Basic properties
Modulus: | \(6041\) | |
Conductor: | \(6041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2586\) | 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.o
\(\chi_{6041}(5,\cdot)\) \(\chi_{6041}(10,\cdot)\) \(\chi_{6041}(26,\cdot)\) \(\chi_{6041}(33,\cdot)\) \(\chi_{6041}(40,\cdot)\) \(\chi_{6041}(45,\cdot)\) \(\chi_{6041}(47,\cdot)\) \(\chi_{6041}(52,\cdot)\) \(\chi_{6041}(66,\cdot)\) \(\chi_{6041}(73,\cdot)\) \(\chi_{6041}(80,\cdot)\) \(\chi_{6041}(89,\cdot)\) \(\chi_{6041}(94,\cdot)\) \(\chi_{6041}(101,\cdot)\) \(\chi_{6041}(117,\cdot)\) \(\chi_{6041}(131,\cdot)\) \(\chi_{6041}(138,\cdot)\) \(\chi_{6041}(145,\cdot)\) \(\chi_{6041}(157,\cdot)\) \(\chi_{6041}(166,\cdot)\) \(\chi_{6041}(173,\cdot)\) \(\chi_{6041}(178,\cdot)\) \(\chi_{6041}(180,\cdot)\) \(\chi_{6041}(185,\cdot)\) \(\chi_{6041}(187,\cdot)\) \(\chi_{6041}(194,\cdot)\) \(\chi_{6041}(201,\cdot)\) \(\chi_{6041}(208,\cdot)\) \(\chi_{6041}(215,\cdot)\) \(\chi_{6041}(227,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1293})$ |
Fixed field: | Number field defined by a degree 2586 polynomial (not computed) |
Values on generators
\((864,4320)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{862}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6041 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{457}{1293}\right)\) | \(e\left(\frac{919}{2586}\right)\) | \(e\left(\frac{914}{1293}\right)\) | \(e\left(\frac{217}{1293}\right)\) | \(e\left(\frac{611}{862}\right)\) | \(e\left(\frac{26}{431}\right)\) | \(e\left(\frac{919}{1293}\right)\) | \(e\left(\frac{674}{1293}\right)\) | \(e\left(\frac{1321}{2586}\right)\) | \(e\left(\frac{161}{2586}\right)\) |