Basic properties
| Modulus: | \(8048\) | |
| Conductor: | \(2012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2012}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8048.t
\(\chi_{8048}(15,\cdot)\) \(\chi_{8048}(31,\cdot)\) \(\chi_{8048}(111,\cdot)\) \(\chi_{8048}(127,\cdot)\) \(\chi_{8048}(159,\cdot)\) \(\chi_{8048}(191,\cdot)\) \(\chi_{8048}(239,\cdot)\) \(\chi_{8048}(287,\cdot)\) \(\chi_{8048}(303,\cdot)\) \(\chi_{8048}(319,\cdot)\) \(\chi_{8048}(335,\cdot)\) \(\chi_{8048}(399,\cdot)\) \(\chi_{8048}(415,\cdot)\) \(\chi_{8048}(431,\cdot)\) \(\chi_{8048}(447,\cdot)\) \(\chi_{8048}(479,\cdot)\) \(\chi_{8048}(495,\cdot)\) \(\chi_{8048}(543,\cdot)\) \(\chi_{8048}(623,\cdot)\) \(\chi_{8048}(639,\cdot)\) \(\chi_{8048}(655,\cdot)\) \(\chi_{8048}(735,\cdot)\) \(\chi_{8048}(751,\cdot)\) \(\chi_{8048}(783,\cdot)\) \(\chi_{8048}(799,\cdot)\) \(\chi_{8048}(831,\cdot)\) \(\chi_{8048}(863,\cdot)\) \(\chi_{8048}(911,\cdot)\) \(\chi_{8048}(927,\cdot)\) \(\chi_{8048}(943,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((-1,1,e\left(\frac{157}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{502}\right)\) | \(e\left(\frac{157}{502}\right)\) | \(e\left(\frac{199}{502}\right)\) | \(e\left(\frac{145}{251}\right)\) | \(e\left(\frac{319}{502}\right)\) | \(e\left(\frac{196}{251}\right)\) | \(e\left(\frac{151}{251}\right)\) | \(e\left(\frac{311}{502}\right)\) | \(e\left(\frac{156}{251}\right)\) | \(e\left(\frac{172}{251}\right)\) |