Basic properties
| Modulus: | \(4022\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(335\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4022.l
\(\chi_{4022}(13,\cdot)\) \(\chi_{4022}(31,\cdot)\) \(\chi_{4022}(33,\cdot)\) \(\chi_{4022}(41,\cdot)\) \(\chi_{4022}(43,\cdot)\) \(\chi_{4022}(45,\cdot)\) \(\chi_{4022}(51,\cdot)\) \(\chi_{4022}(57,\cdot)\) \(\chi_{4022}(77,\cdot)\) \(\chi_{4022}(101,\cdot)\) \(\chi_{4022}(105,\cdot)\) \(\chi_{4022}(119,\cdot)\) \(\chi_{4022}(125,\cdot)\) \(\chi_{4022}(127,\cdot)\) \(\chi_{4022}(151,\cdot)\) \(\chi_{4022}(169,\cdot)\) \(\chi_{4022}(181,\cdot)\) \(\chi_{4022}(183,\cdot)\) \(\chi_{4022}(191,\cdot)\) \(\chi_{4022}(197,\cdot)\) \(\chi_{4022}(201,\cdot)\) \(\chi_{4022}(207,\cdot)\) \(\chi_{4022}(245,\cdot)\) \(\chi_{4022}(283,\cdot)\) \(\chi_{4022}(293,\cdot)\) \(\chi_{4022}(319,\cdot)\) \(\chi_{4022}(355,\cdot)\) \(\chi_{4022}(367,\cdot)\) \(\chi_{4022}(403,\cdot)\) \(\chi_{4022}(407,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 335 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{276}{335}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4022 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{276}{335}\right)\) | \(e\left(\frac{219}{335}\right)\) | \(e\left(\frac{252}{335}\right)\) | \(e\left(\frac{217}{335}\right)\) | \(e\left(\frac{122}{335}\right)\) | \(e\left(\frac{228}{335}\right)\) | \(e\left(\frac{32}{67}\right)\) | \(e\left(\frac{297}{335}\right)\) | \(e\left(\frac{58}{335}\right)\) | \(e\left(\frac{193}{335}\right)\) |