Basic properties
Modulus: | \(2183\) | |
Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1044\) | 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 2183.bj
\(\chi_{2183}(5,\cdot)\) \(\chi_{2183}(15,\cdot)\) \(\chi_{2183}(17,\cdot)\) \(\chi_{2183}(19,\cdot)\) \(\chi_{2183}(20,\cdot)\) \(\chi_{2183}(22,\cdot)\) \(\chi_{2183}(35,\cdot)\) \(\chi_{2183}(57,\cdot)\) \(\chi_{2183}(76,\cdot)\) \(\chi_{2183}(79,\cdot)\) \(\chi_{2183}(87,\cdot)\) \(\chi_{2183}(94,\cdot)\) \(\chi_{2183}(116,\cdot)\) \(\chi_{2183}(130,\cdot)\) \(\chi_{2183}(133,\cdot)\) \(\chi_{2183}(135,\cdot)\) \(\chi_{2183}(143,\cdot)\) \(\chi_{2183}(146,\cdot)\) \(\chi_{2183}(153,\cdot)\) \(\chi_{2183}(163,\cdot)\) \(\chi_{2183}(166,\cdot)\) \(\chi_{2183}(167,\cdot)\) \(\chi_{2183}(180,\cdot)\) \(\chi_{2183}(198,\cdot)\) \(\chi_{2183}(202,\cdot)\) \(\chi_{2183}(203,\cdot)\) \(\chi_{2183}(204,\cdot)\) \(\chi_{2183}(205,\cdot)\) \(\chi_{2183}(239,\cdot)\) \(\chi_{2183}(240,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1044})$ |
Fixed field: | Number field defined by a degree 1044 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{15}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2183 }(116, a) \) | \(-1\) | \(1\) | \(e\left(\frac{163}{1044}\right)\) | \(e\left(\frac{247}{522}\right)\) | \(e\left(\frac{163}{522}\right)\) | \(e\left(\frac{833}{1044}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{197}{261}\right)\) | \(e\left(\frac{163}{348}\right)\) | \(e\left(\frac{247}{261}\right)\) | \(e\left(\frac{83}{87}\right)\) | \(e\left(\frac{17}{174}\right)\) |