Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(9295\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 9295.et
\(\chi_{9295}(43,\cdot)\) \(\chi_{9295}(153,\cdot)\) \(\chi_{9295}(472,\cdot)\) \(\chi_{9295}(582,\cdot)\) \(\chi_{9295}(758,\cdot)\) \(\chi_{9295}(1187,\cdot)\) \(\chi_{9295}(1297,\cdot)\) \(\chi_{9295}(1473,\cdot)\) \(\chi_{9295}(1583,\cdot)\) \(\chi_{9295}(1902,\cdot)\) \(\chi_{9295}(2012,\cdot)\) \(\chi_{9295}(2188,\cdot)\) \(\chi_{9295}(2298,\cdot)\) \(\chi_{9295}(2617,\cdot)\) \(\chi_{9295}(2903,\cdot)\) \(\chi_{9295}(3013,\cdot)\) \(\chi_{9295}(3332,\cdot)\) \(\chi_{9295}(3442,\cdot)\) \(\chi_{9295}(3618,\cdot)\) \(\chi_{9295}(3728,\cdot)\) \(\chi_{9295}(4047,\cdot)\) \(\chi_{9295}(4157,\cdot)\) \(\chi_{9295}(4333,\cdot)\) \(\chi_{9295}(4443,\cdot)\) \(\chi_{9295}(4762,\cdot)\) \(\chi_{9295}(4872,\cdot)\) \(\chi_{9295}(5158,\cdot)\) \(\chi_{9295}(5477,\cdot)\) \(\chi_{9295}(5587,\cdot)\) \(\chi_{9295}(5763,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((-i,-1,e\left(\frac{35}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(2298, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) |