Basic properties
| Modulus: | \(6982\) | |
| Conductor: | \(3491\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3490\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3491}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6982.h
\(\chi_{6982}(11,\cdot)\) \(\chi_{6982}(17,\cdot)\) \(\chi_{6982}(23,\cdot)\) \(\chi_{6982}(29,\cdot)\) \(\chi_{6982}(31,\cdot)\) \(\chi_{6982}(33,\cdot)\) \(\chi_{6982}(37,\cdot)\) \(\chi_{6982}(39,\cdot)\) \(\chi_{6982}(41,\cdot)\) \(\chi_{6982}(51,\cdot)\) \(\chi_{6982}(55,\cdot)\) \(\chi_{6982}(65,\cdot)\) \(\chi_{6982}(71,\cdot)\) \(\chi_{6982}(73,\cdot)\) \(\chi_{6982}(77,\cdot)\) \(\chi_{6982}(87,\cdot)\) \(\chi_{6982}(91,\cdot)\) \(\chi_{6982}(93,\cdot)\) \(\chi_{6982}(103,\cdot)\) \(\chi_{6982}(111,\cdot)\) \(\chi_{6982}(113,\cdot)\) \(\chi_{6982}(115,\cdot)\) \(\chi_{6982}(117,\cdot)\) \(\chi_{6982}(119,\cdot)\) \(\chi_{6982}(123,\cdot)\) \(\chi_{6982}(139,\cdot)\) \(\chi_{6982}(145,\cdot)\) \(\chi_{6982}(153,\cdot)\) \(\chi_{6982}(155,\cdot)\) \(\chi_{6982}(161,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1745})$ |
| Fixed field: | Number field defined by a degree 3490 polynomial (not computed) |
Values on generators
\(3493\) → \(e\left(\frac{1153}{3490}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6982 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1712}{1745}\right)\) | \(e\left(\frac{476}{1745}\right)\) | \(e\left(\frac{843}{1745}\right)\) | \(e\left(\frac{1679}{1745}\right)\) | \(e\left(\frac{1207}{3490}\right)\) | \(e\left(\frac{163}{698}\right)\) | \(e\left(\frac{443}{1745}\right)\) | \(e\left(\frac{2373}{3490}\right)\) | \(e\left(\frac{1361}{1745}\right)\) | \(e\left(\frac{162}{349}\right)\) |