Basic properties
| Modulus: | \(8048\) | |
| Conductor: | \(4024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4024}(2021,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8048.s
\(\chi_{8048}(9,\cdot)\) \(\chi_{8048}(25,\cdot)\) \(\chi_{8048}(73,\cdot)\) \(\chi_{8048}(121,\cdot)\) \(\chi_{8048}(169,\cdot)\) \(\chi_{8048}(185,\cdot)\) \(\chi_{8048}(201,\cdot)\) \(\chi_{8048}(233,\cdot)\) \(\chi_{8048}(249,\cdot)\) \(\chi_{8048}(265,\cdot)\) \(\chi_{8048}(281,\cdot)\) \(\chi_{8048}(297,\cdot)\) \(\chi_{8048}(329,\cdot)\) \(\chi_{8048}(361,\cdot)\) \(\chi_{8048}(393,\cdot)\) \(\chi_{8048}(441,\cdot)\) \(\chi_{8048}(473,\cdot)\) \(\chi_{8048}(505,\cdot)\) \(\chi_{8048}(521,\cdot)\) \(\chi_{8048}(553,\cdot)\) \(\chi_{8048}(569,\cdot)\) \(\chi_{8048}(601,\cdot)\) \(\chi_{8048}(649,\cdot)\) \(\chi_{8048}(665,\cdot)\) \(\chi_{8048}(697,\cdot)\) \(\chi_{8048}(729,\cdot)\) \(\chi_{8048}(745,\cdot)\) \(\chi_{8048}(761,\cdot)\) \(\chi_{8048}(793,\cdot)\) \(\chi_{8048}(825,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((1,-1,e\left(\frac{156}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{229}{502}\right)\) | \(e\left(\frac{61}{502}\right)\) | \(e\left(\frac{113}{251}\right)\) | \(e\left(\frac{229}{251}\right)\) | \(e\left(\frac{303}{502}\right)\) | \(e\left(\frac{285}{502}\right)\) | \(e\left(\frac{145}{251}\right)\) | \(e\left(\frac{82}{251}\right)\) | \(e\left(\frac{401}{502}\right)\) | \(e\left(\frac{455}{502}\right)\) |