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.fh
\(\chi_{3479}(3,\cdot)\) \(\chi_{3479}(292,\cdot)\) \(\chi_{3479}(299,\cdot)\) \(\chi_{3479}(320,\cdot)\) \(\chi_{3479}(367,\cdot)\) \(\chi_{3479}(507,\cdot)\) \(\chi_{3479}(535,\cdot)\) \(\chi_{3479}(537,\cdot)\) \(\chi_{3479}(626,\cdot)\) \(\chi_{3479}(628,\cdot)\) \(\chi_{3479}(642,\cdot)\) \(\chi_{3479}(649,\cdot)\) \(\chi_{3479}(726,\cdot)\) \(\chi_{3479}(929,\cdot)\) \(\chi_{3479}(941,\cdot)\) \(\chi_{3479}(1013,\cdot)\) \(\chi_{3479}(1160,\cdot)\) \(\chi_{3479}(1172,\cdot)\) \(\chi_{3479}(1216,\cdot)\) \(\chi_{3479}(1424,\cdot)\) \(\chi_{3479}(1447,\cdot)\) \(\chi_{3479}(1683,\cdot)\) \(\chi_{3479}(1762,\cdot)\) \(\chi_{3479}(1825,\cdot)\) \(\chi_{3479}(1839,\cdot)\) \(\chi_{3479}(1895,\cdot)\) \(\chi_{3479}(2000,\cdot)\) \(\chi_{3479}(2063,\cdot)\) \(\chi_{3479}(2159,\cdot)\) \(\chi_{3479}(2173,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{1}{42}\right),e\left(\frac{13}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{79}{210}\right)\) |