Basic properties
| Modulus: | \(4024\) | |
| Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(251\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{503}(281,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.i
\(\chi_{4024}(9,\cdot)\) \(\chi_{4024}(25,\cdot)\) \(\chi_{4024}(33,\cdot)\) \(\chi_{4024}(49,\cdot)\) \(\chi_{4024}(73,\cdot)\) \(\chi_{4024}(81,\cdot)\) \(\chi_{4024}(97,\cdot)\) \(\chi_{4024}(113,\cdot)\) \(\chi_{4024}(121,\cdot)\) \(\chi_{4024}(129,\cdot)\) \(\chi_{4024}(145,\cdot)\) \(\chi_{4024}(161,\cdot)\) \(\chi_{4024}(169,\cdot)\) \(\chi_{4024}(177,\cdot)\) \(\chi_{4024}(185,\cdot)\) \(\chi_{4024}(201,\cdot)\) \(\chi_{4024}(225,\cdot)\) \(\chi_{4024}(233,\cdot)\) \(\chi_{4024}(249,\cdot)\) \(\chi_{4024}(257,\cdot)\) \(\chi_{4024}(265,\cdot)\) \(\chi_{4024}(273,\cdot)\) \(\chi_{4024}(281,\cdot)\) \(\chi_{4024}(289,\cdot)\) \(\chi_{4024}(297,\cdot)\) \(\chi_{4024}(329,\cdot)\) \(\chi_{4024}(361,\cdot)\) \(\chi_{4024}(393,\cdot)\) \(\chi_{4024}(401,\cdot)\) \(\chi_{4024}(433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((1,1,e\left(\frac{239}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4024 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{136}{251}\right)\) | \(e\left(\frac{239}{251}\right)\) | \(e\left(\frac{223}{251}\right)\) | \(e\left(\frac{21}{251}\right)\) | \(e\left(\frac{249}{251}\right)\) | \(e\left(\frac{18}{251}\right)\) | \(e\left(\frac{124}{251}\right)\) | \(e\left(\frac{13}{251}\right)\) | \(e\left(\frac{168}{251}\right)\) | \(e\left(\frac{108}{251}\right)\) |