Basic properties
Modulus: | \(6013\) | |
Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(858\) | 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 6013.cw
\(\chi_{6013}(55,\cdot)\) \(\chi_{6013}(62,\cdot)\) \(\chi_{6013}(76,\cdot)\) \(\chi_{6013}(83,\cdot)\) \(\chi_{6013}(90,\cdot)\) \(\chi_{6013}(97,\cdot)\) \(\chi_{6013}(118,\cdot)\) \(\chi_{6013}(139,\cdot)\) \(\chi_{6013}(160,\cdot)\) \(\chi_{6013}(174,\cdot)\) \(\chi_{6013}(237,\cdot)\) \(\chi_{6013}(251,\cdot)\) \(\chi_{6013}(293,\cdot)\) \(\chi_{6013}(328,\cdot)\) \(\chi_{6013}(349,\cdot)\) \(\chi_{6013}(363,\cdot)\) \(\chi_{6013}(377,\cdot)\) \(\chi_{6013}(419,\cdot)\) \(\chi_{6013}(447,\cdot)\) \(\chi_{6013}(454,\cdot)\) \(\chi_{6013}(489,\cdot)\) \(\chi_{6013}(517,\cdot)\) \(\chi_{6013}(538,\cdot)\) \(\chi_{6013}(545,\cdot)\) \(\chi_{6013}(573,\cdot)\) \(\chi_{6013}(580,\cdot)\) \(\chi_{6013}(594,\cdot)\) \(\chi_{6013}(601,\cdot)\) \(\chi_{6013}(615,\cdot)\) \(\chi_{6013}(650,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{429})$ |
Fixed field: | Number field defined by a degree 858 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((-1,e\left(\frac{35}{858}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6013 }(363, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{858}\right)\) | \(e\left(\frac{152}{429}\right)\) | \(e\left(\frac{35}{429}\right)\) | \(e\left(\frac{229}{858}\right)\) | \(e\left(\frac{113}{286}\right)\) | \(e\left(\frac{35}{286}\right)\) | \(e\left(\frac{304}{429}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{225}{286}\right)\) | \(e\left(\frac{17}{39}\right)\) |