Basic properties
| Modulus: | \(1666\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1666.bg
\(\chi_{1666}(81,\cdot)\) \(\chi_{1666}(123,\cdot)\) \(\chi_{1666}(149,\cdot)\) \(\chi_{1666}(191,\cdot)\) \(\chi_{1666}(319,\cdot)\) \(\chi_{1666}(387,\cdot)\) \(\chi_{1666}(429,\cdot)\) \(\chi_{1666}(599,\cdot)\) \(\chi_{1666}(625,\cdot)\) \(\chi_{1666}(795,\cdot)\) \(\chi_{1666}(837,\cdot)\) \(\chi_{1666}(905,\cdot)\) \(\chi_{1666}(1033,\cdot)\) \(\chi_{1666}(1075,\cdot)\) \(\chi_{1666}(1101,\cdot)\) \(\chi_{1666}(1143,\cdot)\) \(\chi_{1666}(1271,\cdot)\) \(\chi_{1666}(1313,\cdot)\) \(\chi_{1666}(1339,\cdot)\) \(\chi_{1666}(1381,\cdot)\) \(\chi_{1666}(1509,\cdot)\) \(\chi_{1666}(1551,\cdot)\) \(\chi_{1666}(1577,\cdot)\) \(\chi_{1666}(1619,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((885,785)\) → \((e\left(\frac{2}{21}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1666 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) |