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.dl
\(\chi_{3479}(160,\cdot)\) \(\chi_{3479}(251,\cdot)\) \(\chi_{3479}(286,\cdot)\) \(\chi_{3479}(860,\cdot)\) \(\chi_{3479}(867,\cdot)\) \(\chi_{3479}(888,\cdot)\) \(\chi_{3479}(1105,\cdot)\) \(\chi_{3479}(1196,\cdot)\) \(\chi_{3479}(1210,\cdot)\) \(\chi_{3479}(1217,\cdot)\) \(\chi_{3479}(1294,\cdot)\) \(\chi_{3479}(1497,\cdot)\) \(\chi_{3479}(1581,\cdot)\) \(\chi_{3479}(1728,\cdot)\) \(\chi_{3479}(1784,\cdot)\) \(\chi_{3479}(2015,\cdot)\) \(\chi_{3479}(2330,\cdot)\) \(\chi_{3479}(2393,\cdot)\) \(\chi_{3479}(2407,\cdot)\) \(\chi_{3479}(2463,\cdot)\) \(\chi_{3479}(2568,\cdot)\) \(\chi_{3479}(2631,\cdot)\) \(\chi_{3479}(2883,\cdot)\) \(\chi_{3479}(3366,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((640,1569)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{29}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(160, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) |