Basic properties
| Modulus: | \(3491\) | |
| Conductor: | \(3491\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3490\) | 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 3491.h
\(\chi_{3491}(2,\cdot)\) \(\chi_{3491}(6,\cdot)\) \(\chi_{3491}(8,\cdot)\) \(\chi_{3491}(11,\cdot)\) \(\chi_{3491}(14,\cdot)\) \(\chi_{3491}(17,\cdot)\) \(\chi_{3491}(18,\cdot)\) \(\chi_{3491}(23,\cdot)\) \(\chi_{3491}(24,\cdot)\) \(\chi_{3491}(29,\cdot)\) \(\chi_{3491}(30,\cdot)\) \(\chi_{3491}(31,\cdot)\) \(\chi_{3491}(33,\cdot)\) \(\chi_{3491}(37,\cdot)\) \(\chi_{3491}(39,\cdot)\) \(\chi_{3491}(40,\cdot)\) \(\chi_{3491}(41,\cdot)\) \(\chi_{3491}(42,\cdot)\) \(\chi_{3491}(44,\cdot)\) \(\chi_{3491}(50,\cdot)\) \(\chi_{3491}(51,\cdot)\) \(\chi_{3491}(52,\cdot)\) \(\chi_{3491}(55,\cdot)\) \(\chi_{3491}(65,\cdot)\) \(\chi_{3491}(68,\cdot)\) \(\chi_{3491}(70,\cdot)\) \(\chi_{3491}(71,\cdot)\) \(\chi_{3491}(72,\cdot)\) \(\chi_{3491}(73,\cdot)\) \(\chi_{3491}(77,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1745})$ |
| Fixed field: | Number field defined by a degree 3490 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1153}{3490}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3491 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1153}{3490}\right)\) | \(e\left(\frac{1712}{1745}\right)\) | \(e\left(\frac{1153}{1745}\right)\) | \(e\left(\frac{476}{1745}\right)\) | \(e\left(\frac{1087}{3490}\right)\) | \(e\left(\frac{843}{1745}\right)\) | \(e\left(\frac{3459}{3490}\right)\) | \(e\left(\frac{1679}{1745}\right)\) | \(e\left(\frac{421}{698}\right)\) | \(e\left(\frac{1207}{3490}\right)\) |