Basic properties
| Modulus: | \(6037\) | |
| Conductor: | \(6037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(6036\) | 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 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
\(5\) → \(e\left(\frac{5165}{6036}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6037 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1435}{2012}\right)\) | \(e\left(\frac{1859}{3018}\right)\) | \(e\left(\frac{429}{1006}\right)\) | \(e\left(\frac{5165}{6036}\right)\) | \(e\left(\frac{1987}{6036}\right)\) | \(e\left(\frac{1985}{2012}\right)\) | \(e\left(\frac{281}{2012}\right)\) | \(e\left(\frac{350}{1509}\right)\) | \(e\left(\frac{1717}{3018}\right)\) | \(e\left(\frac{403}{1006}\right)\) |