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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 539.z
\(\chi_{539}(6,\cdot)\) \(\chi_{539}(13,\cdot)\) \(\chi_{539}(41,\cdot)\) \(\chi_{539}(62,\cdot)\) \(\chi_{539}(83,\cdot)\) \(\chi_{539}(90,\cdot)\) \(\chi_{539}(118,\cdot)\) \(\chi_{539}(139,\cdot)\) \(\chi_{539}(160,\cdot)\) \(\chi_{539}(167,\cdot)\) \(\chi_{539}(216,\cdot)\) \(\chi_{539}(237,\cdot)\) \(\chi_{539}(272,\cdot)\) \(\chi_{539}(314,\cdot)\) \(\chi_{539}(321,\cdot)\) \(\chi_{539}(349,\cdot)\) \(\chi_{539}(370,\cdot)\) \(\chi_{539}(398,\cdot)\) \(\chi_{539}(426,\cdot)\) \(\chi_{539}(447,\cdot)\) \(\chi_{539}(468,\cdot)\) \(\chi_{539}(475,\cdot)\) \(\chi_{539}(503,\cdot)\) \(\chi_{539}(524,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((199,442)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{35}\right)\) |