Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.bn
\(\chi_{6017}(46,\cdot)\) \(\chi_{6017}(237,\cdot)\) \(\chi_{6017}(261,\cdot)\) \(\chi_{6017}(293,\cdot)\) \(\chi_{6017}(475,\cdot)\) \(\chi_{6017}(519,\cdot)\) \(\chi_{6017}(897,\cdot)\) \(\chi_{6017}(987,\cdot)\) \(\chi_{6017}(1064,\cdot)\) \(\chi_{6017}(1140,\cdot)\) \(\chi_{6017}(1355,\cdot)\) \(\chi_{6017}(1447,\cdot)\) \(\chi_{6017}(1469,\cdot)\) \(\chi_{6017}(1569,\cdot)\) \(\chi_{6017}(1603,\cdot)\) \(\chi_{6017}(1613,\cdot)\) \(\chi_{6017}(1878,\cdot)\) \(\chi_{6017}(2081,\cdot)\) \(\chi_{6017}(2158,\cdot)\) \(\chi_{6017}(2449,\cdot)\) \(\chi_{6017}(2481,\cdot)\) \(\chi_{6017}(2538,\cdot)\) \(\chi_{6017}(2697,\cdot)\) \(\chi_{6017}(2972,\cdot)\) \(\chi_{6017}(3088,\cdot)\) \(\chi_{6017}(3110,\cdot)\) \(\chi_{6017}(3175,\cdot)\) \(\chi_{6017}(3252,\cdot)\) \(\chi_{6017}(3328,\cdot)\) \(\chi_{6017}(3632,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{7}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) |