Basic properties
| Modulus: | \(4024\) | |
| 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 \(\chi_{2012}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.n
\(\chi_{4024}(7,\cdot)\) \(\chi_{4024}(23,\cdot)\) \(\chi_{4024}(39,\cdot)\) \(\chi_{4024}(47,\cdot)\) \(\chi_{4024}(63,\cdot)\) \(\chi_{4024}(79,\cdot)\) \(\chi_{4024}(95,\cdot)\) \(\chi_{4024}(143,\cdot)\) \(\chi_{4024}(175,\cdot)\) \(\chi_{4024}(183,\cdot)\) \(\chi_{4024}(199,\cdot)\) \(\chi_{4024}(207,\cdot)\) \(\chi_{4024}(223,\cdot)\) \(\chi_{4024}(231,\cdot)\) \(\chi_{4024}(255,\cdot)\) \(\chi_{4024}(263,\cdot)\) \(\chi_{4024}(271,\cdot)\) \(\chi_{4024}(343,\cdot)\) \(\chi_{4024}(351,\cdot)\) \(\chi_{4024}(367,\cdot)\) \(\chi_{4024}(383,\cdot)\) \(\chi_{4024}(423,\cdot)\) \(\chi_{4024}(463,\cdot)\) \(\chi_{4024}(511,\cdot)\) \(\chi_{4024}(519,\cdot)\) \(\chi_{4024}(527,\cdot)\) \(\chi_{4024}(535,\cdot)\) \(\chi_{4024}(551,\cdot)\) \(\chi_{4024}(559,\cdot)\) \(\chi_{4024}(567,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((-1,1,e\left(\frac{199}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4024 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{91}{502}\right)\) | \(e\left(\frac{199}{251}\right)\) | \(e\left(\frac{343}{502}\right)\) | \(e\left(\frac{91}{251}\right)\) | \(e\left(\frac{401}{502}\right)\) | \(e\left(\frac{78}{251}\right)\) | \(e\left(\frac{489}{502}\right)\) | \(e\left(\frac{140}{251}\right)\) | \(e\left(\frac{201}{502}\right)\) | \(e\left(\frac{217}{251}\right)\) |