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.fa
\(\chi_{5915}(79,\cdot)\) \(\chi_{5915}(144,\cdot)\) \(\chi_{5915}(534,\cdot)\) \(\chi_{5915}(599,\cdot)\) \(\chi_{5915}(989,\cdot)\) \(\chi_{5915}(1054,\cdot)\) \(\chi_{5915}(1444,\cdot)\) \(\chi_{5915}(1509,\cdot)\) \(\chi_{5915}(1899,\cdot)\) \(\chi_{5915}(1964,\cdot)\) \(\chi_{5915}(2354,\cdot)\) \(\chi_{5915}(2419,\cdot)\) \(\chi_{5915}(2809,\cdot)\) \(\chi_{5915}(3264,\cdot)\) \(\chi_{5915}(3329,\cdot)\) \(\chi_{5915}(3784,\cdot)\) \(\chi_{5915}(4174,\cdot)\) \(\chi_{5915}(4239,\cdot)\) \(\chi_{5915}(4629,\cdot)\) \(\chi_{5915}(4694,\cdot)\) \(\chi_{5915}(5084,\cdot)\) \(\chi_{5915}(5149,\cdot)\) \(\chi_{5915}(5539,\cdot)\) \(\chi_{5915}(5604,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) |