Basic properties
| Modulus: | \(4031\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1932\) | 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 4031.bv
\(\chi_{4031}(11,\cdot)\) \(\chi_{4031}(31,\cdot)\) \(\chi_{4031}(37,\cdot)\) \(\chi_{4031}(47,\cdot)\) \(\chi_{4031}(66,\cdot)\) \(\chi_{4031}(69,\cdot)\) \(\chi_{4031}(89,\cdot)\) \(\chi_{4031}(113,\cdot)\) \(\chi_{4031}(118,\cdot)\) \(\chi_{4031}(124,\cdot)\) \(\chi_{4031}(127,\cdot)\) \(\chi_{4031}(137,\cdot)\) \(\chi_{4031}(143,\cdot)\) \(\chi_{4031}(148,\cdot)\) \(\chi_{4031}(155,\cdot)\) \(\chi_{4031}(159,\cdot)\) \(\chi_{4031}(163,\cdot)\) \(\chi_{4031}(164,\cdot)\) \(\chi_{4031}(176,\cdot)\) \(\chi_{4031}(177,\cdot)\) \(\chi_{4031}(185,\cdot)\) \(\chi_{4031}(188,\cdot)\) \(\chi_{4031}(193,\cdot)\) \(\chi_{4031}(205,\cdot)\) \(\chi_{4031}(206,\cdot)\) \(\chi_{4031}(217,\cdot)\) \(\chi_{4031}(222,\cdot)\) \(\chi_{4031}(246,\cdot)\) \(\chi_{4031}(259,\cdot)\) \(\chi_{4031}(263,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{25}{28}\right),e\left(\frac{38}{69}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4031 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{857}{1932}\right)\) | \(e\left(\frac{85}{1932}\right)\) | \(e\left(\frac{857}{966}\right)\) | \(e\left(\frac{5}{966}\right)\) | \(e\left(\frac{157}{322}\right)\) | \(e\left(\frac{121}{483}\right)\) | \(e\left(\frac{213}{644}\right)\) | \(e\left(\frac{85}{966}\right)\) | \(e\left(\frac{289}{644}\right)\) | \(e\left(\frac{341}{1932}\right)\) |