Basic properties
Modulus: | \(1015\) | |
Conductor: | \(1015\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1015.cr
\(\chi_{1015}(37,\cdot)\) \(\chi_{1015}(102,\cdot)\) \(\chi_{1015}(142,\cdot)\) \(\chi_{1015}(172,\cdot)\) \(\chi_{1015}(193,\cdot)\) \(\chi_{1015}(242,\cdot)\) \(\chi_{1015}(247,\cdot)\) \(\chi_{1015}(263,\cdot)\) \(\chi_{1015}(317,\cdot)\) \(\chi_{1015}(333,\cdot)\) \(\chi_{1015}(338,\cdot)\) \(\chi_{1015}(387,\cdot)\) \(\chi_{1015}(408,\cdot)\) \(\chi_{1015}(438,\cdot)\) \(\chi_{1015}(478,\cdot)\) \(\chi_{1015}(543,\cdot)\) \(\chi_{1015}(583,\cdot)\) \(\chi_{1015}(627,\cdot)\) \(\chi_{1015}(688,\cdot)\) \(\chi_{1015}(772,\cdot)\) \(\chi_{1015}(823,\cdot)\) \(\chi_{1015}(907,\cdot)\) \(\chi_{1015}(968,\cdot)\) \(\chi_{1015}(1012,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{3}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1015 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) |