Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1859}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.db
\(\chi_{9295}(21,\cdot)\) \(\chi_{9295}(681,\cdot)\) \(\chi_{9295}(736,\cdot)\) \(\chi_{9295}(1396,\cdot)\) \(\chi_{9295}(2111,\cdot)\) \(\chi_{9295}(2166,\cdot)\) \(\chi_{9295}(2826,\cdot)\) \(\chi_{9295}(2881,\cdot)\) \(\chi_{9295}(3541,\cdot)\) \(\chi_{9295}(3596,\cdot)\) \(\chi_{9295}(4256,\cdot)\) \(\chi_{9295}(4311,\cdot)\) \(\chi_{9295}(5026,\cdot)\) \(\chi_{9295}(5686,\cdot)\) \(\chi_{9295}(5741,\cdot)\) \(\chi_{9295}(6401,\cdot)\) \(\chi_{9295}(6456,\cdot)\) \(\chi_{9295}(7116,\cdot)\) \(\chi_{9295}(7171,\cdot)\) \(\chi_{9295}(7831,\cdot)\) \(\chi_{9295}(7886,\cdot)\) \(\chi_{9295}(8546,\cdot)\) \(\chi_{9295}(8601,\cdot)\) \(\chi_{9295}(9261,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((7437,4226,6931)\) → \((1,-1,e\left(\frac{25}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) |