Basic properties
| Modulus: | \(431\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(43\) | 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 431.e
\(\chi_{431}(2,\cdot)\) \(\chi_{431}(3,\cdot)\) \(\chi_{431}(4,\cdot)\) \(\chi_{431}(6,\cdot)\) \(\chi_{431}(8,\cdot)\) \(\chi_{431}(9,\cdot)\) \(\chi_{431}(12,\cdot)\) \(\chi_{431}(16,\cdot)\) \(\chi_{431}(18,\cdot)\) \(\chi_{431}(24,\cdot)\) \(\chi_{431}(27,\cdot)\) \(\chi_{431}(32,\cdot)\) \(\chi_{431}(36,\cdot)\) \(\chi_{431}(48,\cdot)\) \(\chi_{431}(54,\cdot)\) \(\chi_{431}(55,\cdot)\) \(\chi_{431}(64,\cdot)\) \(\chi_{431}(72,\cdot)\) \(\chi_{431}(81,\cdot)\) \(\chi_{431}(96,\cdot)\) \(\chi_{431}(108,\cdot)\) \(\chi_{431}(110,\cdot)\) \(\chi_{431}(128,\cdot)\) \(\chi_{431}(144,\cdot)\) \(\chi_{431}(145,\cdot)\) \(\chi_{431}(149,\cdot)\) \(\chi_{431}(162,\cdot)\) \(\chi_{431}(165,\cdot)\) \(\chi_{431}(192,\cdot)\) \(\chi_{431}(216,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 43 polynomial |
Values on generators
\(7\) → \(e\left(\frac{34}{43}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 431 }(220, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{22}{43}\right)\) |