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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4031.bu
\(\chi_{4031}(2,\cdot)\) \(\chi_{4031}(3,\cdot)\) \(\chi_{4031}(15,\cdot)\) \(\chi_{4031}(18,\cdot)\) \(\chi_{4031}(19,\cdot)\) \(\chi_{4031}(21,\cdot)\) \(\chi_{4031}(26,\cdot)\) \(\chi_{4031}(32,\cdot)\) \(\chi_{4031}(40,\cdot)\) \(\chi_{4031}(50,\cdot)\) \(\chi_{4031}(56,\cdot)\) \(\chi_{4031}(61,\cdot)\) \(\chi_{4031}(68,\cdot)\) \(\chi_{4031}(72,\cdot)\) \(\chi_{4031}(73,\cdot)\) \(\chi_{4031}(85,\cdot)\) \(\chi_{4031}(90,\cdot)\) \(\chi_{4031}(98,\cdot)\) \(\chi_{4031}(101,\cdot)\) \(\chi_{4031}(102,\cdot)\) \(\chi_{4031}(108,\cdot)\) \(\chi_{4031}(114,\cdot)\) \(\chi_{4031}(119,\cdot)\) \(\chi_{4031}(126,\cdot)\) \(\chi_{4031}(130,\cdot)\) \(\chi_{4031}(134,\cdot)\) \(\chi_{4031}(135,\cdot)\) \(\chi_{4031}(142,\cdot)\) \(\chi_{4031}(156,\cdot)\) \(\chi_{4031}(160,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{13}{28}\right),e\left(\frac{85}{138}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4031 }(72, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{1932}\right)\) | \(e\left(\frac{1111}{1932}\right)\) | \(e\left(\frac{155}{966}\right)\) | \(e\left(\frac{179}{966}\right)\) | \(e\left(\frac{211}{322}\right)\) | \(e\left(\frac{178}{483}\right)\) | \(e\left(\frac{155}{644}\right)\) | \(e\left(\frac{145}{966}\right)\) | \(e\left(\frac{171}{644}\right)\) | \(e\left(\frac{809}{1932}\right)\) |