Basic properties
Modulus: | \(1015\) | |
Conductor: | \(203\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{203}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1015.cy
\(\chi_{1015}(11,\cdot)\) \(\chi_{1015}(156,\cdot)\) \(\chi_{1015}(221,\cdot)\) \(\chi_{1015}(366,\cdot)\) \(\chi_{1015}(396,\cdot)\) \(\chi_{1015}(466,\cdot)\) \(\chi_{1015}(501,\cdot)\) \(\chi_{1015}(536,\cdot)\) \(\chi_{1015}(541,\cdot)\) \(\chi_{1015}(606,\cdot)\) \(\chi_{1015}(611,\cdot)\) \(\chi_{1015}(641,\cdot)\) \(\chi_{1015}(646,\cdot)\) \(\chi_{1015}(681,\cdot)\) \(\chi_{1015}(711,\cdot)\) \(\chi_{1015}(746,\cdot)\) \(\chi_{1015}(751,\cdot)\) \(\chi_{1015}(781,\cdot)\) \(\chi_{1015}(786,\cdot)\) \(\chi_{1015}(851,\cdot)\) \(\chi_{1015}(856,\cdot)\) \(\chi_{1015}(891,\cdot)\) \(\chi_{1015}(926,\cdot)\) \(\chi_{1015}(996,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{25}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1015 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{19}{21}\right)\) |