Basic properties
Modulus: | \(6008\) | |
Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(750\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3004}(623,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.ci
\(\chi_{6008}(15,\cdot)\) \(\chi_{6008}(31,\cdot)\) \(\chi_{6008}(39,\cdot)\) \(\chi_{6008}(55,\cdot)\) \(\chi_{6008}(63,\cdot)\) \(\chi_{6008}(79,\cdot)\) \(\chi_{6008}(103,\cdot)\) \(\chi_{6008}(135,\cdot)\) \(\chi_{6008}(143,\cdot)\) \(\chi_{6008}(159,\cdot)\) \(\chi_{6008}(175,\cdot)\) \(\chi_{6008}(231,\cdot)\) \(\chi_{6008}(263,\cdot)\) \(\chi_{6008}(279,\cdot)\) \(\chi_{6008}(335,\cdot)\) \(\chi_{6008}(351,\cdot)\) \(\chi_{6008}(375,\cdot)\) \(\chi_{6008}(431,\cdot)\) \(\chi_{6008}(487,\cdot)\) \(\chi_{6008}(495,\cdot)\) \(\chi_{6008}(591,\cdot)\) \(\chi_{6008}(599,\cdot)\) \(\chi_{6008}(607,\cdot)\) \(\chi_{6008}(623,\cdot)\) \(\chi_{6008}(647,\cdot)\) \(\chi_{6008}(711,\cdot)\) \(\chi_{6008}(735,\cdot)\) \(\chi_{6008}(775,\cdot)\) \(\chi_{6008}(839,\cdot)\) \(\chi_{6008}(847,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,1,e\left(\frac{287}{750}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(623, a) \) | \(1\) | \(1\) | \(e\left(\frac{331}{375}\right)\) | \(e\left(\frac{241}{375}\right)\) | \(e\left(\frac{77}{125}\right)\) | \(e\left(\frac{287}{375}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{148}{375}\right)\) | \(e\left(\frac{197}{375}\right)\) | \(e\left(\frac{673}{750}\right)\) | \(e\left(\frac{41}{750}\right)\) | \(e\left(\frac{187}{375}\right)\) |