Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(6008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(750\) | 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 6008.cf
\(\chi_{6008}(19,\cdot)\) \(\chi_{6008}(59,\cdot)\) \(\chi_{6008}(115,\cdot)\) \(\chi_{6008}(123,\cdot)\) \(\chi_{6008}(139,\cdot)\) \(\chi_{6008}(203,\cdot)\) \(\chi_{6008}(211,\cdot)\) \(\chi_{6008}(219,\cdot)\) \(\chi_{6008}(235,\cdot)\) \(\chi_{6008}(339,\cdot)\) \(\chi_{6008}(355,\cdot)\) \(\chi_{6008}(387,\cdot)\) \(\chi_{6008}(411,\cdot)\) \(\chi_{6008}(459,\cdot)\) \(\chi_{6008}(483,\cdot)\) \(\chi_{6008}(587,\cdot)\) \(\chi_{6008}(611,\cdot)\) \(\chi_{6008}(635,\cdot)\) \(\chi_{6008}(707,\cdot)\) \(\chi_{6008}(723,\cdot)\) \(\chi_{6008}(739,\cdot)\) \(\chi_{6008}(755,\cdot)\) \(\chi_{6008}(771,\cdot)\) \(\chi_{6008}(835,\cdot)\) \(\chi_{6008}(843,\cdot)\) \(\chi_{6008}(923,\cdot)\) \(\chi_{6008}(939,\cdot)\) \(\chi_{6008}(947,\cdot)\) \(\chi_{6008}(955,\cdot)\) \(\chi_{6008}(963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{217}{375}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(483, a) \) | \(-1\) | \(1\) | \(e\left(\frac{217}{375}\right)\) | \(e\left(\frac{299}{750}\right)\) | \(e\left(\frac{53}{250}\right)\) | \(e\left(\frac{59}{375}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{347}{750}\right)\) | \(e\left(\frac{733}{750}\right)\) | \(e\left(\frac{143}{375}\right)\) | \(e\left(\frac{31}{375}\right)\) | \(e\left(\frac{593}{750}\right)\) |