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.es
\(\chi_{3479}(44,\cdot)\) \(\chi_{3479}(123,\cdot)\) \(\chi_{3479}(163,\cdot)\) \(\chi_{3479}(198,\cdot)\) \(\chi_{3479}(268,\cdot)\) \(\chi_{3479}(291,\cdot)\) \(\chi_{3479}(366,\cdot)\) \(\chi_{3479}(683,\cdot)\) \(\chi_{3479}(723,\cdot)\) \(\chi_{3479}(865,\cdot)\) \(\chi_{3479}(921,\cdot)\) \(\chi_{3479}(991,\cdot)\) \(\chi_{3479}(1087,\cdot)\) \(\chi_{3479}(1171,\cdot)\) \(\chi_{3479}(1178,\cdot)\) \(\chi_{3479}(1334,\cdot)\) \(\chi_{3479}(1339,\cdot)\) \(\chi_{3479}(1544,\cdot)\) \(\chi_{3479}(1556,\cdot)\) \(\chi_{3479}(1621,\cdot)\) \(\chi_{3479}(1698,\cdot)\) \(\chi_{3479}(1803,\cdot)\) \(\chi_{3479}(1808,\cdot)\) \(\chi_{3479}(1810,\cdot)\) \(\chi_{3479}(1822,\cdot)\) \(\chi_{3479}(1913,\cdot)\) \(\chi_{3479}(1948,\cdot)\) \(\chi_{3479}(1969,\cdot)\) \(\chi_{3479}(2090,\cdot)\) \(\chi_{3479}(2193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{4}{21}\right),e\left(\frac{43}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{46}{105}\right)\) |