Basic properties
| Modulus: | \(6042\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(554,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.co
\(\chi_{6042}(13,\cdot)\) \(\chi_{6042}(97,\cdot)\) \(\chi_{6042}(205,\cdot)\) \(\chi_{6042}(307,\cdot)\) \(\chi_{6042}(439,\cdot)\) \(\chi_{6042}(523,\cdot)\) \(\chi_{6042}(649,\cdot)\) \(\chi_{6042}(811,\cdot)\) \(\chi_{6042}(895,\cdot)\) \(\chi_{6042}(925,\cdot)\) \(\chi_{6042}(1003,\cdot)\) \(\chi_{6042}(1123,\cdot)\) \(\chi_{6042}(1321,\cdot)\) \(\chi_{6042}(1447,\cdot)\) \(\chi_{6042}(1459,\cdot)\) \(\chi_{6042}(1477,\cdot)\) \(\chi_{6042}(1561,\cdot)\) \(\chi_{6042}(1573,\cdot)\) \(\chi_{6042}(1579,\cdot)\) \(\chi_{6042}(1687,\cdot)\) \(\chi_{6042}(1777,\cdot)\) \(\chi_{6042}(1891,\cdot)\) \(\chi_{6042}(1921,\cdot)\) \(\chi_{6042}(2005,\cdot)\) \(\chi_{6042}(2029,\cdot)\) \(\chi_{6042}(2275,\cdot)\) \(\chi_{6042}(2347,\cdot)\) \(\chi_{6042}(2485,\cdot)\) \(\chi_{6042}(2713,\cdot)\) \(\chi_{6042}(2719,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{13}{18}\right),e\left(\frac{5}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6042 }(1561, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{8}{117}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{31}{117}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{41}{117}\right)\) |