Basic properties
| Modulus: | \(431\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(430\) | 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 431.h
\(\chi_{431}(7,\cdot)\) \(\chi_{431}(13,\cdot)\) \(\chi_{431}(14,\cdot)\) \(\chi_{431}(17,\cdot)\) \(\chi_{431}(21,\cdot)\) \(\chi_{431}(28,\cdot)\) \(\chi_{431}(31,\cdot)\) \(\chi_{431}(34,\cdot)\) \(\chi_{431}(35,\cdot)\) \(\chi_{431}(37,\cdot)\) \(\chi_{431}(39,\cdot)\) \(\chi_{431}(42,\cdot)\) \(\chi_{431}(43,\cdot)\) \(\chi_{431}(51,\cdot)\) \(\chi_{431}(52,\cdot)\) \(\chi_{431}(56,\cdot)\) \(\chi_{431}(62,\cdot)\) \(\chi_{431}(63,\cdot)\) \(\chi_{431}(65,\cdot)\) \(\chi_{431}(67,\cdot)\) \(\chi_{431}(68,\cdot)\) \(\chi_{431}(70,\cdot)\) \(\chi_{431}(71,\cdot)\) \(\chi_{431}(73,\cdot)\) \(\chi_{431}(74,\cdot)\) \(\chi_{431}(77,\cdot)\) \(\chi_{431}(78,\cdot)\) \(\chi_{431}(79,\cdot)\) \(\chi_{431}(83,\cdot)\) \(\chi_{431}(84,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 430 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{323}{430}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 431 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{193}{215}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{323}{430}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{33}{215}\right)\) | \(e\left(\frac{212}{215}\right)\) |