Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(43\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{431}(337,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.q
\(\chi_{6034}(337,\cdot)\) \(\chi_{6034}(435,\cdot)\) \(\chi_{6034}(449,\cdot)\) \(\chi_{6034}(463,\cdot)\) \(\chi_{6034}(575,\cdot)\) \(\chi_{6034}(687,\cdot)\) \(\chi_{6034}(729,\cdot)\) \(\chi_{6034}(1079,\cdot)\) \(\chi_{6034}(1317,\cdot)\) \(\chi_{6034}(1401,\cdot)\) \(\chi_{6034}(1485,\cdot)\) \(\chi_{6034}(1513,\cdot)\) \(\chi_{6034}(1583,\cdot)\) \(\chi_{6034}(1751,\cdot)\) \(\chi_{6034}(1779,\cdot)\) \(\chi_{6034}(2157,\cdot)\) \(\chi_{6034}(2171,\cdot)\) \(\chi_{6034}(2227,\cdot)\) \(\chi_{6034}(2283,\cdot)\) \(\chi_{6034}(2479,\cdot)\) \(\chi_{6034}(2731,\cdot)\) \(\chi_{6034}(2815,\cdot)\) \(\chi_{6034}(2829,\cdot)\) \(\chi_{6034}(3025,\cdot)\) \(\chi_{6034}(3053,\cdot)\) \(\chi_{6034}(3081,\cdot)\) \(\chi_{6034}(3179,\cdot)\) \(\chi_{6034}(3305,\cdot)\) \(\chi_{6034}(3347,\cdot)\) \(\chi_{6034}(3529,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 43 polynomial |
Values on generators
\((1725,869)\) → \((1,e\left(\frac{32}{43}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(337, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{12}{43}\right)\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{1}{43}\right)\) |