Basic properties
Modulus: | \(643\) | |
Conductor: | \(643\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(214\) | 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 643.f
\(\chi_{643}(2,\cdot)\) \(\chi_{643}(3,\cdot)\) \(\chi_{643}(5,\cdot)\) \(\chi_{643}(8,\cdot)\) \(\chi_{643}(12,\cdot)\) \(\chi_{643}(18,\cdot)\) \(\chi_{643}(20,\cdot)\) \(\chi_{643}(27,\cdot)\) \(\chi_{643}(30,\cdot)\) \(\chi_{643}(32,\cdot)\) \(\chi_{643}(43,\cdot)\) \(\chi_{643}(45,\cdot)\) \(\chi_{643}(48,\cdot)\) \(\chi_{643}(50,\cdot)\) \(\chi_{643}(67,\cdot)\) \(\chi_{643}(71,\cdot)\) \(\chi_{643}(72,\cdot)\) \(\chi_{643}(75,\cdot)\) \(\chi_{643}(77,\cdot)\) \(\chi_{643}(80,\cdot)\) \(\chi_{643}(103,\cdot)\) \(\chi_{643}(107,\cdot)\) \(\chi_{643}(108,\cdot)\) \(\chi_{643}(119,\cdot)\) \(\chi_{643}(120,\cdot)\) \(\chi_{643}(125,\cdot)\) \(\chi_{643}(127,\cdot)\) \(\chi_{643}(128,\cdot)\) \(\chi_{643}(157,\cdot)\) \(\chi_{643}(162,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{107})$ |
Fixed field: | Number field defined by a degree 214 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{25}{214}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 643 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{197}{214}\right)\) | \(e\left(\frac{21}{214}\right)\) | \(e\left(\frac{90}{107}\right)\) | \(e\left(\frac{33}{214}\right)\) | \(e\left(\frac{2}{107}\right)\) | \(e\left(\frac{98}{107}\right)\) | \(e\left(\frac{163}{214}\right)\) | \(e\left(\frac{21}{107}\right)\) | \(e\left(\frac{8}{107}\right)\) | \(e\left(\frac{25}{214}\right)\) |