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 \(\chi_{4024}(2067,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8048.n
\(\chi_{8048}(55,\cdot)\) \(\chi_{8048}(71,\cdot)\) \(\chi_{8048}(87,\cdot)\) \(\chi_{8048}(103,\cdot)\) \(\chi_{8048}(119,\cdot)\) \(\chi_{8048}(135,\cdot)\) \(\chi_{8048}(151,\cdot)\) \(\chi_{8048}(167,\cdot)\) \(\chi_{8048}(215,\cdot)\) \(\chi_{8048}(247,\cdot)\) \(\chi_{8048}(279,\cdot)\) \(\chi_{8048}(295,\cdot)\) \(\chi_{8048}(311,\cdot)\) \(\chi_{8048}(327,\cdot)\) \(\chi_{8048}(359,\cdot)\) \(\chi_{8048}(375,\cdot)\) \(\chi_{8048}(391,\cdot)\) \(\chi_{8048}(407,\cdot)\) \(\chi_{8048}(439,\cdot)\) \(\chi_{8048}(455,\cdot)\) \(\chi_{8048}(471,\cdot)\) \(\chi_{8048}(487,\cdot)\) \(\chi_{8048}(583,\cdot)\) \(\chi_{8048}(663,\cdot)\) \(\chi_{8048}(743,\cdot)\) \(\chi_{8048}(775,\cdot)\) \(\chi_{8048}(807,\cdot)\) \(\chi_{8048}(823,\cdot)\) \(\chi_{8048}(967,\cdot)\) \(\chi_{8048}(983,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,6037,2017)\) → \((-1,-1,e\left(\frac{43}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8048 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{251}\right)\) | \(e\left(\frac{147}{251}\right)\) | \(e\left(\frac{435}{502}\right)\) | \(e\left(\frac{182}{251}\right)\) | \(e\left(\frac{150}{251}\right)\) | \(e\left(\frac{61}{502}\right)\) | \(e\left(\frac{238}{251}\right)\) | \(e\left(\frac{309}{502}\right)\) | \(e\left(\frac{151}{502}\right)\) | \(e\left(\frac{115}{502}\right)\) |