Basic properties
| Modulus: | \(6038\) | |
| Conductor: | \(3019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(503\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3019}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6038.e
\(\chi_{6038}(9,\cdot)\) \(\chi_{6038}(13,\cdot)\) \(\chi_{6038}(21,\cdot)\) \(\chi_{6038}(49,\cdot)\) \(\chi_{6038}(57,\cdot)\) \(\chi_{6038}(79,\cdot)\) \(\chi_{6038}(81,\cdot)\) \(\chi_{6038}(87,\cdot)\) \(\chi_{6038}(97,\cdot)\) \(\chi_{6038}(117,\cdot)\) \(\chi_{6038}(125,\cdot)\) \(\chi_{6038}(131,\cdot)\) \(\chi_{6038}(133,\cdot)\) \(\chi_{6038}(149,\cdot)\) \(\chi_{6038}(151,\cdot)\) \(\chi_{6038}(155,\cdot)\) \(\chi_{6038}(169,\cdot)\) \(\chi_{6038}(173,\cdot)\) \(\chi_{6038}(189,\cdot)\) \(\chi_{6038}(193,\cdot)\) \(\chi_{6038}(203,\cdot)\) \(\chi_{6038}(219,\cdot)\) \(\chi_{6038}(227,\cdot)\) \(\chi_{6038}(249,\cdot)\) \(\chi_{6038}(263,\cdot)\) \(\chi_{6038}(271,\cdot)\) \(\chi_{6038}(273,\cdot)\) \(\chi_{6038}(349,\cdot)\) \(\chi_{6038}(361,\cdot)\) \(\chi_{6038}(381,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{503})$ |
| Fixed field: | Number field defined by a degree 503 polynomial (not computed) |
Values on generators
\(3021\) → \(e\left(\frac{138}{503}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6038 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{293}{503}\right)\) | \(e\left(\frac{161}{503}\right)\) | \(e\left(\frac{239}{503}\right)\) | \(e\left(\frac{83}{503}\right)\) | \(e\left(\frac{306}{503}\right)\) | \(e\left(\frac{217}{503}\right)\) | \(e\left(\frac{454}{503}\right)\) | \(e\left(\frac{21}{503}\right)\) | \(e\left(\frac{184}{503}\right)\) | \(e\left(\frac{29}{503}\right)\) |