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.cb
\(\chi_{1143}(13,\cdot)\) \(\chi_{1143}(31,\cdot)\) \(\chi_{1143}(34,\cdot)\) \(\chi_{1143}(88,\cdot)\) \(\chi_{1143}(121,\cdot)\) \(\chi_{1143}(157,\cdot)\) \(\chi_{1143}(169,\cdot)\) \(\chi_{1143}(196,\cdot)\) \(\chi_{1143}(247,\cdot)\) \(\chi_{1143}(295,\cdot)\) \(\chi_{1143}(430,\cdot)\) \(\chi_{1143}(529,\cdot)\) \(\chi_{1143}(589,\cdot)\) \(\chi_{1143}(592,\cdot)\) \(\chi_{1143}(646,\cdot)\) \(\chi_{1143}(661,\cdot)\) \(\chi_{1143}(670,\cdot)\) \(\chi_{1143}(697,\cdot)\) \(\chi_{1143}(706,\cdot)\) \(\chi_{1143}(709,\cdot)\) \(\chi_{1143}(832,\cdot)\) \(\chi_{1143}(841,\cdot)\) \(\chi_{1143}(844,\cdot)\) \(\chi_{1143}(877,\cdot)\) \(\chi_{1143}(886,\cdot)\) \(\chi_{1143}(898,\cdot)\) \(\chi_{1143}(904,\cdot)\) \(\chi_{1143}(907,\cdot)\) \(\chi_{1143}(925,\cdot)\) \(\chi_{1143}(949,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((128,892)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1143 }(592, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) |