Basic properties
Modulus: | \(6017\) | |
Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1365\) | 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 6017.ci
\(\chi_{6017}(4,\cdot)\) \(\chi_{6017}(15,\cdot)\) \(\chi_{6017}(16,\cdot)\) \(\chi_{6017}(25,\cdot)\) \(\chi_{6017}(36,\cdot)\) \(\chi_{6017}(49,\cdot)\) \(\chi_{6017}(53,\cdot)\) \(\chi_{6017}(60,\cdot)\) \(\chi_{6017}(69,\cdot)\) \(\chi_{6017}(82,\cdot)\) \(\chi_{6017}(86,\cdot)\) \(\chi_{6017}(97,\cdot)\) \(\chi_{6017}(113,\cdot)\) \(\chi_{6017}(115,\cdot)\) \(\chi_{6017}(119,\cdot)\) \(\chi_{6017}(130,\cdot)\) \(\chi_{6017}(135,\cdot)\) \(\chi_{6017}(137,\cdot)\) \(\chi_{6017}(157,\cdot)\) \(\chi_{6017}(158,\cdot)\) \(\chi_{6017}(174,\cdot)\) \(\chi_{6017}(190,\cdot)\) \(\chi_{6017}(191,\cdot)\) \(\chi_{6017}(202,\cdot)\) \(\chi_{6017}(213,\cdot)\) \(\chi_{6017}(214,\cdot)\) \(\chi_{6017}(225,\cdot)\) \(\chi_{6017}(256,\cdot)\) \(\chi_{6017}(269,\cdot)\) \(\chi_{6017}(273,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1365})$ |
Fixed field: | Number field defined by a degree 1365 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{38}{273}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{1282}{1365}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1199}{1365}\right)\) | \(e\left(\frac{158}{1365}\right)\) | \(e\left(\frac{73}{1365}\right)\) | \(e\left(\frac{1279}{1365}\right)\) | \(e\left(\frac{372}{455}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{5}{91}\right)\) | \(e\left(\frac{271}{273}\right)\) |