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
\((1889,297)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{24}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{197}{1044}\right)\) | \(e\left(\frac{401}{522}\right)\) | \(e\left(\frac{197}{522}\right)\) | \(e\left(\frac{283}{1044}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{118}{261}\right)\) | \(e\left(\frac{197}{348}\right)\) | \(e\left(\frac{140}{261}\right)\) | \(e\left(\frac{40}{87}\right)\) | \(e\left(\frac{91}{174}\right)\) |