Basic properties
| Modulus: | \(3479\) | |
| Conductor: | \(3479\) | 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 3479.dv
\(\chi_{3479}(6,\cdot)\) \(\chi_{3479}(216,\cdot)\) \(\chi_{3479}(580,\cdot)\) \(\chi_{3479}(720,\cdot)\) \(\chi_{3479}(748,\cdot)\) \(\chi_{3479}(839,\cdot)\) \(\chi_{3479}(1154,\cdot)\) \(\chi_{3479}(1385,\cdot)\) \(\chi_{3479}(1637,\cdot)\) \(\chi_{3479}(1896,\cdot)\) \(\chi_{3479}(2372,\cdot)\) \(\chi_{3479}(2386,\cdot)\) \(\chi_{3479}(2512,\cdot)\) \(\chi_{3479}(2575,\cdot)\) \(\chi_{3479}(2687,\cdot)\) \(\chi_{3479}(2722,\cdot)\) \(\chi_{3479}(2785,\cdot)\) \(\chi_{3479}(2848,\cdot)\) \(\chi_{3479}(2904,\cdot)\) \(\chi_{3479}(3093,\cdot)\) \(\chi_{3479}(3268,\cdot)\) \(\chi_{3479}(3275,\cdot)\) \(\chi_{3479}(3352,\cdot)\) \(\chi_{3479}(3457,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((640,1569)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{16}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) |