Basic properties
| Modulus: | \(4022\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1005\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4022.o
\(\chi_{4022}(5,\cdot)\) \(\chi_{4022}(9,\cdot)\) \(\chi_{4022}(21,\cdot)\) \(\chi_{4022}(23,\cdot)\) \(\chi_{4022}(25,\cdot)\) \(\chi_{4022}(49,\cdot)\) \(\chi_{4022}(65,\cdot)\) \(\chi_{4022}(71,\cdot)\) \(\chi_{4022}(81,\cdot)\) \(\chi_{4022}(83,\cdot)\) \(\chi_{4022}(87,\cdot)\) \(\chi_{4022}(89,\cdot)\) \(\chi_{4022}(109,\cdot)\) \(\chi_{4022}(111,\cdot)\) \(\chi_{4022}(121,\cdot)\) \(\chi_{4022}(137,\cdot)\) \(\chi_{4022}(141,\cdot)\) \(\chi_{4022}(155,\cdot)\) \(\chi_{4022}(157,\cdot)\) \(\chi_{4022}(159,\cdot)\) \(\chi_{4022}(165,\cdot)\) \(\chi_{4022}(177,\cdot)\) \(\chi_{4022}(187,\cdot)\) \(\chi_{4022}(199,\cdot)\) \(\chi_{4022}(203,\cdot)\) \(\chi_{4022}(215,\cdot)\) \(\chi_{4022}(219,\cdot)\) \(\chi_{4022}(241,\cdot)\) \(\chi_{4022}(255,\cdot)\) \(\chi_{4022}(259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1005})$ |
| Fixed field: | Number field defined by a degree 1005 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{1005}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4022 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{1005}\right)\) | \(e\left(\frac{19}{1005}\right)\) | \(e\left(\frac{802}{1005}\right)\) | \(e\left(\frac{2}{1005}\right)\) | \(e\left(\frac{32}{1005}\right)\) | \(e\left(\frac{311}{335}\right)\) | \(e\left(\frac{4}{201}\right)\) | \(e\left(\frac{347}{1005}\right)\) | \(e\left(\frac{158}{1005}\right)\) | \(e\left(\frac{803}{1005}\right)\) |