Basic properties
| Modulus: | \(3004\) | |
| Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(750\) | 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 3004.be
\(\chi_{3004}(3,\cdot)\) \(\chi_{3004}(15,\cdot)\) \(\chi_{3004}(31,\cdot)\) \(\chi_{3004}(35,\cdot)\) \(\chi_{3004}(39,\cdot)\) \(\chi_{3004}(55,\cdot)\) \(\chi_{3004}(63,\cdot)\) \(\chi_{3004}(67,\cdot)\) \(\chi_{3004}(79,\cdot)\) \(\chi_{3004}(91,\cdot)\) \(\chi_{3004}(103,\cdot)\) \(\chi_{3004}(135,\cdot)\) \(\chi_{3004}(143,\cdot)\) \(\chi_{3004}(147,\cdot)\) \(\chi_{3004}(159,\cdot)\) \(\chi_{3004}(175,\cdot)\) \(\chi_{3004}(227,\cdot)\) \(\chi_{3004}(231,\cdot)\) \(\chi_{3004}(259,\cdot)\) \(\chi_{3004}(263,\cdot)\) \(\chi_{3004}(279,\cdot)\) \(\chi_{3004}(283,\cdot)\) \(\chi_{3004}(335,\cdot)\) \(\chi_{3004}(351,\cdot)\) \(\chi_{3004}(375,\cdot)\) \(\chi_{3004}(427,\cdot)\) \(\chi_{3004}(431,\cdot)\) \(\chi_{3004}(443,\cdot)\) \(\chi_{3004}(487,\cdot)\) \(\chi_{3004}(495,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((-1,e\left(\frac{1}{750}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3004 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{188}{375}\right)\) | \(e\left(\frac{368}{375}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{1}{375}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{254}{375}\right)\) | \(e\left(\frac{181}{375}\right)\) | \(e\left(\frac{329}{750}\right)\) | \(e\left(\frac{643}{750}\right)\) | \(e\left(\frac{326}{375}\right)\) |