Basic properties
| Modulus: | \(2243\) | |
| Conductor: | \(2243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1121\) | 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 2243.g
\(\chi_{2243}(3,\cdot)\) \(\chi_{2243}(4,\cdot)\) \(\chi_{2243}(7,\cdot)\) \(\chi_{2243}(9,\cdot)\) \(\chi_{2243}(10,\cdot)\) \(\chi_{2243}(11,\cdot)\) \(\chi_{2243}(12,\cdot)\) \(\chi_{2243}(16,\cdot)\) \(\chi_{2243}(17,\cdot)\) \(\chi_{2243}(21,\cdot)\) \(\chi_{2243}(25,\cdot)\) \(\chi_{2243}(26,\cdot)\) \(\chi_{2243}(27,\cdot)\) \(\chi_{2243}(28,\cdot)\) \(\chi_{2243}(30,\cdot)\) \(\chi_{2243}(31,\cdot)\) \(\chi_{2243}(33,\cdot)\) \(\chi_{2243}(36,\cdot)\) \(\chi_{2243}(38,\cdot)\) \(\chi_{2243}(40,\cdot)\) \(\chi_{2243}(43,\cdot)\) \(\chi_{2243}(44,\cdot)\) \(\chi_{2243}(46,\cdot)\) \(\chi_{2243}(48,\cdot)\) \(\chi_{2243}(49,\cdot)\) \(\chi_{2243}(51,\cdot)\) \(\chi_{2243}(53,\cdot)\) \(\chi_{2243}(58,\cdot)\) \(\chi_{2243}(61,\cdot)\) \(\chi_{2243}(64,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1121})$ |
| Fixed field: | Number field defined by a degree 1121 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{146}{1121}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2243 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{146}{1121}\right)\) | \(e\left(\frac{17}{1121}\right)\) | \(e\left(\frac{292}{1121}\right)\) | \(e\left(\frac{581}{1121}\right)\) | \(e\left(\frac{163}{1121}\right)\) | \(e\left(\frac{802}{1121}\right)\) | \(e\left(\frac{438}{1121}\right)\) | \(e\left(\frac{34}{1121}\right)\) | \(e\left(\frac{727}{1121}\right)\) | \(e\left(\frac{144}{1121}\right)\) |