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.cg
\(\chi_{1161}(11,\cdot)\) \(\chi_{1161}(41,\cdot)\) \(\chi_{1161}(47,\cdot)\) \(\chi_{1161}(59,\cdot)\) \(\chi_{1161}(140,\cdot)\) \(\chi_{1161}(164,\cdot)\) \(\chi_{1161}(176,\cdot)\) \(\chi_{1161}(236,\cdot)\) \(\chi_{1161}(293,\cdot)\) \(\chi_{1161}(299,\cdot)\) \(\chi_{1161}(317,\cdot)\) \(\chi_{1161}(365,\cdot)\) \(\chi_{1161}(398,\cdot)\) \(\chi_{1161}(428,\cdot)\) \(\chi_{1161}(434,\cdot)\) \(\chi_{1161}(446,\cdot)\) \(\chi_{1161}(527,\cdot)\) \(\chi_{1161}(551,\cdot)\) \(\chi_{1161}(563,\cdot)\) \(\chi_{1161}(623,\cdot)\) \(\chi_{1161}(680,\cdot)\) \(\chi_{1161}(686,\cdot)\) \(\chi_{1161}(704,\cdot)\) \(\chi_{1161}(752,\cdot)\) \(\chi_{1161}(785,\cdot)\) \(\chi_{1161}(815,\cdot)\) \(\chi_{1161}(821,\cdot)\) \(\chi_{1161}(833,\cdot)\) \(\chi_{1161}(914,\cdot)\) \(\chi_{1161}(938,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((947,433)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1161 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{2}{63}\right)\) |