Basic properties
| Modulus: | \(6036\) | |
| Conductor: | \(2012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2012}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6036.p
\(\chi_{6036}(19,\cdot)\) \(\chi_{6036}(31,\cdot)\) \(\chi_{6036}(55,\cdot)\) \(\chi_{6036}(103,\cdot)\) \(\chi_{6036}(115,\cdot)\) \(\chi_{6036}(127,\cdot)\) \(\chi_{6036}(139,\cdot)\) \(\chi_{6036}(151,\cdot)\) \(\chi_{6036}(163,\cdot)\) \(\chi_{6036}(187,\cdot)\) \(\chi_{6036}(211,\cdot)\) \(\chi_{6036}(235,\cdot)\) \(\chi_{6036}(247,\cdot)\) \(\chi_{6036}(259,\cdot)\) \(\chi_{6036}(295,\cdot)\) \(\chi_{6036}(307,\cdot)\) \(\chi_{6036}(319,\cdot)\) \(\chi_{6036}(331,\cdot)\) \(\chi_{6036}(391,\cdot)\) \(\chi_{6036}(403,\cdot)\) \(\chi_{6036}(415,\cdot)\) \(\chi_{6036}(439,\cdot)\) \(\chi_{6036}(451,\cdot)\) \(\chi_{6036}(475,\cdot)\) \(\chi_{6036}(487,\cdot)\) \(\chi_{6036}(499,\cdot)\) \(\chi_{6036}(523,\cdot)\) \(\chi_{6036}(571,\cdot)\) \(\chi_{6036}(583,\cdot)\) \(\chi_{6036}(619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((3019,4025,2017)\) → \((-1,1,e\left(\frac{237}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6036 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{237}{502}\right)\) | \(e\left(\frac{51}{502}\right)\) | \(e\left(\frac{165}{502}\right)\) | \(e\left(\frac{136}{251}\right)\) | \(e\left(\frac{57}{502}\right)\) | \(e\left(\frac{98}{251}\right)\) | \(e\left(\frac{479}{502}\right)\) | \(e\left(\frac{237}{251}\right)\) | \(e\left(\frac{113}{502}\right)\) | \(e\left(\frac{34}{251}\right)\) |