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.eu
\(\chi_{3479}(46,\cdot)\) \(\chi_{3479}(88,\cdot)\) \(\chi_{3479}(137,\cdot)\) \(\chi_{3479}(156,\cdot)\) \(\chi_{3479}(298,\cdot)\) \(\chi_{3479}(401,\cdot)\) \(\chi_{3479}(443,\cdot)\) \(\chi_{3479}(492,\cdot)\) \(\chi_{3479}(543,\cdot)\) \(\chi_{3479}(585,\cdot)\) \(\chi_{3479}(634,\cdot)\) \(\chi_{3479}(653,\cdot)\) \(\chi_{3479}(795,\cdot)\) \(\chi_{3479}(898,\cdot)\) \(\chi_{3479}(940,\cdot)\) \(\chi_{3479}(989,\cdot)\) \(\chi_{3479}(1040,\cdot)\) \(\chi_{3479}(1082,\cdot)\) \(\chi_{3479}(1131,\cdot)\) \(\chi_{3479}(1150,\cdot)\) \(\chi_{3479}(1395,\cdot)\) \(\chi_{3479}(1437,\cdot)\) \(\chi_{3479}(1486,\cdot)\) \(\chi_{3479}(1579,\cdot)\) \(\chi_{3479}(1628,\cdot)\) \(\chi_{3479}(1789,\cdot)\) \(\chi_{3479}(1934,\cdot)\) \(\chi_{3479}(1983,\cdot)\) \(\chi_{3479}(2034,\cdot)\) \(\chi_{3479}(2144,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{11}{21}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{17}{105}\right)\) |