Basic properties
| Modulus: | \(1021\) | |
| Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1021.t
\(\chi_{1021}(19,\cdot)\) \(\chi_{1021}(57,\cdot)\) \(\chi_{1021}(58,\cdot)\) \(\chi_{1021}(88,\cdot)\) \(\chi_{1021}(97,\cdot)\) \(\chi_{1021}(107,\cdot)\) \(\chi_{1021}(136,\cdot)\) \(\chi_{1021}(148,\cdot)\) \(\chi_{1021}(174,\cdot)\) \(\chi_{1021}(200,\cdot)\) \(\chi_{1021}(215,\cdot)\) \(\chi_{1021}(229,\cdot)\) \(\chi_{1021}(242,\cdot)\) \(\chi_{1021}(264,\cdot)\) \(\chi_{1021}(291,\cdot)\) \(\chi_{1021}(295,\cdot)\) \(\chi_{1021}(308,\cdot)\) \(\chi_{1021}(311,\cdot)\) \(\chi_{1021}(321,\cdot)\) \(\chi_{1021}(334,\cdot)\) \(\chi_{1021}(376,\cdot)\) \(\chi_{1021}(407,\cdot)\) \(\chi_{1021}(408,\cdot)\) \(\chi_{1021}(412,\cdot)\) \(\chi_{1021}(421,\cdot)\) \(\chi_{1021}(443,\cdot)\) \(\chi_{1021}(444,\cdot)\) \(\chi_{1021}(476,\cdot)\) \(\chi_{1021}(488,\cdot)\) \(\chi_{1021}(499,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{163}{204}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1021 }(476, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{163}{204}\right)\) | \(e\left(\frac{40}{51}\right)\) |