Basic properties
Modulus: | \(1911\) | |
Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{637}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.ej
\(\chi_{1911}(76,\cdot)\) \(\chi_{1911}(202,\cdot)\) \(\chi_{1911}(223,\cdot)\) \(\chi_{1911}(349,\cdot)\) \(\chi_{1911}(370,\cdot)\) \(\chi_{1911}(475,\cdot)\) \(\chi_{1911}(496,\cdot)\) \(\chi_{1911}(622,\cdot)\) \(\chi_{1911}(643,\cdot)\) \(\chi_{1911}(748,\cdot)\) \(\chi_{1911}(769,\cdot)\) \(\chi_{1911}(895,\cdot)\) \(\chi_{1911}(916,\cdot)\) \(\chi_{1911}(1021,\cdot)\) \(\chi_{1911}(1042,\cdot)\) \(\chi_{1911}(1168,\cdot)\) \(\chi_{1911}(1189,\cdot)\) \(\chi_{1911}(1294,\cdot)\) \(\chi_{1911}(1315,\cdot)\) \(\chi_{1911}(1441,\cdot)\) \(\chi_{1911}(1462,\cdot)\) \(\chi_{1911}(1588,\cdot)\) \(\chi_{1911}(1735,\cdot)\) \(\chi_{1911}(1840,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{7}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1911 }(76, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{84}\right)\) |