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.bw
\(\chi_{6017}(13,\cdot)\) \(\chi_{6017}(117,\cdot)\) \(\chi_{6017}(123,\cdot)\) \(\chi_{6017}(178,\cdot)\) \(\chi_{6017}(360,\cdot)\) \(\chi_{6017}(508,\cdot)\) \(\chi_{6017}(673,\cdot)\) \(\chi_{6017}(743,\cdot)\) \(\chi_{6017}(974,\cdot)\) \(\chi_{6017}(1052,\cdot)\) \(\chi_{6017}(1107,\cdot)\) \(\chi_{6017}(1108,\cdot)\) \(\chi_{6017}(1217,\cdot)\) \(\chi_{6017}(1272,\cdot)\) \(\chi_{6017}(1454,\cdot)\) \(\chi_{6017}(1602,\cdot)\) \(\chi_{6017}(1767,\cdot)\) \(\chi_{6017}(1810,\cdot)\) \(\chi_{6017}(2202,\cdot)\) \(\chi_{6017}(2305,\cdot)\) \(\chi_{6017}(2384,\cdot)\) \(\chi_{6017}(2548,\cdot)\) \(\chi_{6017}(2615,\cdot)\) \(\chi_{6017}(3240,\cdot)\) \(\chi_{6017}(3295,\cdot)\) \(\chi_{6017}(3296,\cdot)\) \(\chi_{6017}(3405,\cdot)\) \(\chi_{6017}(3451,\cdot)\) \(\chi_{6017}(3460,\cdot)\) \(\chi_{6017}(3478,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{10}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(5975, a) \) | \(-1\) | \(1\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) |