Basic properties
Modulus: | \(6043\) | |
Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(3021\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 6043.o
\(\chi_{6043}(6,\cdot)\) \(\chi_{6043}(10,\cdot)\) \(\chi_{6043}(15,\cdot)\) \(\chi_{6043}(17,\cdot)\) \(\chi_{6043}(21,\cdot)\) \(\chi_{6043}(22,\cdot)\) \(\chi_{6043}(25,\cdot)\) \(\chi_{6043}(31,\cdot)\) \(\chi_{6043}(33,\cdot)\) \(\chi_{6043}(36,\cdot)\) \(\chi_{6043}(39,\cdot)\) \(\chi_{6043}(40,\cdot)\) \(\chi_{6043}(49,\cdot)\) \(\chi_{6043}(54,\cdot)\) \(\chi_{6043}(55,\cdot)\) \(\chi_{6043}(56,\cdot)\) \(\chi_{6043}(57,\cdot)\) \(\chi_{6043}(58,\cdot)\) \(\chi_{6043}(61,\cdot)\) \(\chi_{6043}(68,\cdot)\) \(\chi_{6043}(73,\cdot)\) \(\chi_{6043}(79,\cdot)\) \(\chi_{6043}(84,\cdot)\) \(\chi_{6043}(86,\cdot)\) \(\chi_{6043}(87,\cdot)\) \(\chi_{6043}(88,\cdot)\) \(\chi_{6043}(89,\cdot)\) \(\chi_{6043}(90,\cdot)\) \(\chi_{6043}(92,\cdot)\) \(\chi_{6043}(96,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{3021})$ |
Fixed field: | Number field defined by a degree 3021 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{2333}{3021}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6043 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{159}\right)\) | \(e\left(\frac{131}{1007}\right)\) | \(e\left(\frac{76}{159}\right)\) | \(e\left(\frac{2333}{3021}\right)\) | \(e\left(\frac{1115}{3021}\right)\) | \(e\left(\frac{565}{3021}\right)\) | \(e\left(\frac{38}{53}\right)\) | \(e\left(\frac{262}{1007}\right)\) | \(e\left(\frac{34}{3021}\right)\) | \(e\left(\frac{40}{57}\right)\) |