Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(125,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cw
\(\chi_{6004}(125,\cdot)\) \(\chi_{6004}(653,\cdot)\) \(\chi_{6004}(729,\cdot)\) \(\chi_{6004}(733,\cdot)\) \(\chi_{6004}(1037,\cdot)\) \(\chi_{6004}(1489,\cdot)\) \(\chi_{6004}(1565,\cdot)\) \(\chi_{6004}(1645,\cdot)\) \(\chi_{6004}(1721,\cdot)\) \(\chi_{6004}(1869,\cdot)\) \(\chi_{6004}(2021,\cdot)\) \(\chi_{6004}(2329,\cdot)\) \(\chi_{6004}(2629,\cdot)\) \(\chi_{6004}(2933,\cdot)\) \(\chi_{6004}(3089,\cdot)\) \(\chi_{6004}(3541,\cdot)\) \(\chi_{6004}(3617,\cdot)\) \(\chi_{6004}(4225,\cdot)\) \(\chi_{6004}(4761,\cdot)\) \(\chi_{6004}(4837,\cdot)\) \(\chi_{6004}(4985,\cdot)\) \(\chi_{6004}(5597,\cdot)\) \(\chi_{6004}(5673,\cdot)\) \(\chi_{6004}(5977,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{5}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |