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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1015.cx
\(\chi_{1015}(39,\cdot)\) \(\chi_{1015}(44,\cdot)\) \(\chi_{1015}(79,\cdot)\) \(\chi_{1015}(114,\cdot)\) \(\chi_{1015}(184,\cdot)\) \(\chi_{1015}(214,\cdot)\) \(\chi_{1015}(359,\cdot)\) \(\chi_{1015}(424,\cdot)\) \(\chi_{1015}(569,\cdot)\) \(\chi_{1015}(599,\cdot)\) \(\chi_{1015}(669,\cdot)\) \(\chi_{1015}(704,\cdot)\) \(\chi_{1015}(739,\cdot)\) \(\chi_{1015}(744,\cdot)\) \(\chi_{1015}(809,\cdot)\) \(\chi_{1015}(814,\cdot)\) \(\chi_{1015}(844,\cdot)\) \(\chi_{1015}(849,\cdot)\) \(\chi_{1015}(884,\cdot)\) \(\chi_{1015}(914,\cdot)\) \(\chi_{1015}(949,\cdot)\) \(\chi_{1015}(954,\cdot)\) \(\chi_{1015}(984,\cdot)\) \(\chi_{1015}(989,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{27}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1015 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) |