Basic properties
| Modulus: | \(1161\) | |
| Conductor: | \(1161\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1161.cf
\(\chi_{1161}(34,\cdot)\) \(\chi_{1161}(61,\cdot)\) \(\chi_{1161}(76,\cdot)\) \(\chi_{1161}(115,\cdot)\) \(\chi_{1161}(148,\cdot)\) \(\chi_{1161}(175,\cdot)\) \(\chi_{1161}(184,\cdot)\) \(\chi_{1161}(220,\cdot)\) \(\chi_{1161}(241,\cdot)\) \(\chi_{1161}(286,\cdot)\) \(\chi_{1161}(331,\cdot)\) \(\chi_{1161}(364,\cdot)\) \(\chi_{1161}(421,\cdot)\) \(\chi_{1161}(448,\cdot)\) \(\chi_{1161}(463,\cdot)\) \(\chi_{1161}(502,\cdot)\) \(\chi_{1161}(535,\cdot)\) \(\chi_{1161}(562,\cdot)\) \(\chi_{1161}(571,\cdot)\) \(\chi_{1161}(607,\cdot)\) \(\chi_{1161}(628,\cdot)\) \(\chi_{1161}(673,\cdot)\) \(\chi_{1161}(718,\cdot)\) \(\chi_{1161}(751,\cdot)\) \(\chi_{1161}(808,\cdot)\) \(\chi_{1161}(835,\cdot)\) \(\chi_{1161}(850,\cdot)\) \(\chi_{1161}(889,\cdot)\) \(\chi_{1161}(922,\cdot)\) \(\chi_{1161}(949,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((947,433)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{23}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1161 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) |