Basic properties
Modulus: | \(1021\) | |
Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(510\) | 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.w
\(\chi_{1021}(15,\cdot)\) \(\chi_{1021}(17,\cdot)\) \(\chi_{1021}(20,\cdot)\) \(\chi_{1021}(29,\cdot)\) \(\chi_{1021}(33,\cdot)\) \(\chi_{1021}(38,\cdot)\) \(\chi_{1021}(44,\cdot)\) \(\chi_{1021}(61,\cdot)\) \(\chi_{1021}(69,\cdot)\) \(\chi_{1021}(74,\cdot)\) \(\chi_{1021}(75,\cdot)\) \(\chi_{1021}(92,\cdot)\) \(\chi_{1021}(100,\cdot)\) \(\chi_{1021}(106,\cdot)\) \(\chi_{1021}(130,\cdot)\) \(\chi_{1021}(135,\cdot)\) \(\chi_{1021}(141,\cdot)\) \(\chi_{1021}(149,\cdot)\) \(\chi_{1021}(153,\cdot)\) \(\chi_{1021}(163,\cdot)\) \(\chi_{1021}(165,\cdot)\) \(\chi_{1021}(179,\cdot)\) \(\chi_{1021}(180,\cdot)\) \(\chi_{1021}(188,\cdot)\) \(\chi_{1021}(190,\cdot)\) \(\chi_{1021}(194,\cdot)\) \(\chi_{1021}(201,\cdot)\) \(\chi_{1021}(204,\cdot)\) \(\chi_{1021}(205,\cdot)\) \(\chi_{1021}(210,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{255})$ |
Fixed field: | Number field defined by a degree 510 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{487}{510}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1021 }(165, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{170}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{82}{85}\right)\) | \(e\left(\frac{248}{255}\right)\) | \(e\left(\frac{137}{170}\right)\) | \(e\left(\frac{7}{170}\right)\) | \(e\left(\frac{161}{170}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{487}{510}\right)\) | \(e\left(\frac{71}{255}\right)\) |