Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1859}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.ev
\(\chi_{9295}(76,\cdot)\) \(\chi_{9295}(241,\cdot)\) \(\chi_{9295}(461,\cdot)\) \(\chi_{9295}(626,\cdot)\) \(\chi_{9295}(791,\cdot)\) \(\chi_{9295}(956,\cdot)\) \(\chi_{9295}(1176,\cdot)\) \(\chi_{9295}(1341,\cdot)\) \(\chi_{9295}(1506,\cdot)\) \(\chi_{9295}(1891,\cdot)\) \(\chi_{9295}(2056,\cdot)\) \(\chi_{9295}(2221,\cdot)\) \(\chi_{9295}(2386,\cdot)\) \(\chi_{9295}(2606,\cdot)\) \(\chi_{9295}(2771,\cdot)\) \(\chi_{9295}(2936,\cdot)\) \(\chi_{9295}(3101,\cdot)\) \(\chi_{9295}(3321,\cdot)\) \(\chi_{9295}(3486,\cdot)\) \(\chi_{9295}(3651,\cdot)\) \(\chi_{9295}(3816,\cdot)\) \(\chi_{9295}(4036,\cdot)\) \(\chi_{9295}(4201,\cdot)\) \(\chi_{9295}(4366,\cdot)\) \(\chi_{9295}(4531,\cdot)\) \(\chi_{9295}(4916,\cdot)\) \(\chi_{9295}(5081,\cdot)\) \(\chi_{9295}(5246,\cdot)\) \(\chi_{9295}(5466,\cdot)\) \(\chi_{9295}(5631,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((1,-1,e\left(\frac{67}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(76, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |