Basic properties
| Modulus: | \(586971\) | |
| Conductor: | \(53361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2310\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{53361}(13030,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 586971.on
\(\chi_{586971}(40,\cdot)\) \(\chi_{586971}(481,\cdot)\) \(\chi_{586971}(1564,\cdot)\) \(\chi_{586971}(2635,\cdot)\) \(\chi_{586971}(3379,\cdot)\) \(\chi_{586971}(4450,\cdot)\) \(\chi_{586971}(5848,\cdot)\) \(\chi_{586971}(6289,\cdot)\) \(\chi_{586971}(9187,\cdot)\) \(\chi_{586971}(10258,\cdot)\) \(\chi_{586971}(11002,\cdot)\) \(\chi_{586971}(13912,\cdot)\) \(\chi_{586971}(15286,\cdot)\) \(\chi_{586971}(15727,\cdot)\) \(\chi_{586971}(16810,\cdot)\) \(\chi_{586971}(17881,\cdot)\) \(\chi_{586971}(18625,\cdot)\) \(\chi_{586971}(19696,\cdot)\) \(\chi_{586971}(21094,\cdot)\) \(\chi_{586971}(21535,\cdot)\) \(\chi_{586971}(22909,\cdot)\) \(\chi_{586971}(23350,\cdot)\) \(\chi_{586971}(25504,\cdot)\) \(\chi_{586971}(26248,\cdot)\) \(\chi_{586971}(28717,\cdot)\) \(\chi_{586971}(30532,\cdot)\) \(\chi_{586971}(30973,\cdot)\) \(\chi_{586971}(32056,\cdot)\) \(\chi_{586971}(33127,\cdot)\) \(\chi_{586971}(34942,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1155})$ |
| Fixed field: | Number field defined by a degree 2310 polynomial (not computed) |
Values on generators
\((130439,179686,73207)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{31}{42}\right),e\left(\frac{29}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 586971 }(17881, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{770}\right)\) | \(e\left(\frac{93}{385}\right)\) | \(e\left(\frac{571}{2310}\right)\) | \(e\left(\frac{279}{770}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{367}{1155}\right)\) | \(e\left(\frac{186}{385}\right)\) | \(e\left(\frac{428}{1155}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{1129}{2310}\right)\) |