Basic properties
| Modulus: | \(1143\) | |
| Conductor: | \(1143\) | 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 1143.ch
\(\chi_{1143}(11,\cdot)\) \(\chi_{1143}(74,\cdot)\) \(\chi_{1143}(104,\cdot)\) \(\chi_{1143}(113,\cdot)\) \(\chi_{1143}(140,\cdot)\) \(\chi_{1143}(158,\cdot)\) \(\chi_{1143}(209,\cdot)\) \(\chi_{1143}(248,\cdot)\) \(\chi_{1143}(263,\cdot)\) \(\chi_{1143}(272,\cdot)\) \(\chi_{1143}(284,\cdot)\) \(\chi_{1143}(290,\cdot)\) \(\chi_{1143}(326,\cdot)\) \(\chi_{1143}(374,\cdot)\) \(\chi_{1143}(398,\cdot)\) \(\chi_{1143}(425,\cdot)\) \(\chi_{1143}(479,\cdot)\) \(\chi_{1143}(542,\cdot)\) \(\chi_{1143}(596,\cdot)\) \(\chi_{1143}(677,\cdot)\) \(\chi_{1143}(704,\cdot)\) \(\chi_{1143}(716,\cdot)\) \(\chi_{1143}(788,\cdot)\) \(\chi_{1143}(797,\cdot)\) \(\chi_{1143}(803,\cdot)\) \(\chi_{1143}(824,\cdot)\) \(\chi_{1143}(833,\cdot)\) \(\chi_{1143}(938,\cdot)\) \(\chi_{1143}(959,\cdot)\) \(\chi_{1143}(968,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((128,892)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{34}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1143 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) |