Basic properties
| Modulus: | \(4006\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(91\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4006.j
\(\chi_{4006}(53,\cdot)\) \(\chi_{4006}(165,\cdot)\) \(\chi_{4006}(241,\cdot)\) \(\chi_{4006}(289,\cdot)\) \(\chi_{4006}(319,\cdot)\) \(\chi_{4006}(325,\cdot)\) \(\chi_{4006}(349,\cdot)\) \(\chi_{4006}(383,\cdot)\) \(\chi_{4006}(389,\cdot)\) \(\chi_{4006}(557,\cdot)\) \(\chi_{4006}(587,\cdot)\) \(\chi_{4006}(655,\cdot)\) \(\chi_{4006}(711,\cdot)\) \(\chi_{4006}(755,\cdot)\) \(\chi_{4006}(765,\cdot)\) \(\chi_{4006}(883,\cdot)\) \(\chi_{4006}(1009,\cdot)\) \(\chi_{4006}(1141,\cdot)\) \(\chi_{4006}(1173,\cdot)\) \(\chi_{4006}(1201,\cdot)\) \(\chi_{4006}(1391,\cdot)\) \(\chi_{4006}(1399,\cdot)\) \(\chi_{4006}(1419,\cdot)\) \(\chi_{4006}(1469,\cdot)\) \(\chi_{4006}(1479,\cdot)\) \(\chi_{4006}(1501,\cdot)\) \(\chi_{4006}(1547,\cdot)\) \(\chi_{4006}(1611,\cdot)\) \(\chi_{4006}(1615,\cdot)\) \(\chi_{4006}(1621,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{91})$ |
| Fixed field: | Number field defined by a degree 91 polynomial |
Values on generators
\(5\) → \(e\left(\frac{8}{91}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4006 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{91}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{74}{91}\right)\) | \(e\left(\frac{76}{91}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{31}{91}\right)\) | \(e\left(\frac{46}{91}\right)\) | \(e\left(\frac{16}{91}\right)\) | \(e\left(\frac{27}{91}\right)\) | \(e\left(\frac{3}{13}\right)\) |