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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2183.bi
\(\chi_{2183}(2,\cdot)\) \(\chi_{2183}(13,\cdot)\) \(\chi_{2183}(18,\cdot)\) \(\chi_{2183}(24,\cdot)\) \(\chi_{2183}(32,\cdot)\) \(\chi_{2183}(39,\cdot)\) \(\chi_{2183}(42,\cdot)\) \(\chi_{2183}(50,\cdot)\) \(\chi_{2183}(52,\cdot)\) \(\chi_{2183}(54,\cdot)\) \(\chi_{2183}(55,\cdot)\) \(\chi_{2183}(56,\cdot)\) \(\chi_{2183}(61,\cdot)\) \(\chi_{2183}(69,\cdot)\) \(\chi_{2183}(72,\cdot)\) \(\chi_{2183}(89,\cdot)\) \(\chi_{2183}(91,\cdot)\) \(\chi_{2183}(92,\cdot)\) \(\chi_{2183}(93,\cdot)\) \(\chi_{2183}(96,\cdot)\) \(\chi_{2183}(98,\cdot)\) \(\chi_{2183}(106,\cdot)\) \(\chi_{2183}(109,\cdot)\) \(\chi_{2183}(113,\cdot)\) \(\chi_{2183}(124,\cdot)\) \(\chi_{2183}(126,\cdot)\) \(\chi_{2183}(128,\cdot)\) \(\chi_{2183}(129,\cdot)\) \(\chi_{2183}(131,\cdot)\) \(\chi_{2183}(150,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1044})$ |
| Fixed field: | Number field defined by a degree 1044 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{1}{36}\right),e\left(\frac{1}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{1044}\right)\) | \(e\left(\frac{305}{522}\right)\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{775}{1044}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{52}{261}\right)\) | \(e\left(\frac{47}{348}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{23}{87}\right)\) |