Basic properties
Modulus: | \(6037\) | |
Conductor: | \(6037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(6036\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6037.l
\(\chi_{6037}(5,\cdot)\) \(\chi_{6037}(6,\cdot)\) \(\chi_{6037}(13,\cdot)\) \(\chi_{6037}(18,\cdot)\) \(\chi_{6037}(20,\cdot)\) \(\chi_{6037}(21,\cdot)\) \(\chi_{6037}(23,\cdot)\) \(\chi_{6037}(24,\cdot)\) \(\chi_{6037}(31,\cdot)\) \(\chi_{6037}(34,\cdot)\) \(\chi_{6037}(37,\cdot)\) \(\chi_{6037}(39,\cdot)\) \(\chi_{6037}(45,\cdot)\) \(\chi_{6037}(50,\cdot)\) \(\chi_{6037}(52,\cdot)\) \(\chi_{6037}(53,\cdot)\) \(\chi_{6037}(55,\cdot)\) \(\chi_{6037}(57,\cdot)\) \(\chi_{6037}(58,\cdot)\) \(\chi_{6037}(61,\cdot)\) \(\chi_{6037}(63,\cdot)\) \(\chi_{6037}(66,\cdot)\) \(\chi_{6037}(67,\cdot)\) \(\chi_{6037}(69,\cdot)\) \(\chi_{6037}(70,\cdot)\) \(\chi_{6037}(72,\cdot)\) \(\chi_{6037}(73,\cdot)\) \(\chi_{6037}(79,\cdot)\) \(\chi_{6037}(80,\cdot)\) \(\chi_{6037}(82,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{6036})$ |
Fixed field: | Number field defined by a degree 6036 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1751}{6036}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6037 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1585}{2012}\right)\) | \(e\left(\frac{497}{3018}\right)\) | \(e\left(\frac{579}{1006}\right)\) | \(e\left(\frac{1751}{6036}\right)\) | \(e\left(\frac{5749}{6036}\right)\) | \(e\left(\frac{1863}{2012}\right)\) | \(e\left(\frac{731}{2012}\right)\) | \(e\left(\frac{497}{1509}\right)\) | \(e\left(\frac{235}{3018}\right)\) | \(e\left(\frac{361}{1006}\right)\) |