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 \(\chi_{637}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.ei
\(\chi_{1911}(73,\cdot)\) \(\chi_{1911}(187,\cdot)\) \(\chi_{1911}(229,\cdot)\) \(\chi_{1911}(304,\cdot)\) \(\chi_{1911}(346,\cdot)\) \(\chi_{1911}(502,\cdot)\) \(\chi_{1911}(577,\cdot)\) \(\chi_{1911}(733,\cdot)\) \(\chi_{1911}(775,\cdot)\) \(\chi_{1911}(850,\cdot)\) \(\chi_{1911}(892,\cdot)\) \(\chi_{1911}(1006,\cdot)\) \(\chi_{1911}(1123,\cdot)\) \(\chi_{1911}(1165,\cdot)\) \(\chi_{1911}(1279,\cdot)\) \(\chi_{1911}(1321,\cdot)\) \(\chi_{1911}(1396,\cdot)\) \(\chi_{1911}(1438,\cdot)\) \(\chi_{1911}(1552,\cdot)\) \(\chi_{1911}(1594,\cdot)\) \(\chi_{1911}(1669,\cdot)\) \(\chi_{1911}(1711,\cdot)\) \(\chi_{1911}(1825,\cdot)\) \(\chi_{1911}(1867,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{37}{42}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1911 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{3}{28}\right)\) |