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.ch
\(\chi_{1161}(22,\cdot)\) \(\chi_{1161}(70,\cdot)\) \(\chi_{1161}(88,\cdot)\) \(\chi_{1161}(94,\cdot)\) \(\chi_{1161}(151,\cdot)\) \(\chi_{1161}(211,\cdot)\) \(\chi_{1161}(223,\cdot)\) \(\chi_{1161}(247,\cdot)\) \(\chi_{1161}(328,\cdot)\) \(\chi_{1161}(340,\cdot)\) \(\chi_{1161}(346,\cdot)\) \(\chi_{1161}(376,\cdot)\) \(\chi_{1161}(409,\cdot)\) \(\chi_{1161}(457,\cdot)\) \(\chi_{1161}(475,\cdot)\) \(\chi_{1161}(481,\cdot)\) \(\chi_{1161}(538,\cdot)\) \(\chi_{1161}(598,\cdot)\) \(\chi_{1161}(610,\cdot)\) \(\chi_{1161}(634,\cdot)\) \(\chi_{1161}(715,\cdot)\) \(\chi_{1161}(727,\cdot)\) \(\chi_{1161}(733,\cdot)\) \(\chi_{1161}(763,\cdot)\) \(\chi_{1161}(796,\cdot)\) \(\chi_{1161}(844,\cdot)\) \(\chi_{1161}(862,\cdot)\) \(\chi_{1161}(868,\cdot)\) \(\chi_{1161}(925,\cdot)\) \(\chi_{1161}(985,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((947,433)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1161 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) |