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.ci
\(\chi_{1143}(7,\cdot)\) \(\chi_{1143}(58,\cdot)\) \(\chi_{1143}(85,\cdot)\) \(\chi_{1143}(97,\cdot)\) \(\chi_{1143}(133,\cdot)\) \(\chi_{1143}(166,\cdot)\) \(\chi_{1143}(220,\cdot)\) \(\chi_{1143}(223,\cdot)\) \(\chi_{1143}(241,\cdot)\) \(\chi_{1143}(268,\cdot)\) \(\chi_{1143}(277,\cdot)\) \(\chi_{1143}(283,\cdot)\) \(\chi_{1143}(337,\cdot)\) \(\chi_{1143}(364,\cdot)\) \(\chi_{1143}(436,\cdot)\) \(\chi_{1143}(448,\cdot)\) \(\chi_{1143}(472,\cdot)\) \(\chi_{1143}(490,\cdot)\) \(\chi_{1143}(493,\cdot)\) \(\chi_{1143}(499,\cdot)\) \(\chi_{1143}(511,\cdot)\) \(\chi_{1143}(520,\cdot)\) \(\chi_{1143}(553,\cdot)\) \(\chi_{1143}(556,\cdot)\) \(\chi_{1143}(565,\cdot)\) \(\chi_{1143}(688,\cdot)\) \(\chi_{1143}(691,\cdot)\) \(\chi_{1143}(700,\cdot)\) \(\chi_{1143}(727,\cdot)\) \(\chi_{1143}(736,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((128,892)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{115}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1143 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{11}{21}\right)\) |