Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(217,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.do
\(\chi_{6004}(217,\cdot)\) \(\chi_{6004}(297,\cdot)\) \(\chi_{6004}(601,\cdot)\) \(\chi_{6004}(825,\cdot)\) \(\chi_{6004}(829,\cdot)\) \(\chi_{6004}(1665,\cdot)\) \(\chi_{6004}(2041,\cdot)\) \(\chi_{6004}(2045,\cdot)\) \(\chi_{6004}(2117,\cdot)\) \(\chi_{6004}(2345,\cdot)\) \(\chi_{6004}(2953,\cdot)\) \(\chi_{6004}(3637,\cdot)\) \(\chi_{6004}(3641,\cdot)\) \(\chi_{6004}(3945,\cdot)\) \(\chi_{6004}(4097,\cdot)\) \(\chi_{6004}(4477,\cdot)\) \(\chi_{6004}(4625,\cdot)\) \(\chi_{6004}(4629,\cdot)\) \(\chi_{6004}(4777,\cdot)\) \(\chi_{6004}(4853,\cdot)\) \(\chi_{6004}(5005,\cdot)\) \(\chi_{6004}(5085,\cdot)\) \(\chi_{6004}(5765,\cdot)\) \(\chi_{6004}(5921,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{31}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(217, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) |