Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{547}(316,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.bi
\(\chi_{6017}(573,\cdot)\) \(\chi_{6017}(606,\cdot)\) \(\chi_{6017}(958,\cdot)\) \(\chi_{6017}(1200,\cdot)\) \(\chi_{6017}(1222,\cdot)\) \(\chi_{6017}(1442,\cdot)\) \(\chi_{6017}(2333,\cdot)\) \(\chi_{6017}(2410,\cdot)\) \(\chi_{6017}(3235,\cdot)\) \(\chi_{6017}(3598,\cdot)\) \(\chi_{6017}(3708,\cdot)\) \(\chi_{6017}(3818,\cdot)\) \(\chi_{6017}(4137,\cdot)\) \(\chi_{6017}(4159,\cdot)\) \(\chi_{6017}(4247,\cdot)\) \(\chi_{6017}(4280,\cdot)\) \(\chi_{6017}(4478,\cdot)\) \(\chi_{6017}(4621,\cdot)\) \(\chi_{6017}(4742,\cdot)\) \(\chi_{6017}(5006,\cdot)\) \(\chi_{6017}(5237,\cdot)\) \(\chi_{6017}(5721,\cdot)\) \(\chi_{6017}(5963,\cdot)\) \(\chi_{6017}(5996,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3830,2190)\) → \((1,e\left(\frac{47}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(3598, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(-1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{55}{78}\right)\) |