Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.fr
\(\chi_{5915}(179,\cdot)\) \(\chi_{5915}(394,\cdot)\) \(\chi_{5915}(634,\cdot)\) \(\chi_{5915}(849,\cdot)\) \(\chi_{5915}(1089,\cdot)\) \(\chi_{5915}(1304,\cdot)\) \(\chi_{5915}(1759,\cdot)\) \(\chi_{5915}(1999,\cdot)\) \(\chi_{5915}(2214,\cdot)\) \(\chi_{5915}(2454,\cdot)\) \(\chi_{5915}(2669,\cdot)\) \(\chi_{5915}(2909,\cdot)\) \(\chi_{5915}(3124,\cdot)\) \(\chi_{5915}(3364,\cdot)\) \(\chi_{5915}(3579,\cdot)\) \(\chi_{5915}(3819,\cdot)\) \(\chi_{5915}(4274,\cdot)\) \(\chi_{5915}(4489,\cdot)\) \(\chi_{5915}(4729,\cdot)\) \(\chi_{5915}(4944,\cdot)\) \(\chi_{5915}(5184,\cdot)\) \(\chi_{5915}(5399,\cdot)\) \(\chi_{5915}(5639,\cdot)\) \(\chi_{5915}(5854,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{5}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) |