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.dr
\(\chi_{6004}(151,\cdot)\) \(\chi_{6004}(683,\cdot)\) \(\chi_{6004}(835,\cdot)\) \(\chi_{6004}(911,\cdot)\) \(\chi_{6004}(1063,\cdot)\) \(\chi_{6004}(1747,\cdot)\) \(\chi_{6004}(2051,\cdot)\) \(\chi_{6004}(2127,\cdot)\) \(\chi_{6004}(2735,\cdot)\) \(\chi_{6004}(2963,\cdot)\) \(\chi_{6004}(3191,\cdot)\) \(\chi_{6004}(3343,\cdot)\) \(\chi_{6004}(3495,\cdot)\) \(\chi_{6004}(3571,\cdot)\) \(\chi_{6004}(3647,\cdot)\) \(\chi_{6004}(3875,\cdot)\) \(\chi_{6004}(4711,\cdot)\) \(\chi_{6004}(4863,\cdot)\) \(\chi_{6004}(5167,\cdot)\) \(\chi_{6004}(5319,\cdot)\) \(\chi_{6004}(5471,\cdot)\) \(\chi_{6004}(5699,\cdot)\) \(\chi_{6004}(5851,\cdot)\) \(\chi_{6004}(5927,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,-1,e\left(\frac{7}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) |