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.cv
\(\chi_{6013}(40,\cdot)\) \(\chi_{6013}(73,\cdot)\) \(\chi_{6013}(82,\cdot)\) \(\chi_{6013}(101,\cdot)\) \(\chi_{6013}(122,\cdot)\) \(\chi_{6013}(129,\cdot)\) \(\chi_{6013}(157,\cdot)\) \(\chi_{6013}(185,\cdot)\) \(\chi_{6013}(187,\cdot)\) \(\chi_{6013}(206,\cdot)\) \(\chi_{6013}(220,\cdot)\) \(\chi_{6013}(222,\cdot)\) \(\chi_{6013}(248,\cdot)\) \(\chi_{6013}(264,\cdot)\) \(\chi_{6013}(283,\cdot)\) \(\chi_{6013}(311,\cdot)\) \(\chi_{6013}(383,\cdot)\) \(\chi_{6013}(451,\cdot)\) \(\chi_{6013}(460,\cdot)\) \(\chi_{6013}(481,\cdot)\) \(\chi_{6013}(530,\cdot)\) \(\chi_{6013}(535,\cdot)\) \(\chi_{6013}(542,\cdot)\) \(\chi_{6013}(565,\cdot)\) \(\chi_{6013}(570,\cdot)\) \(\chi_{6013}(572,\cdot)\) \(\chi_{6013}(577,\cdot)\) \(\chi_{6013}(642,\cdot)\) \(\chi_{6013}(675,\cdot)\) \(\chi_{6013}(684,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{429})$ |
| Fixed field: | Number field defined by a degree 858 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{365}{858}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{858}\right)\) | \(e\left(\frac{196}{429}\right)\) | \(e\left(\frac{79}{429}\right)\) | \(e\left(\frac{47}{286}\right)\) | \(e\left(\frac{157}{286}\right)\) | \(e\left(\frac{79}{286}\right)\) | \(e\left(\frac{392}{429}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{829}{858}\right)\) | \(e\left(\frac{25}{39}\right)\) |