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.ep
\(\chi_{1911}(59,\cdot)\) \(\chi_{1911}(89,\cdot)\) \(\chi_{1911}(236,\cdot)\) \(\chi_{1911}(332,\cdot)\) \(\chi_{1911}(500,\cdot)\) \(\chi_{1911}(605,\cdot)\) \(\chi_{1911}(635,\cdot)\) \(\chi_{1911}(773,\cdot)\) \(\chi_{1911}(782,\cdot)\) \(\chi_{1911}(878,\cdot)\) \(\chi_{1911}(908,\cdot)\) \(\chi_{1911}(1046,\cdot)\) \(\chi_{1911}(1055,\cdot)\) \(\chi_{1911}(1151,\cdot)\) \(\chi_{1911}(1181,\cdot)\) \(\chi_{1911}(1319,\cdot)\) \(\chi_{1911}(1328,\cdot)\) \(\chi_{1911}(1424,\cdot)\) \(\chi_{1911}(1454,\cdot)\) \(\chi_{1911}(1592,\cdot)\) \(\chi_{1911}(1601,\cdot)\) \(\chi_{1911}(1727,\cdot)\) \(\chi_{1911}(1865,\cdot)\) \(\chi_{1911}(1874,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((-1,e\left(\frac{29}{42}\right),e\left(\frac{7}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1911 }(1181, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{71}{84}\right)\) |