Basic properties
| Modulus: | \(3479\) | |
| Conductor: | \(3479\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.fm
\(\chi_{3479}(12,\cdot)\) \(\chi_{3479}(152,\cdot)\) \(\chi_{3479}(171,\cdot)\) \(\chi_{3479}(180,\cdot)\) \(\chi_{3479}(206,\cdot)\) \(\chi_{3479}(271,\cdot)\) \(\chi_{3479}(290,\cdot)\) \(\chi_{3479}(586,\cdot)\) \(\chi_{3479}(689,\cdot)\) \(\chi_{3479}(817,\cdot)\) \(\chi_{3479}(871,\cdot)\) \(\chi_{3479}(1018,\cdot)\) \(\chi_{3479}(1069,\cdot)\) \(\chi_{3479}(1123,\cdot)\) \(\chi_{3479}(1151,\cdot)\) \(\chi_{3479}(1179,\cdot)\) \(\chi_{3479}(1328,\cdot)\) \(\chi_{3479}(1494,\cdot)\) \(\chi_{3479}(1529,\cdot)\) \(\chi_{3479}(1753,\cdot)\) \(\chi_{3479}(1804,\cdot)\) \(\chi_{3479}(1818,\cdot)\) \(\chi_{3479}(1944,\cdot)\) \(\chi_{3479}(1977,\cdot)\) \(\chi_{3479}(2007,\cdot)\) \(\chi_{3479}(2061,\cdot)\) \(\chi_{3479}(2075,\cdot)\) \(\chi_{3479}(2119,\cdot)\) \(\chi_{3479}(2154,\cdot)\) \(\chi_{3479}(2166,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{11}{42}\right),e\left(\frac{19}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{107}{210}\right)\) |