Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(5915\) | 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 5915.eo
\(\chi_{5915}(27,\cdot)\) \(\chi_{5915}(118,\cdot)\) \(\chi_{5915}(482,\cdot)\) \(\chi_{5915}(573,\cdot)\) \(\chi_{5915}(937,\cdot)\) \(\chi_{5915}(1028,\cdot)\) \(\chi_{5915}(1392,\cdot)\) \(\chi_{5915}(1483,\cdot)\) \(\chi_{5915}(1847,\cdot)\) \(\chi_{5915}(1938,\cdot)\) \(\chi_{5915}(2302,\cdot)\) \(\chi_{5915}(2393,\cdot)\) \(\chi_{5915}(2757,\cdot)\) \(\chi_{5915}(2848,\cdot)\) \(\chi_{5915}(3303,\cdot)\) \(\chi_{5915}(3667,\cdot)\) \(\chi_{5915}(3758,\cdot)\) \(\chi_{5915}(4122,\cdot)\) \(\chi_{5915}(4213,\cdot)\) \(\chi_{5915}(4577,\cdot)\) \(\chi_{5915}(4668,\cdot)\) \(\chi_{5915}(5032,\cdot)\) \(\chi_{5915}(5123,\cdot)\) \(\chi_{5915}(5487,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-i,-1,e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(1028, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) |