Basic properties
| Modulus: | \(539\) | |
| Conductor: | \(539\) | 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 539.bb
\(\chi_{539}(20,\cdot)\) \(\chi_{539}(27,\cdot)\) \(\chi_{539}(69,\cdot)\) \(\chi_{539}(104,\cdot)\) \(\chi_{539}(125,\cdot)\) \(\chi_{539}(174,\cdot)\) \(\chi_{539}(181,\cdot)\) \(\chi_{539}(202,\cdot)\) \(\chi_{539}(223,\cdot)\) \(\chi_{539}(251,\cdot)\) \(\chi_{539}(258,\cdot)\) \(\chi_{539}(279,\cdot)\) \(\chi_{539}(300,\cdot)\) \(\chi_{539}(328,\cdot)\) \(\chi_{539}(335,\cdot)\) \(\chi_{539}(356,\cdot)\) \(\chi_{539}(377,\cdot)\) \(\chi_{539}(405,\cdot)\) \(\chi_{539}(412,\cdot)\) \(\chi_{539}(433,\cdot)\) \(\chi_{539}(454,\cdot)\) \(\chi_{539}(482,\cdot)\) \(\chi_{539}(510,\cdot)\) \(\chi_{539}(531,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((199,442)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{53}{70}\right)\) |