Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.z
\(\chi_{6017}(9,\cdot)\) \(\chi_{6017}(81,\cdot)\) \(\chi_{6017}(520,\cdot)\) \(\chi_{6017}(544,\cdot)\) \(\chi_{6017}(729,\cdot)\) \(\chi_{6017}(851,\cdot)\) \(\chi_{6017}(1103,\cdot)\) \(\chi_{6017}(1175,\cdot)\) \(\chi_{6017}(1945,\cdot)\) \(\chi_{6017}(2161,\cdot)\) \(\chi_{6017}(2269,\cdot)\) \(\chi_{6017}(2370,\cdot)\) \(\chi_{6017}(2732,\cdot)\) \(\chi_{6017}(2744,\cdot)\) \(\chi_{6017}(3039,\cdot)\) \(\chi_{6017}(3826,\cdot)\) \(\chi_{6017}(3910,\cdot)\) \(\chi_{6017}(4349,\cdot)\) \(\chi_{6017}(4558,\cdot)\) \(\chi_{6017}(4680,\cdot)\) \(\chi_{6017}(4920,\cdot)\) \(\chi_{6017}(4932,\cdot)\) \(\chi_{6017}(5443,\cdot)\) \(\chi_{6017}(5652,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((3830,2190)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |