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.w
\(\chi_{8048}(13,\cdot)\) \(\chi_{8048}(21,\cdot)\) \(\chi_{8048}(61,\cdot)\) \(\chi_{8048}(69,\cdot)\) \(\chi_{8048}(77,\cdot)\) \(\chi_{8048}(85,\cdot)\) \(\chi_{8048}(117,\cdot)\) \(\chi_{8048}(141,\cdot)\) \(\chi_{8048}(173,\cdot)\) \(\chi_{8048}(189,\cdot)\) \(\chi_{8048}(197,\cdot)\) \(\chi_{8048}(205,\cdot)\) \(\chi_{8048}(229,\cdot)\) \(\chi_{8048}(237,\cdot)\) \(\chi_{8048}(253,\cdot)\) \(\chi_{8048}(285,\cdot)\) \(\chi_{8048}(293,\cdot)\) \(\chi_{8048}(301,\cdot)\) \(\chi_{8048}(317,\cdot)\) \(\chi_{8048}(325,\cdot)\) \(\chi_{8048}(373,\cdot)\) \(\chi_{8048}(389,\cdot)\) \(\chi_{8048}(397,\cdot)\) \(\chi_{8048}(413,\cdot)\) \(\chi_{8048}(421,\cdot)\) \(\chi_{8048}(429,\cdot)\) \(\chi_{8048}(445,\cdot)\) \(\chi_{8048}(469,\cdot)\) \(\chi_{8048}(493,\cdot)\) \(\chi_{8048}(509,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1004})$ |
| Fixed field: | Number field defined by a degree 1004 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((1,-i,e\left(\frac{62}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{787}{1004}\right)\) | \(e\left(\frac{1001}{1004}\right)\) | \(e\left(\frac{373}{502}\right)\) | \(e\left(\frac{285}{502}\right)\) | \(e\left(\frac{125}{1004}\right)\) | \(e\left(\frac{883}{1004}\right)\) | \(e\left(\frac{196}{251}\right)\) | \(e\left(\frac{142}{251}\right)\) | \(e\left(\frac{795}{1004}\right)\) | \(e\left(\frac{529}{1004}\right)\) |