Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.bf
\(\chi_{6017}(3,\cdot)\) \(\chi_{6017}(27,\cdot)\) \(\chi_{6017}(466,\cdot)\) \(\chi_{6017}(790,\cdot)\) \(\chi_{6017}(1560,\cdot)\) \(\chi_{6017}(1632,\cdot)\) \(\chi_{6017}(1644,\cdot)\) \(\chi_{6017}(1884,\cdot)\) \(\chi_{6017}(2006,\cdot)\) \(\chi_{6017}(2215,\cdot)\) \(\chi_{6017}(2654,\cdot)\) \(\chi_{6017}(2726,\cdot)\) \(\chi_{6017}(3100,\cdot)\) \(\chi_{6017}(3309,\cdot)\) \(\chi_{6017}(3525,\cdot)\) \(\chi_{6017}(3820,\cdot)\) \(\chi_{6017}(3832,\cdot)\) \(\chi_{6017}(4194,\cdot)\) \(\chi_{6017}(4295,\cdot)\) \(\chi_{6017}(4403,\cdot)\) \(\chi_{6017}(4926,\cdot)\) \(\chi_{6017}(5461,\cdot)\) \(\chi_{6017}(5713,\cdot)\) \(\chi_{6017}(5835,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((3830,2190)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) |