\) | \(e\left(\frac{141}{184}\right)\) | \(e\left(\frac{183}{184}\right)\) | \(e\left(\frac{535}{736}\right)\) | \(e\left(\frac{125}{736}\right)\) |
| \(\chi_{6016}(427,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{641}{736}\right)\) | \(e\left(\frac{507}{736}\right)\) | \(e\left(\frac{223}{368}\right)\) | \(e\left(\frac{273}{368}\right)\) | \(e\left(\frac{7}{736}\right)\) | \(e\left(\frac{149}{736}\right)\) | \(e\left(\frac{103}{184}\right)\) | \(e\left(\frac{165}{184}\right)\) | \(e\left(\frac{413}{736}\right)\) | \(e\left(\frac{351}{736}\right)\) |
| \(\chi_{6016}(435,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{555}{736}\right)\) | \(e\left(\frac{137}{736}\right)\) | \(e\left(\frac{53}{368}\right)\) | \(e\left(\frac{187}{368}\right)\) | \(e\left(\frac{269}{736}\right)\) | \(e\left(\frac{679}{736}\right)\) | \(e\left(\frac{173}{184}\right)\) | \(e\left(\frac{111}{184}\right)\) | \(e\left(\frac{415}{736}\right)\) | \(e\left(\frac{661}{736}\right)\) |
| \(\chi_{6016}(451,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{623}{736}\right)\) | \(e\left(\frac{53}{736}\right)\) | \(e\left(\frac{273}{368}\right)\) | \(e\left(\frac{255}{368}\right)\) | \(e\left(\frac{233}{736}\right)\) | \(e\left(\frac{123}{736}\right)\) | \(e\left(\frac{169}{184}\right)\) | \(e\left(\frac{51}{184}\right)\) | \(e\left(\frac{499}{736}\right)\) | \(e\left(\frac{433}{736}\right)\) |
| \(\chi_{6016}(459,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{736}\right)\) | \(e\left(\frac{595}{736}\right)\) | \(e\left(\frac{343}{368}\right)\) | \(e\left(\frac{9}{368}\right)\) | \(e\left(\frac{255}{736}\right)\) | \(e\left(\frac{381}{736}\right)\) | \(e\left(\frac{151}{184}\right)\) | \(e\left(\frac{149}{184}\right)\) | \(e\left(\frac{325}{736}\right)\) | \(e\left(\frac{695}{736}\right)\) |
| \(\chi_{6016}(491,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{241}{736}\right)\) | \(e\left(\frac{395}{736}\right)\) | \(e\left(\frac{271}{368}\right)\) | \(e\left(\frac{241}{368}\right)\) | \(e\left(\frac{695}{736}\right)\) | \(e\left(\frac{389}{736}\right)\) | \(e\left(\frac{159}{184}\right)\) | \(e\left(\frac{85}{184}\right)\) | \(e\left(\frac{525}{736}\right)\) | \(e\left(\frac{47}{736}\right)\) |
| \(\chi_{6016}(507,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{629}{736}\right)\) | \(e\left(\frac{695}{736}\right)\) | \(e\left(\frac{11}{368}\right)\) | \(e\left(\frac{261}{368}\right)\) | \(e\left(\frac{403}{736}\right)\) | \(e\left(\frac{377}{736}\right)\) | \(e\left(\frac{147}{184}\right)\) | \(e\left(\frac{89}{184}\right)\) | \(e\left(\frac{225}{736}\right)\) | \(e\left(\frac{651}{736}\right)\) |
| \(\chi_{6016}(523,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{729}{736}\right)\) | \(e\left(\frac{355}{736}\right)\) | \(e\left(\frac{183}{368}\right)\) | \(e\left(\frac{361}{368}\right)\) | \(e\left(\frac{47}{736}\right)\) | \(e\left(\frac{685}{736}\right)\) | \(e\left(\frac{87}{184}\right)\) | \(e\left(\frac{109}{184}\right)\) | \(e\left(\frac{565}{736}\right)\) | \(e\left(\frac{359}{736}\right)\) |