Basic properties
| Modulus: | \(4022\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(402\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4022.m
\(\chi_{4022}(15,\cdot)\) \(\chi_{4022}(37,\cdot)\) \(\chi_{4022}(67,\cdot)\) \(\chi_{4022}(91,\cdot)\) \(\chi_{4022}(139,\cdot)\) \(\chi_{4022}(143,\cdot)\) \(\chi_{4022}(163,\cdot)\) \(\chi_{4022}(171,\cdot)\) \(\chi_{4022}(217,\cdot)\) \(\chi_{4022}(221,\cdot)\) \(\chi_{4022}(231,\cdot)\) \(\chi_{4022}(243,\cdot)\) \(\chi_{4022}(275,\cdot)\) \(\chi_{4022}(277,\cdot)\) \(\chi_{4022}(281,\cdot)\) \(\chi_{4022}(341,\cdot)\) \(\chi_{4022}(357,\cdot)\) \(\chi_{4022}(363,\cdot)\) \(\chi_{4022}(365,\cdot)\) \(\chi_{4022}(377,\cdot)\) \(\chi_{4022}(425,\cdot)\) \(\chi_{4022}(433,\cdot)\) \(\chi_{4022}(477,\cdot)\) \(\chi_{4022}(527,\cdot)\) \(\chi_{4022}(561,\cdot)\) \(\chi_{4022}(573,\cdot)\) \(\chi_{4022}(643,\cdot)\) \(\chi_{4022}(655,\cdot)\) \(\chi_{4022}(701,\cdot)\) \(\chi_{4022}(707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{201})$ |
| Fixed field: | Number field defined by a degree 402 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{205}{402}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4022 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{205}{402}\right)\) | \(e\left(\frac{38}{201}\right)\) | \(e\left(\frac{193}{402}\right)\) | \(e\left(\frac{4}{201}\right)\) | \(e\left(\frac{329}{402}\right)\) | \(e\left(\frac{19}{67}\right)\) | \(e\left(\frac{281}{402}\right)\) | \(e\left(\frac{383}{402}\right)\) | \(e\left(\frac{29}{402}\right)\) | \(e\left(\frac{199}{201}\right)\) |