Basic properties
Modulus: | \(1021\) | |
Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(255\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1021.u
\(\chi_{1021}(5,\cdot)\) \(\chi_{1021}(11,\cdot)\) \(\chi_{1021}(23,\cdot)\) \(\chi_{1021}(25,\cdot)\) \(\chi_{1021}(45,\cdot)\) \(\chi_{1021}(47,\cdot)\) \(\chi_{1021}(51,\cdot)\) \(\chi_{1021}(55,\cdot)\) \(\chi_{1021}(60,\cdot)\) \(\chi_{1021}(68,\cdot)\) \(\chi_{1021}(70,\cdot)\) \(\chi_{1021}(87,\cdot)\) \(\chi_{1021}(99,\cdot)\) \(\chi_{1021}(114,\cdot)\) \(\chi_{1021}(116,\cdot)\) \(\chi_{1021}(121,\cdot)\) \(\chi_{1021}(133,\cdot)\) \(\chi_{1021}(154,\cdot)\) \(\chi_{1021}(164,\cdot)\) \(\chi_{1021}(167,\cdot)\) \(\chi_{1021}(176,\cdot)\) \(\chi_{1021}(183,\cdot)\) \(\chi_{1021}(193,\cdot)\) \(\chi_{1021}(197,\cdot)\) \(\chi_{1021}(206,\cdot)\) \(\chi_{1021}(207,\cdot)\) \(\chi_{1021}(222,\cdot)\) \(\chi_{1021}(225,\cdot)\) \(\chi_{1021}(233,\cdot)\) \(\chi_{1021}(244,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{255})$ |
Fixed field: | Number field defined by a degree 255 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{227}{255}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1021 }(207, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{85}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{74}{85}\right)\) | \(e\left(\frac{116}{255}\right)\) | \(e\left(\frac{67}{85}\right)\) | \(e\left(\frac{27}{85}\right)\) | \(e\left(\frac{26}{85}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{227}{255}\right)\) | \(e\left(\frac{62}{255}\right)\) |