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.en
\(\chi_{6004}(155,\cdot)\) \(\chi_{6004}(167,\cdot)\) \(\chi_{6004}(439,\cdot)\) \(\chi_{6004}(547,\cdot)\) \(\chi_{6004}(751,\cdot)\) \(\chi_{6004}(755,\cdot)\) \(\chi_{6004}(839,\cdot)\) \(\chi_{6004}(979,\cdot)\) \(\chi_{6004}(1047,\cdot)\) \(\chi_{6004}(1115,\cdot)\) \(\chi_{6004}(1283,\cdot)\) \(\chi_{6004}(1363,\cdot)\) \(\chi_{6004}(1383,\cdot)\) \(\chi_{6004}(1447,\cdot)\) \(\chi_{6004}(1495,\cdot)\) \(\chi_{6004}(1503,\cdot)\) \(\chi_{6004}(1611,\cdot)\) \(\chi_{6004}(1663,\cdot)\) \(\chi_{6004}(1675,\cdot)\) \(\chi_{6004}(1751,\cdot)\) \(\chi_{6004}(1819,\cdot)\) \(\chi_{6004}(1915,\cdot)\) \(\chi_{6004}(2263,\cdot)\) \(\chi_{6004}(2295,\cdot)\) \(\chi_{6004}(2331,\cdot)\) \(\chi_{6004}(2415,\cdot)\) \(\chi_{6004}(2491,\cdot)\) \(\chi_{6004}(2499,\cdot)\) \(\chi_{6004}(2559,\cdot)\) \(\chi_{6004}(2579,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{20}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{117}\right)\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{5}{18}\right)\) |