Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.bv
\(\chi_{6017}(42,\cdot)\) \(\chi_{6017}(378,\cdot)\) \(\chi_{6017}(421,\cdot)\) \(\chi_{6017}(533,\cdot)\) \(\chi_{6017}(586,\cdot)\) \(\chi_{6017}(916,\cdot)\) \(\chi_{6017}(971,\cdot)\) \(\chi_{6017}(977,\cdot)\) \(\chi_{6017}(1081,\cdot)\) \(\chi_{6017}(1136,\cdot)\) \(\chi_{6017}(1214,\cdot)\) \(\chi_{6017}(1281,\cdot)\) \(\chi_{6017}(1445,\cdot)\) \(\chi_{6017}(1472,\cdot)\) \(\chi_{6017}(2062,\cdot)\) \(\chi_{6017}(2071,\cdot)\) \(\chi_{6017}(2227,\cdot)\) \(\chi_{6017}(2308,\cdot)\) \(\chi_{6017}(2539,\cdot)\) \(\chi_{6017}(2557,\cdot)\) \(\chi_{6017}(2566,\cdot)\) \(\chi_{6017}(2612,\cdot)\) \(\chi_{6017}(2721,\cdot)\) \(\chi_{6017}(2722,\cdot)\) \(\chi_{6017}(2777,\cdot)\) \(\chi_{6017}(3402,\cdot)\) \(\chi_{6017}(3469,\cdot)\) \(\chi_{6017}(3633,\cdot)\) \(\chi_{6017}(3712,\cdot)\) \(\chi_{6017}(3815,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(2071, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{23}{42}\right)\) |