Basic properties
| Modulus: | \(283920\) | |
| Conductor: | \(283920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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)
|
Galois orbit 283920.dzl
\(\chi_{283920}(59,\cdot)\) \(\chi_{283920}(13739,\cdot)\) \(\chi_{283920}(17699,\cdot)\) \(\chi_{283920}(19619,\cdot)\) \(\chi_{283920}(21899,\cdot)\) \(\chi_{283920}(39539,\cdot)\) \(\chi_{283920}(41459,\cdot)\) \(\chi_{283920}(43739,\cdot)\) \(\chi_{283920}(57419,\cdot)\) \(\chi_{283920}(61379,\cdot)\) \(\chi_{283920}(63299,\cdot)\) \(\chi_{283920}(65579,\cdot)\) \(\chi_{283920}(79259,\cdot)\) \(\chi_{283920}(83219,\cdot)\) \(\chi_{283920}(85139,\cdot)\) \(\chi_{283920}(87419,\cdot)\) \(\chi_{283920}(101099,\cdot)\) \(\chi_{283920}(105059,\cdot)\) \(\chi_{283920}(106979,\cdot)\) \(\chi_{283920}(109259,\cdot)\) \(\chi_{283920}(122939,\cdot)\) \(\chi_{283920}(126899,\cdot)\) \(\chi_{283920}(128819,\cdot)\) \(\chi_{283920}(131099,\cdot)\) \(\chi_{283920}(144779,\cdot)\) \(\chi_{283920}(152939,\cdot)\) \(\chi_{283920}(166619,\cdot)\) \(\chi_{283920}(170579,\cdot)\) \(\chi_{283920}(172499,\cdot)\) \(\chi_{283920}(174779,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((248431,70981,189281,227137,40561,255361)\) → \((-1,i,-1,-1,e\left(\frac{5}{6}\right),e\left(\frac{79}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 283920 }(79259, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{89}{156}\right)\) |