Basic properties
| Modulus: | \(6041\) | |
| Conductor: | \(6041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1293\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 6041.m
\(\chi_{6041}(2,\cdot)\) \(\chi_{6041}(4,\cdot)\) \(\chi_{6041}(9,\cdot)\) \(\chi_{6041}(16,\cdot)\) \(\chi_{6041}(18,\cdot)\) \(\chi_{6041}(25,\cdot)\) \(\chi_{6041}(32,\cdot)\) \(\chi_{6041}(37,\cdot)\) \(\chi_{6041}(51,\cdot)\) \(\chi_{6041}(53,\cdot)\) \(\chi_{6041}(58,\cdot)\) \(\chi_{6041}(65,\cdot)\) \(\chi_{6041}(72,\cdot)\) \(\chi_{6041}(74,\cdot)\) \(\chi_{6041}(81,\cdot)\) \(\chi_{6041}(86,\cdot)\) \(\chi_{6041}(93,\cdot)\) \(\chi_{6041}(100,\cdot)\) \(\chi_{6041}(102,\cdot)\) \(\chi_{6041}(107,\cdot)\) \(\chi_{6041}(109,\cdot)\) \(\chi_{6041}(114,\cdot)\) \(\chi_{6041}(116,\cdot)\) \(\chi_{6041}(121,\cdot)\) \(\chi_{6041}(123,\cdot)\) \(\chi_{6041}(128,\cdot)\) \(\chi_{6041}(130,\cdot)\) \(\chi_{6041}(142,\cdot)\) \(\chi_{6041}(144,\cdot)\) \(\chi_{6041}(149,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1293})$ |
| Fixed field: | Number field defined by a degree 1293 polynomial (not computed) |
Values on generators
\((864,4320)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{296}{431}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6041 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{307}{1293}\right)\) | \(e\left(\frac{494}{1293}\right)\) | \(e\left(\frac{614}{1293}\right)\) | \(e\left(\frac{457}{1293}\right)\) | \(e\left(\frac{267}{431}\right)\) | \(e\left(\frac{307}{431}\right)\) | \(e\left(\frac{988}{1293}\right)\) | \(e\left(\frac{764}{1293}\right)\) | \(e\left(\frac{530}{1293}\right)\) | \(e\left(\frac{1108}{1293}\right)\) |