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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ej
\(\chi_{6004}(67,\cdot)\) \(\chi_{6004}(143,\cdot)\) \(\chi_{6004}(223,\cdot)\) \(\chi_{6004}(299,\cdot)\) \(\chi_{6004}(383,\cdot)\) \(\chi_{6004}(447,\cdot)\) \(\chi_{6004}(459,\cdot)\) \(\chi_{6004}(591,\cdot)\) \(\chi_{6004}(599,\cdot)\) \(\chi_{6004}(699,\cdot)\) \(\chi_{6004}(763,\cdot)\) \(\chi_{6004}(775,\cdot)\) \(\chi_{6004}(811,\cdot)\) \(\chi_{6004}(887,\cdot)\) \(\chi_{6004}(907,\cdot)\) \(\chi_{6004}(915,\cdot)\) \(\chi_{6004}(1079,\cdot)\) \(\chi_{6004}(1207,\cdot)\) \(\chi_{6004}(1231,\cdot)\) \(\chi_{6004}(1351,\cdot)\) \(\chi_{6004}(1511,\cdot)\) \(\chi_{6004}(1523,\cdot)\) \(\chi_{6004}(1647,\cdot)\) \(\chi_{6004}(1667,\cdot)\) \(\chi_{6004}(1723,\cdot)\) \(\chi_{6004}(1827,\cdot)\) \(\chi_{6004}(1839,\cdot)\) \(\chi_{6004}(2027,\cdot)\) \(\chi_{6004}(2119,\cdot)\) \(\chi_{6004}(2143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{11}{18}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(2143, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{13}{18}\right)\) |