Basic properties
Modulus: | \(6017\) | |
Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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.bk
\(\chi_{6017}(692,\cdot)\) \(\chi_{6017}(769,\cdot)\) \(\chi_{6017}(1594,\cdot)\) \(\chi_{6017}(1957,\cdot)\) \(\chi_{6017}(2067,\cdot)\) \(\chi_{6017}(2177,\cdot)\) \(\chi_{6017}(2496,\cdot)\) \(\chi_{6017}(2518,\cdot)\) \(\chi_{6017}(2606,\cdot)\) \(\chi_{6017}(2639,\cdot)\) \(\chi_{6017}(2837,\cdot)\) \(\chi_{6017}(2980,\cdot)\) \(\chi_{6017}(3101,\cdot)\) \(\chi_{6017}(3365,\cdot)\) \(\chi_{6017}(3596,\cdot)\) \(\chi_{6017}(4080,\cdot)\) \(\chi_{6017}(4322,\cdot)\) \(\chi_{6017}(4355,\cdot)\) \(\chi_{6017}(4949,\cdot)\) \(\chi_{6017}(4982,\cdot)\) \(\chi_{6017}(5334,\cdot)\) \(\chi_{6017}(5576,\cdot)\) \(\chi_{6017}(5598,\cdot)\) \(\chi_{6017}(5818,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3830,2190)\) → \((-1,e\left(\frac{71}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(692, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(-1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{25}{78}\right)\) |