Basic properties
Modulus: | \(6017\) | |
Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{547}(54,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.ba
\(\chi_{6017}(199,\cdot)\) \(\chi_{6017}(419,\cdot)\) \(\chi_{6017}(441,\cdot)\) \(\chi_{6017}(683,\cdot)\) \(\chi_{6017}(1035,\cdot)\) \(\chi_{6017}(1068,\cdot)\) \(\chi_{6017}(1662,\cdot)\) \(\chi_{6017}(1695,\cdot)\) \(\chi_{6017}(1937,\cdot)\) \(\chi_{6017}(2421,\cdot)\) \(\chi_{6017}(2652,\cdot)\) \(\chi_{6017}(2916,\cdot)\) \(\chi_{6017}(3037,\cdot)\) \(\chi_{6017}(3180,\cdot)\) \(\chi_{6017}(3378,\cdot)\) \(\chi_{6017}(3411,\cdot)\) \(\chi_{6017}(3499,\cdot)\) \(\chi_{6017}(3521,\cdot)\) \(\chi_{6017}(3840,\cdot)\) \(\chi_{6017}(3950,\cdot)\) \(\chi_{6017}(4060,\cdot)\) \(\chi_{6017}(4423,\cdot)\) \(\chi_{6017}(5248,\cdot)\) \(\chi_{6017}(5325,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3830,2190)\) → \((1,e\left(\frac{14}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(1695, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |