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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.cj
\(\chi_{6008}(3,\cdot)\) \(\chi_{6008}(35,\cdot)\) \(\chi_{6008}(67,\cdot)\) \(\chi_{6008}(91,\cdot)\) \(\chi_{6008}(147,\cdot)\) \(\chi_{6008}(227,\cdot)\) \(\chi_{6008}(259,\cdot)\) \(\chi_{6008}(283,\cdot)\) \(\chi_{6008}(427,\cdot)\) \(\chi_{6008}(443,\cdot)\) \(\chi_{6008}(515,\cdot)\) \(\chi_{6008}(539,\cdot)\) \(\chi_{6008}(547,\cdot)\) \(\chi_{6008}(555,\cdot)\) \(\chi_{6008}(563,\cdot)\) \(\chi_{6008}(579,\cdot)\) \(\chi_{6008}(659,\cdot)\) \(\chi_{6008}(667,\cdot)\) \(\chi_{6008}(731,\cdot)\) \(\chi_{6008}(747,\cdot)\) \(\chi_{6008}(763,\cdot)\) \(\chi_{6008}(779,\cdot)\) \(\chi_{6008}(795,\cdot)\) \(\chi_{6008}(867,\cdot)\) \(\chi_{6008}(891,\cdot)\) \(\chi_{6008}(915,\cdot)\) \(\chi_{6008}(1019,\cdot)\) \(\chi_{6008}(1043,\cdot)\) \(\chi_{6008}(1091,\cdot)\) \(\chi_{6008}(1115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{37}{750}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(547, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{750}\right)\) | \(e\left(\frac{607}{750}\right)\) | \(e\left(\frac{77}{125}\right)\) | \(e\left(\frac{37}{375}\right)\) | \(e\left(\frac{41}{150}\right)\) | \(e\left(\frac{421}{750}\right)\) | \(e\left(\frac{322}{375}\right)\) | \(e\left(\frac{173}{750}\right)\) | \(e\left(\frac{83}{375}\right)\) | \(e\left(\frac{499}{750}\right)\) |