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.ew
\(\chi_{3479}(53,\cdot)\) \(\chi_{3479}(65,\cdot)\) \(\chi_{3479}(149,\cdot)\) \(\chi_{3479}(184,\cdot)\) \(\chi_{3479}(326,\cdot)\) \(\chi_{3479}(457,\cdot)\) \(\chi_{3479}(485,\cdot)\) \(\chi_{3479}(541,\cdot)\) \(\chi_{3479}(702,\cdot)\) \(\chi_{3479}(809,\cdot)\) \(\chi_{3479}(842,\cdot)\) \(\chi_{3479}(905,\cdot)\) \(\chi_{3479}(919,\cdot)\) \(\chi_{3479}(1061,\cdot)\) \(\chi_{3479}(1124,\cdot)\) \(\chi_{3479}(1229,\cdot)\) \(\chi_{3479}(1269,\cdot)\) \(\chi_{3479}(1285,\cdot)\) \(\chi_{3479}(1299,\cdot)\) \(\chi_{3479}(1362,\cdot)\) \(\chi_{3479}(1668,\cdot)\) \(\chi_{3479}(1677,\cdot)\) \(\chi_{3479}(1759,\cdot)\) \(\chi_{3479}(1773,\cdot)\) \(\chi_{3479}(1857,\cdot)\) \(\chi_{3479}(1908,\cdot)\) \(\chi_{3479}(1964,\cdot)\) \(\chi_{3479}(2081,\cdot)\) \(\chi_{3479}(2111,\cdot)\) \(\chi_{3479}(2195,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{23}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{11}{105}\right)\) |