Basic properties
| Modulus: | \(862\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(430\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{431}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 862.h
\(\chi_{862}(7,\cdot)\) \(\chi_{862}(13,\cdot)\) \(\chi_{862}(17,\cdot)\) \(\chi_{862}(21,\cdot)\) \(\chi_{862}(31,\cdot)\) \(\chi_{862}(35,\cdot)\) \(\chi_{862}(37,\cdot)\) \(\chi_{862}(39,\cdot)\) \(\chi_{862}(43,\cdot)\) \(\chi_{862}(51,\cdot)\) \(\chi_{862}(63,\cdot)\) \(\chi_{862}(65,\cdot)\) \(\chi_{862}(67,\cdot)\) \(\chi_{862}(71,\cdot)\) \(\chi_{862}(73,\cdot)\) \(\chi_{862}(77,\cdot)\) \(\chi_{862}(79,\cdot)\) \(\chi_{862}(83,\cdot)\) \(\chi_{862}(85,\cdot)\) \(\chi_{862}(89,\cdot)\) \(\chi_{862}(93,\cdot)\) \(\chi_{862}(103,\cdot)\) \(\chi_{862}(105,\cdot)\) \(\chi_{862}(111,\cdot)\) \(\chi_{862}(113,\cdot)\) \(\chi_{862}(117,\cdot)\) \(\chi_{862}(127,\cdot)\) \(\chi_{862}(129,\cdot)\) \(\chi_{862}(131,\cdot)\) \(\chi_{862}(137,\cdot)\) ...
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
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 862 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{193}{215}\right)\) | \(e\left(\frac{323}{430}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{212}{215}\right)\) | \(e\left(\frac{191}{430}\right)\) | \(e\left(\frac{48}{215}\right)\) | \(e\left(\frac{123}{430}\right)\) | \(e\left(\frac{151}{215}\right)\) | \(e\left(\frac{33}{430}\right)\) |