Basic properties
| Modulus: | \(8044\) | |
| Conductor: | \(8044\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2010\) | 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 8044.bd
\(\chi_{8044}(3,\cdot)\) \(\chi_{8044}(7,\cdot)\) \(\chi_{8044}(11,\cdot)\) \(\chi_{8044}(19,\cdot)\) \(\chi_{8044}(35,\cdot)\) \(\chi_{8044}(39,\cdot)\) \(\chi_{8044}(79,\cdot)\) \(\chi_{8044}(99,\cdot)\) \(\chi_{8044}(107,\cdot)\) \(\chi_{8044}(123,\cdot)\) \(\chi_{8044}(131,\cdot)\) \(\chi_{8044}(135,\cdot)\) \(\chi_{8044}(167,\cdot)\) \(\chi_{8044}(179,\cdot)\) \(\chi_{8044}(195,\cdot)\) \(\chi_{8044}(223,\cdot)\) \(\chi_{8044}(227,\cdot)\) \(\chi_{8044}(235,\cdot)\) \(\chi_{8044}(239,\cdot)\) \(\chi_{8044}(247,\cdot)\) \(\chi_{8044}(251,\cdot)\) \(\chi_{8044}(271,\cdot)\) \(\chi_{8044}(287,\cdot)\) \(\chi_{8044}(295,\cdot)\) \(\chi_{8044}(303,\cdot)\) \(\chi_{8044}(315,\cdot)\) \(\chi_{8044}(327,\cdot)\) \(\chi_{8044}(331,\cdot)\) \(\chi_{8044}(359,\cdot)\) \(\chi_{8044}(375,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1005})$ |
| Fixed field: | Number field defined by a degree 2010 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((-1,e\left(\frac{1}{2010}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8044 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{503}{1005}\right)\) | \(e\left(\frac{512}{1005}\right)\) | \(e\left(\frac{401}{1005}\right)\) | \(e\left(\frac{1}{1005}\right)\) | \(e\left(\frac{16}{1005}\right)\) | \(e\left(\frac{323}{335}\right)\) | \(e\left(\frac{2}{201}\right)\) | \(e\left(\frac{347}{2010}\right)\) | \(e\left(\frac{79}{1005}\right)\) | \(e\left(\frac{904}{1005}\right)\) |