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
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{338}{375}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(1077, a) \) | \(1\) | \(1\) | \(e\left(\frac{301}{750}\right)\) | \(e\left(\frac{661}{750}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{301}{375}\right)\) | \(e\left(\frac{143}{150}\right)\) | \(e\left(\frac{283}{750}\right)\) | \(e\left(\frac{106}{375}\right)\) | \(e\left(\frac{202}{375}\right)\) | \(e\left(\frac{43}{750}\right)\) | \(e\left(\frac{127}{750}\right)\) |