Basic properties
| Modulus: | \(8048\) | |
| Conductor: | \(8048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1004\) | 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 8048.u
\(\chi_{8048}(19,\cdot)\) \(\chi_{8048}(35,\cdot)\) \(\chi_{8048}(51,\cdot)\) \(\chi_{8048}(107,\cdot)\) \(\chi_{8048}(115,\cdot)\) \(\chi_{8048}(123,\cdot)\) \(\chi_{8048}(139,\cdot)\) \(\chi_{8048}(163,\cdot)\) \(\chi_{8048}(171,\cdot)\) \(\chi_{8048}(179,\cdot)\) \(\chi_{8048}(187,\cdot)\) \(\chi_{8048}(195,\cdot)\) \(\chi_{8048}(203,\cdot)\) \(\chi_{8048}(211,\cdot)\) \(\chi_{8048}(227,\cdot)\) \(\chi_{8048}(235,\cdot)\) \(\chi_{8048}(251,\cdot)\) \(\chi_{8048}(259,\cdot)\) \(\chi_{8048}(267,\cdot)\) \(\chi_{8048}(307,\cdot)\) \(\chi_{8048}(315,\cdot)\) \(\chi_{8048}(331,\cdot)\) \(\chi_{8048}(347,\cdot)\) \(\chi_{8048}(371,\cdot)\) \(\chi_{8048}(395,\cdot)\) \(\chi_{8048}(403,\cdot)\) \(\chi_{8048}(411,\cdot)\) \(\chi_{8048}(419,\cdot)\) \(\chi_{8048}(451,\cdot)\) \(\chi_{8048}(459,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1004})$ |
| Fixed field: | Number field defined by a degree 1004 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((-1,-i,e\left(\frac{237}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{401}{1004}\right)\) | \(e\left(\frac{223}{1004}\right)\) | \(e\left(\frac{151}{251}\right)\) | \(e\left(\frac{401}{502}\right)\) | \(e\left(\frac{79}{1004}\right)\) | \(e\left(\frac{795}{1004}\right)\) | \(e\left(\frac{156}{251}\right)\) | \(e\left(\frac{57}{502}\right)\) | \(e\left(\frac{643}{1004}\right)\) | \(e\left(\frac{1}{1004}\right)\) |