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.ds
\(\chi_{3479}(202,\cdot)\) \(\chi_{3479}(300,\cdot)\) \(\chi_{3479}(370,\cdot)\) \(\chi_{3479}(405,\cdot)\) \(\chi_{3479}(524,\cdot)\) \(\chi_{3479}(657,\cdot)\) \(\chi_{3479}(713,\cdot)\) \(\chi_{3479}(790,\cdot)\) \(\chi_{3479}(895,\cdot)\) \(\chi_{3479}(916,\cdot)\) \(\chi_{3479}(1574,\cdot)\) \(\chi_{3479}(1777,\cdot)\) \(\chi_{3479}(1854,\cdot)\) \(\chi_{3479}(2078,\cdot)\) \(\chi_{3479}(2099,\cdot)\) \(\chi_{3479}(2134,\cdot)\) \(\chi_{3479}(2225,\cdot)\) \(\chi_{3479}(2239,\cdot)\) \(\chi_{3479}(2491,\cdot)\) \(\chi_{3479}(2708,\cdot)\) \(\chi_{3479}(2869,\cdot)\) \(\chi_{3479}(2876,\cdot)\) \(\chi_{3479}(2960,\cdot)\) \(\chi_{3479}(3324,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((640,1569)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{33}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(202, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) |