Basic properties
| Modulus: | \(1911\) | |
| Conductor: | \(1911\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 1911.el
\(\chi_{1911}(11,\cdot)\) \(\chi_{1911}(149,\cdot)\) \(\chi_{1911}(158,\cdot)\) \(\chi_{1911}(254,\cdot)\) \(\chi_{1911}(284,\cdot)\) \(\chi_{1911}(431,\cdot)\) \(\chi_{1911}(527,\cdot)\) \(\chi_{1911}(695,\cdot)\) \(\chi_{1911}(800,\cdot)\) \(\chi_{1911}(830,\cdot)\) \(\chi_{1911}(968,\cdot)\) \(\chi_{1911}(977,\cdot)\) \(\chi_{1911}(1073,\cdot)\) \(\chi_{1911}(1103,\cdot)\) \(\chi_{1911}(1241,\cdot)\) \(\chi_{1911}(1250,\cdot)\) \(\chi_{1911}(1346,\cdot)\) \(\chi_{1911}(1376,\cdot)\) \(\chi_{1911}(1514,\cdot)\) \(\chi_{1911}(1523,\cdot)\) \(\chi_{1911}(1619,\cdot)\) \(\chi_{1911}(1649,\cdot)\) \(\chi_{1911}(1787,\cdot)\) \(\chi_{1911}(1796,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1911 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(i\) | \(e\left(\frac{5}{84}\right)\) |