Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.dn
\(\chi_{6004}(31,\cdot)\) \(\chi_{6004}(335,\cdot)\) \(\chi_{6004}(715,\cdot)\) \(\chi_{6004}(787,\cdot)\) \(\chi_{6004}(1471,\cdot)\) \(\chi_{6004}(1551,\cdot)\) \(\chi_{6004}(2007,\cdot)\) \(\chi_{6004}(2079,\cdot)\) \(\chi_{6004}(2159,\cdot)\) \(\chi_{6004}(2307,\cdot)\) \(\chi_{6004}(2383,\cdot)\) \(\chi_{6004}(2539,\cdot)\) \(\chi_{6004}(2691,\cdot)\) \(\chi_{6004}(2995,\cdot)\) \(\chi_{6004}(3599,\cdot)\) \(\chi_{6004}(4207,\cdot)\) \(\chi_{6004}(4591,\cdot)\) \(\chi_{6004}(4663,\cdot)\) \(\chi_{6004}(4971,\cdot)\) \(\chi_{6004}(5423,\cdot)\) \(\chi_{6004}(5575,\cdot)\) \(\chi_{6004}(5651,\cdot)\) \(\chi_{6004}(5803,\cdot)\) \(\chi_{6004}(5807,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{28}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) |