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.eo
\(\chi_{9295}(54,\cdot)\) \(\chi_{9295}(219,\cdot)\) \(\chi_{9295}(384,\cdot)\) \(\chi_{9295}(604,\cdot)\) \(\chi_{9295}(769,\cdot)\) \(\chi_{9295}(1099,\cdot)\) \(\chi_{9295}(1319,\cdot)\) \(\chi_{9295}(1484,\cdot)\) \(\chi_{9295}(1649,\cdot)\) \(\chi_{9295}(1814,\cdot)\) \(\chi_{9295}(2034,\cdot)\) \(\chi_{9295}(2199,\cdot)\) \(\chi_{9295}(2364,\cdot)\) \(\chi_{9295}(2529,\cdot)\) \(\chi_{9295}(2749,\cdot)\) \(\chi_{9295}(2914,\cdot)\) \(\chi_{9295}(3079,\cdot)\) \(\chi_{9295}(3244,\cdot)\) \(\chi_{9295}(3464,\cdot)\) \(\chi_{9295}(3794,\cdot)\) \(\chi_{9295}(3959,\cdot)\) \(\chi_{9295}(4179,\cdot)\) \(\chi_{9295}(4344,\cdot)\) \(\chi_{9295}(4509,\cdot)\) \(\chi_{9295}(4674,\cdot)\) \(\chi_{9295}(4894,\cdot)\) \(\chi_{9295}(5059,\cdot)\) \(\chi_{9295}(5224,\cdot)\) \(\chi_{9295}(5609,\cdot)\) \(\chi_{9295}(5774,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((-1,-1,e\left(\frac{61}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(54, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) |