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.cd
\(\chi_{1161}(14,\cdot)\) \(\chi_{1161}(38,\cdot)\) \(\chi_{1161}(68,\cdot)\) \(\chi_{1161}(74,\cdot)\) \(\chi_{1161}(83,\cdot)\) \(\chi_{1161}(95,\cdot)\) \(\chi_{1161}(110,\cdot)\) \(\chi_{1161}(182,\cdot)\) \(\chi_{1161}(185,\cdot)\) \(\chi_{1161}(230,\cdot)\) \(\chi_{1161}(275,\cdot)\) \(\chi_{1161}(281,\cdot)\) \(\chi_{1161}(401,\cdot)\) \(\chi_{1161}(425,\cdot)\) \(\chi_{1161}(455,\cdot)\) \(\chi_{1161}(461,\cdot)\) \(\chi_{1161}(470,\cdot)\) \(\chi_{1161}(482,\cdot)\) \(\chi_{1161}(497,\cdot)\) \(\chi_{1161}(569,\cdot)\) \(\chi_{1161}(572,\cdot)\) \(\chi_{1161}(617,\cdot)\) \(\chi_{1161}(662,\cdot)\) \(\chi_{1161}(668,\cdot)\) \(\chi_{1161}(788,\cdot)\) \(\chi_{1161}(812,\cdot)\) \(\chi_{1161}(842,\cdot)\) \(\chi_{1161}(848,\cdot)\) \(\chi_{1161}(857,\cdot)\) \(\chi_{1161}(869,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((947,433)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{10}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1161 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{13}{63}\right)\) |