Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(9295\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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.df
\(\chi_{9295}(417,\cdot)\) \(\chi_{9295}(703,\cdot)\) \(\chi_{9295}(1132,\cdot)\) \(\chi_{9295}(1418,\cdot)\) \(\chi_{9295}(1847,\cdot)\) \(\chi_{9295}(2133,\cdot)\) \(\chi_{9295}(2562,\cdot)\) \(\chi_{9295}(2848,\cdot)\) \(\chi_{9295}(3277,\cdot)\) \(\chi_{9295}(3563,\cdot)\) \(\chi_{9295}(3992,\cdot)\) \(\chi_{9295}(4278,\cdot)\) \(\chi_{9295}(4707,\cdot)\) \(\chi_{9295}(4993,\cdot)\) \(\chi_{9295}(5422,\cdot)\) \(\chi_{9295}(5708,\cdot)\) \(\chi_{9295}(6137,\cdot)\) \(\chi_{9295}(6852,\cdot)\) \(\chi_{9295}(7138,\cdot)\) \(\chi_{9295}(7567,\cdot)\) \(\chi_{9295}(7853,\cdot)\) \(\chi_{9295}(8568,\cdot)\) \(\chi_{9295}(8997,\cdot)\) \(\chi_{9295}(9283,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((7437,4226,6931)\) → \((i,-1,e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(417, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) |