Basic properties
| Modulus: | \(869\) | |
| Conductor: | \(79\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{79}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 869.y
\(\chi_{869}(34,\cdot)\) \(\chi_{869}(122,\cdot)\) \(\chi_{869}(133,\cdot)\) \(\chi_{869}(188,\cdot)\) \(\chi_{869}(221,\cdot)\) \(\chi_{869}(232,\cdot)\) \(\chi_{869}(243,\cdot)\) \(\chi_{869}(265,\cdot)\) \(\chi_{869}(276,\cdot)\) \(\chi_{869}(353,\cdot)\) \(\chi_{869}(364,\cdot)\) \(\chi_{869}(375,\cdot)\) \(\chi_{869}(386,\cdot)\) \(\chi_{869}(430,\cdot)\) \(\chi_{869}(463,\cdot)\) \(\chi_{869}(540,\cdot)\) \(\chi_{869}(551,\cdot)\) \(\chi_{869}(606,\cdot)\) \(\chi_{869}(628,\cdot)\) \(\chi_{869}(639,\cdot)\) \(\chi_{869}(661,\cdot)\) \(\chi_{869}(771,\cdot)\) \(\chi_{869}(793,\cdot)\) \(\chi_{869}(837,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((475,793)\) → \((1,e\left(\frac{25}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 869 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) |