Basic properties
| Modulus: | \(862\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(215\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{431}(75,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 862.g
\(\chi_{862}(5,\cdot)\) \(\chi_{862}(11,\cdot)\) \(\chi_{862}(15,\cdot)\) \(\chi_{862}(19,\cdot)\) \(\chi_{862}(23,\cdot)\) \(\chi_{862}(25,\cdot)\) \(\chi_{862}(29,\cdot)\) \(\chi_{862}(33,\cdot)\) \(\chi_{862}(41,\cdot)\) \(\chi_{862}(45,\cdot)\) \(\chi_{862}(49,\cdot)\) \(\chi_{862}(53,\cdot)\) \(\chi_{862}(57,\cdot)\) \(\chi_{862}(59,\cdot)\) \(\chi_{862}(61,\cdot)\) \(\chi_{862}(69,\cdot)\) \(\chi_{862}(75,\cdot)\) \(\chi_{862}(87,\cdot)\) \(\chi_{862}(91,\cdot)\) \(\chi_{862}(97,\cdot)\) \(\chi_{862}(99,\cdot)\) \(\chi_{862}(109,\cdot)\) \(\chi_{862}(115,\cdot)\) \(\chi_{862}(119,\cdot)\) \(\chi_{862}(121,\cdot)\) \(\chi_{862}(123,\cdot)\) \(\chi_{862}(125,\cdot)\) \(\chi_{862}(135,\cdot)\) \(\chi_{862}(139,\cdot)\) \(\chi_{862}(147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 215 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{52}{215}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 862 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{154}{215}\right)\) | \(e\left(\frac{52}{215}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{21}{215}\right)\) | \(e\left(\frac{84}{215}\right)\) | \(e\left(\frac{94}{215}\right)\) | \(e\left(\frac{107}{215}\right)\) | \(e\left(\frac{18}{215}\right)\) | \(e\left(\frac{207}{215}\right)\) |