Basic properties
| Modulus: | \(6036\) | |
| Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(251\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{503}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6036.i
\(\chi_{6036}(13,\cdot)\) \(\chi_{6036}(25,\cdot)\) \(\chi_{6036}(49,\cdot)\) \(\chi_{6036}(61,\cdot)\) \(\chi_{6036}(73,\cdot)\) \(\chi_{6036}(85,\cdot)\) \(\chi_{6036}(97,\cdot)\) \(\chi_{6036}(121,\cdot)\) \(\chi_{6036}(145,\cdot)\) \(\chi_{6036}(169,\cdot)\) \(\chi_{6036}(205,\cdot)\) \(\chi_{6036}(229,\cdot)\) \(\chi_{6036}(253,\cdot)\) \(\chi_{6036}(265,\cdot)\) \(\chi_{6036}(289,\cdot)\) \(\chi_{6036}(301,\cdot)\) \(\chi_{6036}(325,\cdot)\) \(\chi_{6036}(361,\cdot)\) \(\chi_{6036}(373,\cdot)\) \(\chi_{6036}(397,\cdot)\) \(\chi_{6036}(421,\cdot)\) \(\chi_{6036}(433,\cdot)\) \(\chi_{6036}(445,\cdot)\) \(\chi_{6036}(469,\cdot)\) \(\chi_{6036}(493,\cdot)\) \(\chi_{6036}(505,\cdot)\) \(\chi_{6036}(517,\cdot)\) \(\chi_{6036}(529,\cdot)\) \(\chi_{6036}(553,\cdot)\) \(\chi_{6036}(589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\((3019,4025,2017)\) → \((1,1,e\left(\frac{62}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6036 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{251}\right)\) | \(e\left(\frac{61}{251}\right)\) | \(e\left(\frac{94}{251}\right)\) | \(e\left(\frac{158}{251}\right)\) | \(e\left(\frac{142}{251}\right)\) | \(e\left(\frac{136}{251}\right)\) | \(e\left(\frac{66}{251}\right)\) | \(e\left(\frac{124}{251}\right)\) | \(e\left(\frac{145}{251}\right)\) | \(e\left(\frac{165}{251}\right)\) |