Basic properties
| Modulus: | \(431\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(215\) | 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.g
\(\chi_{431}(5,\cdot)\) \(\chi_{431}(10,\cdot)\) \(\chi_{431}(11,\cdot)\) \(\chi_{431}(15,\cdot)\) \(\chi_{431}(19,\cdot)\) \(\chi_{431}(20,\cdot)\) \(\chi_{431}(22,\cdot)\) \(\chi_{431}(23,\cdot)\) \(\chi_{431}(25,\cdot)\) \(\chi_{431}(29,\cdot)\) \(\chi_{431}(30,\cdot)\) \(\chi_{431}(33,\cdot)\) \(\chi_{431}(38,\cdot)\) \(\chi_{431}(40,\cdot)\) \(\chi_{431}(41,\cdot)\) \(\chi_{431}(44,\cdot)\) \(\chi_{431}(45,\cdot)\) \(\chi_{431}(46,\cdot)\) \(\chi_{431}(49,\cdot)\) \(\chi_{431}(50,\cdot)\) \(\chi_{431}(53,\cdot)\) \(\chi_{431}(57,\cdot)\) \(\chi_{431}(58,\cdot)\) \(\chi_{431}(59,\cdot)\) \(\chi_{431}(60,\cdot)\) \(\chi_{431}(61,\cdot)\) \(\chi_{431}(66,\cdot)\) \(\chi_{431}(69,\cdot)\) \(\chi_{431}(75,\cdot)\) \(\chi_{431}(76,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 215 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{161}{215}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 431 }(135, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{22}{215}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{161}{215}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{182}{215}\right)\) | \(e\left(\frac{3}{215}\right)\) |