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.dq
\(\chi_{6004}(387,\cdot)\) \(\chi_{6004}(543,\cdot)\) \(\chi_{6004}(847,\cdot)\) \(\chi_{6004}(1147,\cdot)\) \(\chi_{6004}(1455,\cdot)\) \(\chi_{6004}(1607,\cdot)\) \(\chi_{6004}(1755,\cdot)\) \(\chi_{6004}(1831,\cdot)\) \(\chi_{6004}(1911,\cdot)\) \(\chi_{6004}(1987,\cdot)\) \(\chi_{6004}(2439,\cdot)\) \(\chi_{6004}(2743,\cdot)\) \(\chi_{6004}(2747,\cdot)\) \(\chi_{6004}(2823,\cdot)\) \(\chi_{6004}(3351,\cdot)\) \(\chi_{6004}(3503,\cdot)\) \(\chi_{6004}(3807,\cdot)\) \(\chi_{6004}(3883,\cdot)\) \(\chi_{6004}(4495,\cdot)\) \(\chi_{6004}(4643,\cdot)\) \(\chi_{6004}(4719,\cdot)\) \(\chi_{6004}(5255,\cdot)\) \(\chi_{6004}(5863,\cdot)\) \(\chi_{6004}(5939,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{17}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(387, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) |