Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 6004.ep
\(\chi_{6004}(15,\cdot)\) \(\chi_{6004}(71,\cdot)\) \(\chi_{6004}(91,\cdot)\) \(\chi_{6004}(219,\cdot)\) \(\chi_{6004}(295,\cdot)\) \(\chi_{6004}(507,\cdot)\) \(\chi_{6004}(515,\cdot)\) \(\chi_{6004}(535,\cdot)\) \(\chi_{6004}(611,\cdot)\) \(\chi_{6004}(659,\cdot)\) \(\chi_{6004}(831,\cdot)\) \(\chi_{6004}(851,\cdot)\) \(\chi_{6004}(927,\cdot)\) \(\chi_{6004}(963,\cdot)\) \(\chi_{6004}(1039,\cdot)\) \(\chi_{6004}(1123,\cdot)\) \(\chi_{6004}(1199,\cdot)\) \(\chi_{6004}(1439,\cdot)\) \(\chi_{6004}(1515,\cdot)\) \(\chi_{6004}(1799,\cdot)\) \(\chi_{6004}(1807,\cdot)\) \(\chi_{6004}(1875,\cdot)\) \(\chi_{6004}(1967,\cdot)\) \(\chi_{6004}(2111,\cdot)\) \(\chi_{6004}(2123,\cdot)\) \(\chi_{6004}(2283,\cdot)\) \(\chi_{6004}(2427,\cdot)\) \(\chi_{6004}(2599,\cdot)\) \(\chi_{6004}(2719,\cdot)\) \(\chi_{6004}(2727,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{11}{18}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{234}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{59}{117}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{17}{234}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{13}{18}\right)\) |