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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8048.v
\(\chi_{8048}(3,\cdot)\) \(\chi_{8048}(11,\cdot)\) \(\chi_{8048}(27,\cdot)\) \(\chi_{8048}(43,\cdot)\) \(\chi_{8048}(59,\cdot)\) \(\chi_{8048}(67,\cdot)\) \(\chi_{8048}(75,\cdot)\) \(\chi_{8048}(83,\cdot)\) \(\chi_{8048}(91,\cdot)\) \(\chi_{8048}(99,\cdot)\) \(\chi_{8048}(131,\cdot)\) \(\chi_{8048}(147,\cdot)\) \(\chi_{8048}(155,\cdot)\) \(\chi_{8048}(219,\cdot)\) \(\chi_{8048}(243,\cdot)\) \(\chi_{8048}(275,\cdot)\) \(\chi_{8048}(283,\cdot)\) \(\chi_{8048}(291,\cdot)\) \(\chi_{8048}(299,\cdot)\) \(\chi_{8048}(323,\cdot)\) \(\chi_{8048}(339,\cdot)\) \(\chi_{8048}(355,\cdot)\) \(\chi_{8048}(363,\cdot)\) \(\chi_{8048}(379,\cdot)\) \(\chi_{8048}(387,\cdot)\) \(\chi_{8048}(427,\cdot)\) \(\chi_{8048}(435,\cdot)\) \(\chi_{8048}(443,\cdot)\) \(\chi_{8048}(483,\cdot)\) \(\chi_{8048}(507,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1004})$ |
| Fixed field: | Number field defined by a degree 1004 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((-1,i,e\left(\frac{105}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(91, a) \) | \(-1\) | \(1\) | \(e\left(\frac{511}{1004}\right)\) | \(e\left(\frac{671}{1004}\right)\) | \(e\left(\frac{245}{251}\right)\) | \(e\left(\frac{9}{502}\right)\) | \(e\left(\frac{321}{1004}\right)\) | \(e\left(\frac{625}{1004}\right)\) | \(e\left(\frac{89}{502}\right)\) | \(e\left(\frac{200}{251}\right)\) | \(e\left(\frac{395}{1004}\right)\) | \(e\left(\frac{487}{1004}\right)\) |