Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(546\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{547}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.ce
\(\chi_{6017}(12,\cdot)\) \(\chi_{6017}(23,\cdot)\) \(\chi_{6017}(45,\cdot)\) \(\chi_{6017}(221,\cdot)\) \(\chi_{6017}(298,\cdot)\) \(\chi_{6017}(320,\cdot)\) \(\chi_{6017}(364,\cdot)\) \(\chi_{6017}(397,\cdot)\) \(\chi_{6017}(408,\cdot)\) \(\chi_{6017}(474,\cdot)\) \(\chi_{6017}(485,\cdot)\) \(\chi_{6017}(496,\cdot)\) \(\chi_{6017}(584,\cdot)\) \(\chi_{6017}(595,\cdot)\) \(\chi_{6017}(617,\cdot)\) \(\chi_{6017}(639,\cdot)\) \(\chi_{6017}(694,\cdot)\) \(\chi_{6017}(727,\cdot)\) \(\chi_{6017}(782,\cdot)\) \(\chi_{6017}(793,\cdot)\) \(\chi_{6017}(881,\cdot)\) \(\chi_{6017}(892,\cdot)\) \(\chi_{6017}(903,\cdot)\) \(\chi_{6017}(936,\cdot)\) \(\chi_{6017}(1079,\cdot)\) \(\chi_{6017}(1090,\cdot)\) \(\chi_{6017}(1101,\cdot)\) \(\chi_{6017}(1112,\cdot)\) \(\chi_{6017}(1189,\cdot)\) \(\chi_{6017}(1354,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((1,e\left(\frac{293}{546}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{293}{546}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{20}{273}\right)\) | \(e\left(\frac{31}{546}\right)\) | \(e\left(\frac{205}{273}\right)\) | \(e\left(\frac{149}{546}\right)\) | \(e\left(\frac{111}{182}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{54}{91}\right)\) | \(e\left(\frac{157}{546}\right)\) |