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 \(\chi_{3004}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.cg
\(\chi_{6008}(23,\cdot)\) \(\chi_{6008}(47,\cdot)\) \(\chi_{6008}(87,\cdot)\) \(\chi_{6008}(95,\cdot)\) \(\chi_{6008}(127,\cdot)\) \(\chi_{6008}(167,\cdot)\) \(\chi_{6008}(199,\cdot)\) \(\chi_{6008}(247,\cdot)\) \(\chi_{6008}(255,\cdot)\) \(\chi_{6008}(295,\cdot)\) \(\chi_{6008}(311,\cdot)\) \(\chi_{6008}(319,\cdot)\) \(\chi_{6008}(439,\cdot)\) \(\chi_{6008}(479,\cdot)\) \(\chi_{6008}(511,\cdot)\) \(\chi_{6008}(527,\cdot)\) \(\chi_{6008}(559,\cdot)\) \(\chi_{6008}(615,\cdot)\) \(\chi_{6008}(655,\cdot)\) \(\chi_{6008}(663,\cdot)\) \(\chi_{6008}(727,\cdot)\) \(\chi_{6008}(767,\cdot)\) \(\chi_{6008}(791,\cdot)\) \(\chi_{6008}(855,\cdot)\) \(\chi_{6008}(879,\cdot)\) \(\chi_{6008}(895,\cdot)\) \(\chi_{6008}(903,\cdot)\) \(\chi_{6008}(911,\cdot)\) \(\chi_{6008}(1007,\cdot)\) \(\chi_{6008}(1015,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,1,e\left(\frac{266}{375}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{157}{750}\right)\) | \(e\left(\frac{26}{375}\right)\) | \(e\left(\frac{69}{250}\right)\) | \(e\left(\frac{157}{375}\right)\) | \(e\left(\frac{101}{150}\right)\) | \(e\left(\frac{128}{375}\right)\) | \(e\left(\frac{209}{750}\right)\) | \(e\left(\frac{139}{375}\right)\) | \(e\left(\frac{451}{750}\right)\) | \(e\left(\frac{182}{375}\right)\) |