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.ek
\(\chi_{5915}(34,\cdot)\) \(\chi_{5915}(174,\cdot)\) \(\chi_{5915}(489,\cdot)\) \(\chi_{5915}(629,\cdot)\) \(\chi_{5915}(1399,\cdot)\) \(\chi_{5915}(1539,\cdot)\) \(\chi_{5915}(1854,\cdot)\) \(\chi_{5915}(1994,\cdot)\) \(\chi_{5915}(2309,\cdot)\) \(\chi_{5915}(2449,\cdot)\) \(\chi_{5915}(2764,\cdot)\) \(\chi_{5915}(2904,\cdot)\) \(\chi_{5915}(3219,\cdot)\) \(\chi_{5915}(3359,\cdot)\) \(\chi_{5915}(3674,\cdot)\) \(\chi_{5915}(3814,\cdot)\) \(\chi_{5915}(4129,\cdot)\) \(\chi_{5915}(4269,\cdot)\) \(\chi_{5915}(4584,\cdot)\) \(\chi_{5915}(4724,\cdot)\) \(\chi_{5915}(5039,\cdot)\) \(\chi_{5915}(5179,\cdot)\) \(\chi_{5915}(5494,\cdot)\) \(\chi_{5915}(5634,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,-1,e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(34, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) |