Basic properties
| Modulus: | \(1143\) | |
| Conductor: | \(1143\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1143.cc
\(\chi_{1143}(49,\cdot)\) \(\chi_{1143}(70,\cdot)\) \(\chi_{1143}(79,\cdot)\) \(\chi_{1143}(115,\cdot)\) \(\chi_{1143}(124,\cdot)\) \(\chi_{1143}(142,\cdot)\) \(\chi_{1143}(148,\cdot)\) \(\chi_{1143}(187,\cdot)\) \(\chi_{1143}(211,\cdot)\) \(\chi_{1143}(265,\cdot)\) \(\chi_{1143}(328,\cdot)\) \(\chi_{1143}(358,\cdot)\) \(\chi_{1143}(367,\cdot)\) \(\chi_{1143}(394,\cdot)\) \(\chi_{1143}(412,\cdot)\) \(\chi_{1143}(463,\cdot)\) \(\chi_{1143}(502,\cdot)\) \(\chi_{1143}(517,\cdot)\) \(\chi_{1143}(526,\cdot)\) \(\chi_{1143}(538,\cdot)\) \(\chi_{1143}(544,\cdot)\) \(\chi_{1143}(580,\cdot)\) \(\chi_{1143}(628,\cdot)\) \(\chi_{1143}(652,\cdot)\) \(\chi_{1143}(679,\cdot)\) \(\chi_{1143}(733,\cdot)\) \(\chi_{1143}(796,\cdot)\) \(\chi_{1143}(850,\cdot)\) \(\chi_{1143}(931,\cdot)\) \(\chi_{1143}(958,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((128,892)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{52}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1143 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) |