Basic properties
| Modulus: | \(4006\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(182\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4006.m
\(\chi_{4006}(17,\cdot)\) \(\chi_{4006}(69,\cdot)\) \(\chi_{4006}(233,\cdot)\) \(\chi_{4006}(295,\cdot)\) \(\chi_{4006}(331,\cdot)\) \(\chi_{4006}(387,\cdot)\) \(\chi_{4006}(481,\cdot)\) \(\chi_{4006}(567,\cdot)\) \(\chi_{4006}(603,\cdot)\) \(\chi_{4006}(605,\cdot)\) \(\chi_{4006}(707,\cdot)\) \(\chi_{4006}(817,\cdot)\) \(\chi_{4006}(837,\cdot)\) \(\chi_{4006}(901,\cdot)\) \(\chi_{4006}(907,\cdot)\) \(\chi_{4006}(937,\cdot)\) \(\chi_{4006}(987,\cdot)\) \(\chi_{4006}(1107,\cdot)\) \(\chi_{4006}(1197,\cdot)\) \(\chi_{4006}(1211,\cdot)\) \(\chi_{4006}(1273,\cdot)\) \(\chi_{4006}(1339,\cdot)\) \(\chi_{4006}(1417,\cdot)\) \(\chi_{4006}(1433,\cdot)\) \(\chi_{4006}(1457,\cdot)\) \(\chi_{4006}(1481,\cdot)\) \(\chi_{4006}(1513,\cdot)\) \(\chi_{4006}(1533,\cdot)\) \(\chi_{4006}(1589,\cdot)\) \(\chi_{4006}(1733,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{91})$ |
| Fixed field: | Number field defined by a degree 182 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{25}{182}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4006 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{48}{91}\right)\) | \(e\left(\frac{25}{182}\right)\) | \(e\left(\frac{163}{182}\right)\) | \(e\left(\frac{5}{91}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{121}{182}\right)\) | \(e\left(\frac{141}{182}\right)\) | \(e\left(\frac{82}{91}\right)\) | \(e\left(\frac{11}{26}\right)\) |