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.ft
\(\chi_{5915}(74,\cdot)\) \(\chi_{5915}(289,\cdot)\) \(\chi_{5915}(744,\cdot)\) \(\chi_{5915}(984,\cdot)\) \(\chi_{5915}(1199,\cdot)\) \(\chi_{5915}(1439,\cdot)\) \(\chi_{5915}(1654,\cdot)\) \(\chi_{5915}(1894,\cdot)\) \(\chi_{5915}(2109,\cdot)\) \(\chi_{5915}(2349,\cdot)\) \(\chi_{5915}(2564,\cdot)\) \(\chi_{5915}(2804,\cdot)\) \(\chi_{5915}(3259,\cdot)\) \(\chi_{5915}(3474,\cdot)\) \(\chi_{5915}(3714,\cdot)\) \(\chi_{5915}(3929,\cdot)\) \(\chi_{5915}(4169,\cdot)\) \(\chi_{5915}(4384,\cdot)\) \(\chi_{5915}(4624,\cdot)\) \(\chi_{5915}(4839,\cdot)\) \(\chi_{5915}(5079,\cdot)\) \(\chi_{5915}(5294,\cdot)\) \(\chi_{5915}(5534,\cdot)\) \(\chi_{5915}(5749,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{38}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(74, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) |