Basic properties
| Modulus: | \(431\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(86\) | 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.f
\(\chi_{431}(47,\cdot)\) \(\chi_{431}(94,\cdot)\) \(\chi_{431}(101,\cdot)\) \(\chi_{431}(107,\cdot)\) \(\chi_{431}(133,\cdot)\) \(\chi_{431}(141,\cdot)\) \(\chi_{431}(143,\cdot)\) \(\chi_{431}(175,\cdot)\) \(\chi_{431}(188,\cdot)\) \(\chi_{431}(202,\cdot)\) \(\chi_{431}(211,\cdot)\) \(\chi_{431}(214,\cdot)\) \(\chi_{431}(215,\cdot)\) \(\chi_{431}(239,\cdot)\) \(\chi_{431}(266,\cdot)\) \(\chi_{431}(269,\cdot)\) \(\chi_{431}(282,\cdot)\) \(\chi_{431}(286,\cdot)\) \(\chi_{431}(287,\cdot)\) \(\chi_{431}(303,\cdot)\) \(\chi_{431}(321,\cdot)\) \(\chi_{431}(323,\cdot)\) \(\chi_{431}(335,\cdot)\) \(\chi_{431}(350,\cdot)\) \(\chi_{431}(359,\cdot)\) \(\chi_{431}(367,\cdot)\) \(\chi_{431}(376,\cdot)\) \(\chi_{431}(377,\cdot)\) \(\chi_{431}(383,\cdot)\) \(\chi_{431}(395,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 86 polynomial |
Values on generators
\(7\) → \(e\left(\frac{49}{86}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 431 }(367, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{49}{86}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{7}{43}\right)\) |