Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2730\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.cj
\(\chi_{6017}(5,\cdot)\) \(\chi_{6017}(20,\cdot)\) \(\chi_{6017}(37,\cdot)\) \(\chi_{6017}(48,\cdot)\) \(\chi_{6017}(58,\cdot)\) \(\chi_{6017}(70,\cdot)\) \(\chi_{6017}(71,\cdot)\) \(\chi_{6017}(75,\cdot)\) \(\chi_{6017}(91,\cdot)\) \(\chi_{6017}(92,\cdot)\) \(\chi_{6017}(104,\cdot)\) \(\chi_{6017}(108,\cdot)\) \(\chi_{6017}(124,\cdot)\) \(\chi_{6017}(141,\cdot)\) \(\chi_{6017}(146,\cdot)\) \(\chi_{6017}(147,\cdot)\) \(\chi_{6017}(152,\cdot)\) \(\chi_{6017}(159,\cdot)\) \(\chi_{6017}(163,\cdot)\) \(\chi_{6017}(168,\cdot)\) \(\chi_{6017}(170,\cdot)\) \(\chi_{6017}(180,\cdot)\) \(\chi_{6017}(201,\cdot)\) \(\chi_{6017}(203,\cdot)\) \(\chi_{6017}(207,\cdot)\) \(\chi_{6017}(223,\cdot)\) \(\chi_{6017}(229,\cdot)\) \(\chi_{6017}(234,\cdot)\) \(\chi_{6017}(235,\cdot)\) \(\chi_{6017}(246,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1365})$ |
| Fixed field: | Number field defined by a degree 2730 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{181}{546}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2543}{2730}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{1178}{1365}\right)\) | \(e\left(\frac{2017}{2730}\right)\) | \(e\left(\frac{1291}{1365}\right)\) | \(e\left(\frac{941}{2730}\right)\) | \(e\left(\frac{723}{910}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{61}{91}\right)\) | \(e\left(\frac{479}{546}\right)\) |