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.ch
\(\chi_{6008}(5,\cdot)\) \(\chi_{6008}(13,\cdot)\) \(\chi_{6008}(21,\cdot)\) \(\chi_{6008}(37,\cdot)\) \(\chi_{6008}(77,\cdot)\) \(\chi_{6008}(109,\cdot)\) \(\chi_{6008}(149,\cdot)\) \(\chi_{6008}(181,\cdot)\) \(\chi_{6008}(245,\cdot)\) \(\chi_{6008}(269,\cdot)\) \(\chi_{6008}(309,\cdot)\) \(\chi_{6008}(333,\cdot)\) \(\chi_{6008}(397,\cdot)\) \(\chi_{6008}(461,\cdot)\) \(\chi_{6008}(469,\cdot)\) \(\chi_{6008}(477,\cdot)\) \(\chi_{6008}(549,\cdot)\) \(\chi_{6008}(581,\cdot)\) \(\chi_{6008}(613,\cdot)\) \(\chi_{6008}(669,\cdot)\) \(\chi_{6008}(853,\cdot)\) \(\chi_{6008}(893,\cdot)\) \(\chi_{6008}(925,\cdot)\) \(\chi_{6008}(965,\cdot)\) \(\chi_{6008}(981,\cdot)\) \(\chi_{6008}(989,\cdot)\) \(\chi_{6008}(1029,\cdot)\) \(\chi_{6008}(1053,\cdot)\) \(\chi_{6008}(1077,\cdot)\) \(\chi_{6008}(1093,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{326}{375}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{750}\right)\) | \(e\left(\frac{247}{750}\right)\) | \(e\left(\frac{117}{125}\right)\) | \(e\left(\frac{277}{375}\right)\) | \(e\left(\frac{11}{150}\right)\) | \(e\left(\frac{91}{750}\right)\) | \(e\left(\frac{262}{375}\right)\) | \(e\left(\frac{4}{375}\right)\) | \(e\left(\frac{361}{750}\right)\) | \(e\left(\frac{229}{750}\right)\) |