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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.ea
\(\chi_{1911}(110,\cdot)\) \(\chi_{1911}(206,\cdot)\) \(\chi_{1911}(353,\cdot)\) \(\chi_{1911}(383,\cdot)\) \(\chi_{1911}(479,\cdot)\) \(\chi_{1911}(488,\cdot)\) \(\chi_{1911}(626,\cdot)\) \(\chi_{1911}(752,\cdot)\) \(\chi_{1911}(761,\cdot)\) \(\chi_{1911}(899,\cdot)\) \(\chi_{1911}(929,\cdot)\) \(\chi_{1911}(1025,\cdot)\) \(\chi_{1911}(1034,\cdot)\) \(\chi_{1911}(1172,\cdot)\) \(\chi_{1911}(1202,\cdot)\) \(\chi_{1911}(1298,\cdot)\) \(\chi_{1911}(1307,\cdot)\) \(\chi_{1911}(1445,\cdot)\) \(\chi_{1911}(1475,\cdot)\) \(\chi_{1911}(1571,\cdot)\) \(\chi_{1911}(1580,\cdot)\) \(\chi_{1911}(1718,\cdot)\) \(\chi_{1911}(1748,\cdot)\) \(\chi_{1911}(1853,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((-1,e\left(\frac{37}{42}\right),e\left(\frac{1}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1911 }(1445, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(i\) | \(e\left(\frac{65}{84}\right)\) |