Basic properties
| Modulus: | \(4024\) | |
| Conductor: | \(4024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | 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 4024.l
\(\chi_{4024}(3,\cdot)\) \(\chi_{4024}(11,\cdot)\) \(\chi_{4024}(27,\cdot)\) \(\chi_{4024}(43,\cdot)\) \(\chi_{4024}(59,\cdot)\) \(\chi_{4024}(67,\cdot)\) \(\chi_{4024}(75,\cdot)\) \(\chi_{4024}(83,\cdot)\) \(\chi_{4024}(91,\cdot)\) \(\chi_{4024}(99,\cdot)\) \(\chi_{4024}(131,\cdot)\) \(\chi_{4024}(147,\cdot)\) \(\chi_{4024}(155,\cdot)\) \(\chi_{4024}(219,\cdot)\) \(\chi_{4024}(243,\cdot)\) \(\chi_{4024}(275,\cdot)\) \(\chi_{4024}(283,\cdot)\) \(\chi_{4024}(291,\cdot)\) \(\chi_{4024}(299,\cdot)\) \(\chi_{4024}(323,\cdot)\) \(\chi_{4024}(339,\cdot)\) \(\chi_{4024}(355,\cdot)\) \(\chi_{4024}(363,\cdot)\) \(\chi_{4024}(379,\cdot)\) \(\chi_{4024}(387,\cdot)\) \(\chi_{4024}(427,\cdot)\) \(\chi_{4024}(435,\cdot)\) \(\chi_{4024}(443,\cdot)\) \(\chi_{4024}(483,\cdot)\) \(\chi_{4024}(507,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((-1,-1,e\left(\frac{33}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4024 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{128}{251}\right)\) | \(e\left(\frac{317}{502}\right)\) | \(e\left(\frac{405}{502}\right)\) | \(e\left(\frac{5}{251}\right)\) | \(e\left(\frac{131}{251}\right)\) | \(e\left(\frac{403}{502}\right)\) | \(e\left(\frac{71}{502}\right)\) | \(e\left(\frac{27}{251}\right)\) | \(e\left(\frac{40}{251}\right)\) | \(e\left(\frac{159}{502}\right)\) |