Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(91\) | 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 8281.de
\(\chi_{8281}(92,\cdot)\) \(\chi_{8281}(183,\cdot)\) \(\chi_{8281}(274,\cdot)\) \(\chi_{8281}(365,\cdot)\) \(\chi_{8281}(456,\cdot)\) \(\chi_{8281}(547,\cdot)\) \(\chi_{8281}(729,\cdot)\) \(\chi_{8281}(820,\cdot)\) \(\chi_{8281}(911,\cdot)\) \(\chi_{8281}(1002,\cdot)\) \(\chi_{8281}(1093,\cdot)\) \(\chi_{8281}(1366,\cdot)\) \(\chi_{8281}(1457,\cdot)\) \(\chi_{8281}(1548,\cdot)\) \(\chi_{8281}(1639,\cdot)\) \(\chi_{8281}(1730,\cdot)\) \(\chi_{8281}(1821,\cdot)\) \(\chi_{8281}(2003,\cdot)\) \(\chi_{8281}(2094,\cdot)\) \(\chi_{8281}(2185,\cdot)\) \(\chi_{8281}(2276,\cdot)\) \(\chi_{8281}(2458,\cdot)\) \(\chi_{8281}(2640,\cdot)\) \(\chi_{8281}(2731,\cdot)\) \(\chi_{8281}(2822,\cdot)\) \(\chi_{8281}(2913,\cdot)\) \(\chi_{8281}(3004,\cdot)\) \(\chi_{8281}(3095,\cdot)\) \(\chi_{8281}(3277,\cdot)\) \(\chi_{8281}(3368,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{91})$ |
| Fixed field: | Number field defined by a degree 91 polynomial |
Values on generators
\((1522,3382)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{91}\right)\) | \(e\left(\frac{6}{91}\right)\) | \(e\left(\frac{11}{91}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{57}{91}\right)\) | \(e\left(\frac{62}{91}\right)\) | \(e\left(\frac{12}{91}\right)\) | \(e\left(\frac{29}{91}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{17}{91}\right)\) |