Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(273\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{547}(177,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.bx
\(\chi_{6017}(34,\cdot)\) \(\chi_{6017}(56,\cdot)\) \(\chi_{6017}(67,\cdot)\) \(\chi_{6017}(78,\cdot)\) \(\chi_{6017}(111,\cdot)\) \(\chi_{6017}(122,\cdot)\) \(\chi_{6017}(144,\cdot)\) \(\chi_{6017}(155,\cdot)\) \(\chi_{6017}(166,\cdot)\) \(\chi_{6017}(177,\cdot)\) \(\chi_{6017}(188,\cdot)\) \(\chi_{6017}(210,\cdot)\) \(\chi_{6017}(276,\cdot)\) \(\chi_{6017}(287,\cdot)\) \(\chi_{6017}(452,\cdot)\) \(\chi_{6017}(529,\cdot)\) \(\chi_{6017}(540,\cdot)\) \(\chi_{6017}(551,\cdot)\) \(\chi_{6017}(562,\cdot)\) \(\chi_{6017}(705,\cdot)\) \(\chi_{6017}(738,\cdot)\) \(\chi_{6017}(749,\cdot)\) \(\chi_{6017}(760,\cdot)\) \(\chi_{6017}(848,\cdot)\) \(\chi_{6017}(859,\cdot)\) \(\chi_{6017}(914,\cdot)\) \(\chi_{6017}(947,\cdot)\) \(\chi_{6017}(1002,\cdot)\) \(\chi_{6017}(1024,\cdot)\) \(\chi_{6017}(1046,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((1,e\left(\frac{197}{273}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(177, a) \) | \(1\) | \(1\) | \(e\left(\frac{197}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{121}{273}\right)\) | \(e\left(\frac{46}{273}\right)\) | \(e\left(\frac{80}{273}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{15}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{81}{91}\right)\) | \(e\left(\frac{4}{273}\right)\) |