Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | 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 6003.cp
\(\chi_{6003}(160,\cdot)\) \(\chi_{6003}(229,\cdot)\) \(\chi_{6003}(367,\cdot)\) \(\chi_{6003}(781,\cdot)\) \(\chi_{6003}(988,\cdot)\) \(\chi_{6003}(1402,\cdot)\) \(\chi_{6003}(1471,\cdot)\) \(\chi_{6003}(1609,\cdot)\) \(\chi_{6003}(1816,\cdot)\) \(\chi_{6003}(2230,\cdot)\) \(\chi_{6003}(2299,\cdot)\) \(\chi_{6003}(3472,\cdot)\) \(\chi_{6003}(3541,\cdot)\) \(\chi_{6003}(3955,\cdot)\) \(\chi_{6003}(4162,\cdot)\) \(\chi_{6003}(4300,\cdot)\) \(\chi_{6003}(4369,\cdot)\) \(\chi_{6003}(4783,\cdot)\) \(\chi_{6003}(4990,\cdot)\) \(\chi_{6003}(5404,\cdot)\) \(\chi_{6003}(5542,\cdot)\) \(\chi_{6003}(5611,\cdot)\) \(\chi_{6003}(5818,\cdot)\) \(\chi_{6003}(5956,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{11}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(5818, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) |