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.fi
\(\chi_{3479}(10,\cdot)\) \(\chi_{3479}(24,\cdot)\) \(\chi_{3479}(89,\cdot)\) \(\chi_{3479}(145,\cdot)\) \(\chi_{3479}(222,\cdot)\) \(\chi_{3479}(327,\cdot)\) \(\chi_{3479}(348,\cdot)\) \(\chi_{3479}(430,\cdot)\) \(\chi_{3479}(486,\cdot)\) \(\chi_{3479}(584,\cdot)\) \(\chi_{3479}(759,\cdot)\) \(\chi_{3479}(1006,\cdot)\) \(\chi_{3479}(1032,\cdot)\) \(\chi_{3479}(1074,\cdot)\) \(\chi_{3479}(1144,\cdot)\) \(\chi_{3479}(1165,\cdot)\) \(\chi_{3479}(1186,\cdot)\) \(\chi_{3479}(1209,\cdot)\) \(\chi_{3479}(1286,\cdot)\) \(\chi_{3479}(1389,\cdot)\) \(\chi_{3479}(1510,\cdot)\) \(\chi_{3479}(1531,\cdot)\) \(\chi_{3479}(1566,\cdot)\) \(\chi_{3479}(1657,\cdot)\) \(\chi_{3479}(1669,\cdot)\) \(\chi_{3479}(1671,\cdot)\) \(\chi_{3479}(1676,\cdot)\) \(\chi_{3479}(1781,\cdot)\) \(\chi_{3479}(1858,\cdot)\) \(\chi_{3479}(1923,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{13}{42}\right),e\left(\frac{17}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{181}{210}\right)\) |