Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(261,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.eg
\(\chi_{5915}(261,\cdot)\) \(\chi_{5915}(326,\cdot)\) \(\chi_{5915}(716,\cdot)\) \(\chi_{5915}(781,\cdot)\) \(\chi_{5915}(1171,\cdot)\) \(\chi_{5915}(1236,\cdot)\) \(\chi_{5915}(1626,\cdot)\) \(\chi_{5915}(2081,\cdot)\) \(\chi_{5915}(2146,\cdot)\) \(\chi_{5915}(2601,\cdot)\) \(\chi_{5915}(2991,\cdot)\) \(\chi_{5915}(3056,\cdot)\) \(\chi_{5915}(3446,\cdot)\) \(\chi_{5915}(3511,\cdot)\) \(\chi_{5915}(3901,\cdot)\) \(\chi_{5915}(3966,\cdot)\) \(\chi_{5915}(4356,\cdot)\) \(\chi_{5915}(4421,\cdot)\) \(\chi_{5915}(4811,\cdot)\) \(\chi_{5915}(4876,\cdot)\) \(\chi_{5915}(5266,\cdot)\) \(\chi_{5915}(5331,\cdot)\) \(\chi_{5915}(5721,\cdot)\) \(\chi_{5915}(5786,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((2367,5071,1016)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(261, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) |