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.eu
\(\chi_{5915}(4,\cdot)\) \(\chi_{5915}(114,\cdot)\) \(\chi_{5915}(459,\cdot)\) \(\chi_{5915}(569,\cdot)\) \(\chi_{5915}(914,\cdot)\) \(\chi_{5915}(1024,\cdot)\) \(\chi_{5915}(1369,\cdot)\) \(\chi_{5915}(1479,\cdot)\) \(\chi_{5915}(1824,\cdot)\) \(\chi_{5915}(1934,\cdot)\) \(\chi_{5915}(2279,\cdot)\) \(\chi_{5915}(2734,\cdot)\) \(\chi_{5915}(2844,\cdot)\) \(\chi_{5915}(3299,\cdot)\) \(\chi_{5915}(3644,\cdot)\) \(\chi_{5915}(3754,\cdot)\) \(\chi_{5915}(4099,\cdot)\) \(\chi_{5915}(4209,\cdot)\) \(\chi_{5915}(4554,\cdot)\) \(\chi_{5915}(4664,\cdot)\) \(\chi_{5915}(5009,\cdot)\) \(\chi_{5915}(5119,\cdot)\) \(\chi_{5915}(5464,\cdot)\) \(\chi_{5915}(5574,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) |