Basic properties
| Modulus: | \(2243\) | |
| Conductor: | \(2243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2242\) | 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 2243.h
\(\chi_{2243}(2,\cdot)\) \(\chi_{2243}(5,\cdot)\) \(\chi_{2243}(6,\cdot)\) \(\chi_{2243}(8,\cdot)\) \(\chi_{2243}(13,\cdot)\) \(\chi_{2243}(14,\cdot)\) \(\chi_{2243}(15,\cdot)\) \(\chi_{2243}(18,\cdot)\) \(\chi_{2243}(19,\cdot)\) \(\chi_{2243}(20,\cdot)\) \(\chi_{2243}(22,\cdot)\) \(\chi_{2243}(23,\cdot)\) \(\chi_{2243}(24,\cdot)\) \(\chi_{2243}(29,\cdot)\) \(\chi_{2243}(32,\cdot)\) \(\chi_{2243}(34,\cdot)\) \(\chi_{2243}(35,\cdot)\) \(\chi_{2243}(37,\cdot)\) \(\chi_{2243}(39,\cdot)\) \(\chi_{2243}(41,\cdot)\) \(\chi_{2243}(42,\cdot)\) \(\chi_{2243}(45,\cdot)\) \(\chi_{2243}(47,\cdot)\) \(\chi_{2243}(50,\cdot)\) \(\chi_{2243}(52,\cdot)\) \(\chi_{2243}(54,\cdot)\) \(\chi_{2243}(55,\cdot)\) \(\chi_{2243}(56,\cdot)\) \(\chi_{2243}(59,\cdot)\) \(\chi_{2243}(60,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1121})$ |
| Fixed field: | Number field defined by a degree 2242 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1715}{2242}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2243 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1715}{2242}\right)\) | \(e\left(\frac{764}{1121}\right)\) | \(e\left(\frac{594}{1121}\right)\) | \(e\left(\frac{1381}{2242}\right)\) | \(e\left(\frac{1001}{2242}\right)\) | \(e\left(\frac{1094}{1121}\right)\) | \(e\left(\frac{661}{2242}\right)\) | \(e\left(\frac{407}{1121}\right)\) | \(e\left(\frac{427}{1121}\right)\) | \(e\left(\frac{339}{1121}\right)\) |