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.et
\(\chi_{3479}(207,\cdot)\) \(\chi_{3479}(235,\cdot)\) \(\chi_{3479}(282,\cdot)\) \(\chi_{3479}(317,\cdot)\) \(\chi_{3479}(340,\cdot)\) \(\chi_{3479}(408,\cdot)\) \(\chi_{3479}(417,\cdot)\) \(\chi_{3479}(424,\cdot)\) \(\chi_{3479}(599,\cdot)\) \(\chi_{3479}(681,\cdot)\) \(\chi_{3479}(788,\cdot)\) \(\chi_{3479}(844,\cdot)\) \(\chi_{3479}(907,\cdot)\) \(\chi_{3479}(970,\cdot)\) \(\chi_{3479}(1005,\cdot)\) \(\chi_{3479}(1117,\cdot)\) \(\chi_{3479}(1164,\cdot)\) \(\chi_{3479}(1180,\cdot)\) \(\chi_{3479}(1306,\cdot)\) \(\chi_{3479}(1320,\cdot)\) \(\chi_{3479}(1416,\cdot)\) \(\chi_{3479}(1479,\cdot)\) \(\chi_{3479}(1584,\cdot)\) \(\chi_{3479}(1640,\cdot)\) \(\chi_{3479}(1654,\cdot)\) \(\chi_{3479}(1717,\cdot)\) \(\chi_{3479}(1796,\cdot)\) \(\chi_{3479}(2032,\cdot)\) \(\chi_{3479}(2055,\cdot)\) \(\chi_{3479}(2263,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{20}{21}\right),e\left(\frac{67}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(207, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{89}{105}\right)\) |