Basic properties
Modulus: | \(9067\) | |
Conductor: | \(9067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4533\) | 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 9067.g
\(\chi_{9067}(6,\cdot)\) \(\chi_{9067}(9,\cdot)\) \(\chi_{9067}(10,\cdot)\) \(\chi_{9067}(15,\cdot)\) \(\chi_{9067}(21,\cdot)\) \(\chi_{9067}(23,\cdot)\) \(\chi_{9067}(24,\cdot)\) \(\chi_{9067}(25,\cdot)\) \(\chi_{9067}(26,\cdot)\) \(\chi_{9067}(31,\cdot)\) \(\chi_{9067}(33,\cdot)\) \(\chi_{9067}(34,\cdot)\) \(\chi_{9067}(35,\cdot)\) \(\chi_{9067}(36,\cdot)\) \(\chi_{9067}(38,\cdot)\) \(\chi_{9067}(40,\cdot)\) \(\chi_{9067}(47,\cdot)\) \(\chi_{9067}(51,\cdot)\) \(\chi_{9067}(55,\cdot)\) \(\chi_{9067}(57,\cdot)\) \(\chi_{9067}(58,\cdot)\) \(\chi_{9067}(59,\cdot)\) \(\chi_{9067}(60,\cdot)\) \(\chi_{9067}(61,\cdot)\) \(\chi_{9067}(74,\cdot)\) \(\chi_{9067}(79,\cdot)\) \(\chi_{9067}(81,\cdot)\) \(\chi_{9067}(82,\cdot)\) \(\chi_{9067}(83,\cdot)\) \(\chi_{9067}(84,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4533})$ |
Fixed field: | Number field defined by a degree 4533 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{4142}{4533}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 9067 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{775}{1511}\right)\) | \(e\left(\frac{4142}{4533}\right)\) | \(e\left(\frac{39}{1511}\right)\) | \(e\left(\frac{3824}{4533}\right)\) | \(e\left(\frac{1934}{4533}\right)\) | \(e\left(\frac{207}{1511}\right)\) | \(e\left(\frac{814}{1511}\right)\) | \(e\left(\frac{3751}{4533}\right)\) | \(e\left(\frac{1616}{4533}\right)\) | \(e\left(\frac{1464}{1511}\right)\) |