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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6017.bh
\(\chi_{6017}(365,\cdot)\) \(\chi_{6017}(574,\cdot)\) \(\chi_{6017}(1085,\cdot)\) \(\chi_{6017}(1097,\cdot)\) \(\chi_{6017}(1337,\cdot)\) \(\chi_{6017}(1459,\cdot)\) \(\chi_{6017}(1668,\cdot)\) \(\chi_{6017}(2107,\cdot)\) \(\chi_{6017}(2191,\cdot)\) \(\chi_{6017}(2978,\cdot)\) \(\chi_{6017}(3273,\cdot)\) \(\chi_{6017}(3285,\cdot)\) \(\chi_{6017}(3647,\cdot)\) \(\chi_{6017}(3748,\cdot)\) \(\chi_{6017}(3856,\cdot)\) \(\chi_{6017}(4072,\cdot)\) \(\chi_{6017}(4842,\cdot)\) \(\chi_{6017}(4914,\cdot)\) \(\chi_{6017}(5166,\cdot)\) \(\chi_{6017}(5288,\cdot)\) \(\chi_{6017}(5473,\cdot)\) \(\chi_{6017}(5497,\cdot)\) \(\chi_{6017}(5936,\cdot)\) \(\chi_{6017}(6008,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((3830,2190)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{11}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(3285, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) |