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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.ba
\(\chi_{3004}(7,\cdot)\) \(\chi_{3004}(27,\cdot)\) \(\chi_{3004}(75,\cdot)\) \(\chi_{3004}(99,\cdot)\) \(\chi_{3004}(111,\cdot)\) \(\chi_{3004}(155,\cdot)\) \(\chi_{3004}(183,\cdot)\) \(\chi_{3004}(239,\cdot)\) \(\chi_{3004}(267,\cdot)\) \(\chi_{3004}(275,\cdot)\) \(\chi_{3004}(315,\cdot)\) \(\chi_{3004}(323,\cdot)\) \(\chi_{3004}(327,\cdot)\) \(\chi_{3004}(343,\cdot)\) \(\chi_{3004}(363,\cdot)\) \(\chi_{3004}(371,\cdot)\) \(\chi_{3004}(383,\cdot)\) \(\chi_{3004}(391,\cdot)\) \(\chi_{3004}(395,\cdot)\) \(\chi_{3004}(407,\cdot)\) \(\chi_{3004}(415,\cdot)\) \(\chi_{3004}(447,\cdot)\) \(\chi_{3004}(463,\cdot)\) \(\chi_{3004}(491,\cdot)\) \(\chi_{3004}(507,\cdot)\) \(\chi_{3004}(543,\cdot)\) \(\chi_{3004}(603,\cdot)\) \(\chi_{3004}(619,\cdot)\) \(\chi_{3004}(651,\cdot)\) \(\chi_{3004}(687,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((-1,e\left(\frac{1}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3004 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{118}{125}\right)\) | \(e\left(\frac{13}{125}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{4}{125}\right)\) | \(e\left(\frac{56}{125}\right)\) | \(e\left(\frac{79}{250}\right)\) | \(e\left(\frac{143}{250}\right)\) | \(e\left(\frac{76}{125}\right)\) |