Basic properties
Modulus: | \(6013\) | |
Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{859}(120,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6013.bi
\(\chi_{6013}(120,\cdot)\) \(\chi_{6013}(316,\cdot)\) \(\chi_{6013}(666,\cdot)\) \(\chi_{6013}(1135,\cdot)\) \(\chi_{6013}(1443,\cdot)\) \(\chi_{6013}(1695,\cdot)\) \(\chi_{6013}(1751,\cdot)\) \(\chi_{6013}(1891,\cdot)\) \(\chi_{6013}(1996,\cdot)\) \(\chi_{6013}(2374,\cdot)\) \(\chi_{6013}(2689,\cdot)\) \(\chi_{6013}(3095,\cdot)\) \(\chi_{6013}(3410,\cdot)\) \(\chi_{6013}(3424,\cdot)\) \(\chi_{6013}(3648,\cdot)\) \(\chi_{6013}(3893,\cdot)\) \(\chi_{6013}(4159,\cdot)\) \(\chi_{6013}(4439,\cdot)\) \(\chi_{6013}(4572,\cdot)\) \(\chi_{6013}(4607,\cdot)\) \(\chi_{6013}(4796,\cdot)\) \(\chi_{6013}(4824,\cdot)\) \(\chi_{6013}(4971,\cdot)\) \(\chi_{6013}(5384,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((5155,3438)\) → \((1,e\left(\frac{22}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6013 }(120, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) |