Basic properties
| Modulus: | \(6036\) | |
| Conductor: | \(6036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | 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 6036.o
\(\chi_{6036}(11,\cdot)\) \(\chi_{6036}(23,\cdot)\) \(\chi_{6036}(47,\cdot)\) \(\chi_{6036}(59,\cdot)\) \(\chi_{6036}(83,\cdot)\) \(\chi_{6036}(95,\cdot)\) \(\chi_{6036}(131,\cdot)\) \(\chi_{6036}(143,\cdot)\) \(\chi_{6036}(155,\cdot)\) \(\chi_{6036}(263,\cdot)\) \(\chi_{6036}(275,\cdot)\) \(\chi_{6036}(299,\cdot)\) \(\chi_{6036}(323,\cdot)\) \(\chi_{6036}(383,\cdot)\) \(\chi_{6036}(443,\cdot)\) \(\chi_{6036}(515,\cdot)\) \(\chi_{6036}(527,\cdot)\) \(\chi_{6036}(539,\cdot)\) \(\chi_{6036}(551,\cdot)\) \(\chi_{6036}(575,\cdot)\) \(\chi_{6036}(587,\cdot)\) \(\chi_{6036}(599,\cdot)\) \(\chi_{6036}(611,\cdot)\) \(\chi_{6036}(635,\cdot)\) \(\chi_{6036}(647,\cdot)\) \(\chi_{6036}(659,\cdot)\) \(\chi_{6036}(671,\cdot)\) \(\chi_{6036}(695,\cdot)\) \(\chi_{6036}(719,\cdot)\) \(\chi_{6036}(755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((3019,4025,2017)\) → \((-1,-1,e\left(\frac{21}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6036 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{293}{502}\right)\) | \(e\left(\frac{349}{502}\right)\) | \(e\left(\frac{129}{251}\right)\) | \(e\left(\frac{94}{251}\right)\) | \(e\left(\frac{331}{502}\right)\) | \(e\left(\frac{165}{502}\right)\) | \(e\left(\frac{160}{251}\right)\) | \(e\left(\frac{42}{251}\right)\) | \(e\left(\frac{163}{502}\right)\) | \(e\left(\frac{47}{502}\right)\) |