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.eb
\(\chi_{3479}(92,\cdot)\) \(\chi_{3479}(106,\cdot)\) \(\chi_{3479}(260,\cdot)\) \(\chi_{3479}(281,\cdot)\) \(\chi_{3479}(407,\cdot)\) \(\chi_{3479}(414,\cdot)\) \(\chi_{3479}(624,\cdot)\) \(\chi_{3479}(743,\cdot)\) \(\chi_{3479}(1198,\cdot)\) \(\chi_{3479}(1268,\cdot)\) \(\chi_{3479}(1604,\cdot)\) \(\chi_{3479}(1646,\cdot)\) \(\chi_{3479}(1688,\cdot)\) \(\chi_{3479}(1786,\cdot)\) \(\chi_{3479}(1828,\cdot)\) \(\chi_{3479}(2066,\cdot)\) \(\chi_{3479}(2199,\cdot)\) \(\chi_{3479}(2339,\cdot)\) \(\chi_{3479}(2458,\cdot)\) \(\chi_{3479}(2479,\cdot)\) \(\chi_{3479}(2871,\cdot)\) \(\chi_{3479}(3004,\cdot)\) \(\chi_{3479}(3081,\cdot)\) \(\chi_{3479}(3116,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((640,1569)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{27}{70}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 3479 }(92, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) |