Basic properties
Modulus: | \(6047\) | |
Conductor: | \(6047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(6046\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6047.d
\(\chi_{6047}(5,\cdot)\) \(\chi_{6047}(10,\cdot)\) \(\chi_{6047}(13,\cdot)\) \(\chi_{6047}(15,\cdot)\) \(\chi_{6047}(17,\cdot)\) \(\chi_{6047}(19,\cdot)\) \(\chi_{6047}(20,\cdot)\) \(\chi_{6047}(26,\cdot)\) \(\chi_{6047}(29,\cdot)\) \(\chi_{6047}(30,\cdot)\) \(\chi_{6047}(31,\cdot)\) \(\chi_{6047}(34,\cdot)\) \(\chi_{6047}(35,\cdot)\) \(\chi_{6047}(38,\cdot)\) \(\chi_{6047}(39,\cdot)\) \(\chi_{6047}(40,\cdot)\) \(\chi_{6047}(45,\cdot)\) \(\chi_{6047}(51,\cdot)\) \(\chi_{6047}(52,\cdot)\) \(\chi_{6047}(53,\cdot)\) \(\chi_{6047}(55,\cdot)\) \(\chi_{6047}(57,\cdot)\) \(\chi_{6047}(58,\cdot)\) \(\chi_{6047}(59,\cdot)\) \(\chi_{6047}(60,\cdot)\) \(\chi_{6047}(61,\cdot)\) \(\chi_{6047}(62,\cdot)\) \(\chi_{6047}(67,\cdot)\) \(\chi_{6047}(68,\cdot)\) \(\chi_{6047}(70,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{3023})$ |
Fixed field: | Number field defined by a degree 6046 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{3891}{6046}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6047 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1954}{3023}\right)\) | \(e\left(\frac{1426}{3023}\right)\) | \(e\left(\frac{885}{3023}\right)\) | \(e\left(\frac{3891}{6046}\right)\) | \(e\left(\frac{357}{3023}\right)\) | \(e\left(\frac{1067}{3023}\right)\) | \(e\left(\frac{2839}{3023}\right)\) | \(e\left(\frac{2852}{3023}\right)\) | \(e\left(\frac{1753}{6046}\right)\) | \(e\left(\frac{2325}{3023}\right)\) |