Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(186,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.fu
\(\chi_{5915}(186,\cdot)\) \(\chi_{5915}(296,\cdot)\) \(\chi_{5915}(641,\cdot)\) \(\chi_{5915}(751,\cdot)\) \(\chi_{5915}(1096,\cdot)\) \(\chi_{5915}(1551,\cdot)\) \(\chi_{5915}(1661,\cdot)\) \(\chi_{5915}(2116,\cdot)\) \(\chi_{5915}(2461,\cdot)\) \(\chi_{5915}(2571,\cdot)\) \(\chi_{5915}(2916,\cdot)\) \(\chi_{5915}(3026,\cdot)\) \(\chi_{5915}(3371,\cdot)\) \(\chi_{5915}(3481,\cdot)\) \(\chi_{5915}(3826,\cdot)\) \(\chi_{5915}(3936,\cdot)\) \(\chi_{5915}(4281,\cdot)\) \(\chi_{5915}(4391,\cdot)\) \(\chi_{5915}(4736,\cdot)\) \(\chi_{5915}(4846,\cdot)\) \(\chi_{5915}(5191,\cdot)\) \(\chi_{5915}(5301,\cdot)\) \(\chi_{5915}(5646,\cdot)\) \(\chi_{5915}(5756,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(186, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) |