Basic properties
| Modulus: | \(1123\) | |
| Conductor: | \(1123\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1122\) | 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 1123.p
\(\chi_{1123}(2,\cdot)\) \(\chi_{1123}(3,\cdot)\) \(\chi_{1123}(12,\cdot)\) \(\chi_{1123}(14,\cdot)\) \(\chi_{1123}(18,\cdot)\) \(\chi_{1123}(20,\cdot)\) \(\chi_{1123}(21,\cdot)\) \(\chi_{1123}(29,\cdot)\) \(\chi_{1123}(32,\cdot)\) \(\chi_{1123}(37,\cdot)\) \(\chi_{1123}(44,\cdot)\) \(\chi_{1123}(45,\cdot)\) \(\chi_{1123}(47,\cdot)\) \(\chi_{1123}(50,\cdot)\) \(\chi_{1123}(51,\cdot)\) \(\chi_{1123}(52,\cdot)\) \(\chi_{1123}(57,\cdot)\) \(\chi_{1123}(69,\cdot)\) \(\chi_{1123}(71,\cdot)\) \(\chi_{1123}(72,\cdot)\) \(\chi_{1123}(75,\cdot)\) \(\chi_{1123}(78,\cdot)\) \(\chi_{1123}(80,\cdot)\) \(\chi_{1123}(82,\cdot)\) \(\chi_{1123}(84,\cdot)\) \(\chi_{1123}(86,\cdot)\) \(\chi_{1123}(95,\cdot)\) \(\chi_{1123}(98,\cdot)\) \(\chi_{1123}(99,\cdot)\) \(\chi_{1123}(103,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{561})$ |
| Fixed field: | Number field defined by a degree 1122 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1122}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1123 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1122}\right)\) | \(e\left(\frac{197}{1122}\right)\) | \(e\left(\frac{1}{561}\right)\) | \(e\left(\frac{81}{374}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{374}\right)\) | \(e\left(\frac{197}{561}\right)\) | \(e\left(\frac{122}{561}\right)\) | \(e\left(\frac{59}{374}\right)\) |