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.bo
\(\chi_{6017}(38,\cdot)\) \(\chi_{6017}(575,\cdot)\) \(\chi_{6017}(577,\cdot)\) \(\chi_{6017}(619,\cdot)\) \(\chi_{6017}(654,\cdot)\) \(\chi_{6017}(719,\cdot)\) \(\chi_{6017}(741,\cdot)\) \(\chi_{6017}(801,\cdot)\) \(\chi_{6017}(1048,\cdot)\) \(\chi_{6017}(1291,\cdot)\) \(\chi_{6017}(1380,\cdot)\) \(\chi_{6017}(1813,\cdot)\) \(\chi_{6017}(1835,\cdot)\) \(\chi_{6017}(1895,\cdot)\) \(\chi_{6017}(1951,\cdot)\) \(\chi_{6017}(2216,\cdot)\) \(\chi_{6017}(2226,\cdot)\) \(\chi_{6017}(2260,\cdot)\) \(\chi_{6017}(2385,\cdot)\) \(\chi_{6017}(2689,\cdot)\) \(\chi_{6017}(2765,\cdot)\) \(\chi_{6017}(2842,\cdot)\) \(\chi_{6017}(2907,\cdot)\) \(\chi_{6017}(2929,\cdot)\) \(\chi_{6017}(3045,\cdot)\) \(\chi_{6017}(3320,\cdot)\) \(\chi_{6017}(3479,\cdot)\) \(\chi_{6017}(3536,\cdot)\) \(\chi_{6017}(3568,\cdot)\) \(\chi_{6017}(3859,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{19}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(2929, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) |