Basic properties
| Modulus: | \(3004\) | |
| Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.bb
\(\chi_{3004}(43,\cdot)\) \(\chi_{3004}(71,\cdot)\) \(\chi_{3004}(151,\cdot)\) \(\chi_{3004}(187,\cdot)\) \(\chi_{3004}(191,\cdot)\) \(\chi_{3004}(207,\cdot)\) \(\chi_{3004}(271,\cdot)\) \(\chi_{3004}(287,\cdot)\) \(\chi_{3004}(303,\cdot)\) \(\chi_{3004}(347,\cdot)\) \(\chi_{3004}(367,\cdot)\) \(\chi_{3004}(419,\cdot)\) \(\chi_{3004}(423,\cdot)\) \(\chi_{3004}(435,\cdot)\) \(\chi_{3004}(523,\cdot)\) \(\chi_{3004}(531,\cdot)\) \(\chi_{3004}(535,\cdot)\) \(\chi_{3004}(575,\cdot)\) \(\chi_{3004}(595,\cdot)\) \(\chi_{3004}(627,\cdot)\) \(\chi_{3004}(683,\cdot)\) \(\chi_{3004}(691,\cdot)\) \(\chi_{3004}(695,\cdot)\) \(\chi_{3004}(759,\cdot)\) \(\chi_{3004}(787,\cdot)\) \(\chi_{3004}(815,\cdot)\) \(\chi_{3004}(851,\cdot)\) \(\chi_{3004}(883,\cdot)\) \(\chi_{3004}(899,\cdot)\) \(\chi_{3004}(959,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((-1,e\left(\frac{19}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3004 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{163}{250}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{113}{250}\right)\) | \(e\left(\frac{38}{125}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{27}{125}\right)\) | \(e\left(\frac{131}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{59}{250}\right)\) | \(e\left(\frac{13}{125}\right)\) |