Basic properties
Modulus: | \(1021\) | |
Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(170\) | 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.s
\(\chi_{1021}(4,\cdot)\) \(\chi_{1021}(36,\cdot)\) \(\chi_{1021}(42,\cdot)\) \(\chi_{1021}(48,\cdot)\) \(\chi_{1021}(49,\cdot)\) \(\chi_{1021}(56,\cdot)\) \(\chi_{1021}(64,\cdot)\) \(\chi_{1021}(79,\cdot)\) \(\chi_{1021}(85,\cdot)\) \(\chi_{1021}(187,\cdot)\) \(\chi_{1021}(202,\cdot)\) \(\chi_{1021}(213,\cdot)\) \(\chi_{1021}(234,\cdot)\) \(\chi_{1021}(273,\cdot)\) \(\chi_{1021}(278,\cdot)\) \(\chi_{1021}(312,\cdot)\) \(\chi_{1021}(314,\cdot)\) \(\chi_{1021}(319,\cdot)\) \(\chi_{1021}(324,\cdot)\) \(\chi_{1021}(339,\cdot)\) \(\chi_{1021}(364,\cdot)\) \(\chi_{1021}(375,\cdot)\) \(\chi_{1021}(378,\cdot)\) \(\chi_{1021}(382,\cdot)\) \(\chi_{1021}(415,\cdot)\) \(\chi_{1021}(441,\cdot)\) \(\chi_{1021}(452,\cdot)\) \(\chi_{1021}(460,\cdot)\) \(\chi_{1021}(504,\cdot)\) \(\chi_{1021}(530,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{85})$ |
Fixed field: | Number field defined by a degree 170 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{33}{170}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1021 }(319, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{170}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{24}{85}\right)\) | \(e\left(\frac{47}{85}\right)\) | \(e\left(\frac{9}{170}\right)\) | \(e\left(\frac{29}{170}\right)\) | \(e\left(\frac{157}{170}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{33}{170}\right)\) | \(e\left(\frac{9}{85}\right)\) |