Basic properties
| Modulus: | \(283920\) | |
| Conductor: | \(47320\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{47320}(29587,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 283920.dcy
\(\chi_{283920}(103,\cdot)\) \(\chi_{283920}(3223,\cdot)\) \(\chi_{283920}(13207,\cdot)\) \(\chi_{283920}(16327,\cdot)\) \(\chi_{283920}(21943,\cdot)\) \(\chi_{283920}(25063,\cdot)\) \(\chi_{283920}(35047,\cdot)\) \(\chi_{283920}(38167,\cdot)\) \(\chi_{283920}(43783,\cdot)\) \(\chi_{283920}(46903,\cdot)\) \(\chi_{283920}(56887,\cdot)\) \(\chi_{283920}(60007,\cdot)\) \(\chi_{283920}(65623,\cdot)\) \(\chi_{283920}(68743,\cdot)\) \(\chi_{283920}(78727,\cdot)\) \(\chi_{283920}(81847,\cdot)\) \(\chi_{283920}(87463,\cdot)\) \(\chi_{283920}(100567,\cdot)\) \(\chi_{283920}(103687,\cdot)\) \(\chi_{283920}(109303,\cdot)\) \(\chi_{283920}(112423,\cdot)\) \(\chi_{283920}(122407,\cdot)\) \(\chi_{283920}(125527,\cdot)\) \(\chi_{283920}(134263,\cdot)\) \(\chi_{283920}(144247,\cdot)\) \(\chi_{283920}(152983,\cdot)\) \(\chi_{283920}(156103,\cdot)\) \(\chi_{283920}(166087,\cdot)\) \(\chi_{283920}(169207,\cdot)\) \(\chi_{283920}(174823,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((248431,70981,189281,227137,40561,255361)\) → \((-1,-1,1,i,e\left(\frac{5}{6}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 283920 }(100567, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{125}{156}\right)\) |