Basic properties
| Modulus: | \(6042\) | |
| Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3021}(941,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cm
\(\chi_{6042}(29,\cdot)\) \(\chi_{6042}(59,\cdot)\) \(\chi_{6042}(143,\cdot)\) \(\chi_{6042}(269,\cdot)\) \(\chi_{6042}(431,\cdot)\) \(\chi_{6042}(515,\cdot)\) \(\chi_{6042}(623,\cdot)\) \(\chi_{6042}(857,\cdot)\) \(\chi_{6042}(941,\cdot)\) \(\chi_{6042}(965,\cdot)\) \(\chi_{6042}(971,\cdot)\) \(\chi_{6042}(983,\cdot)\) \(\chi_{6042}(1067,\cdot)\) \(\chi_{6042}(1085,\cdot)\) \(\chi_{6042}(1097,\cdot)\) \(\chi_{6042}(1283,\cdot)\) \(\chi_{6042}(1421,\cdot)\) \(\chi_{6042}(1541,\cdot)\) \(\chi_{6042}(1649,\cdot)\) \(\chi_{6042}(1739,\cdot)\) \(\chi_{6042}(1895,\cdot)\) \(\chi_{6042}(1967,\cdot)\) \(\chi_{6042}(2105,\cdot)\) \(\chi_{6042}(2237,\cdot)\) \(\chi_{6042}(2255,\cdot)\) \(\chi_{6042}(2339,\cdot)\) \(\chi_{6042}(2369,\cdot)\) \(\chi_{6042}(2423,\cdot)\) \(\chi_{6042}(2447,\cdot)\) \(\chi_{6042}(2561,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{17}{18}\right),e\left(\frac{25}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6042 }(941, a) \) | \(1\) | \(1\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{131}{234}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{109}{117}\right)\) |