Basic properties
| Modulus: | \(223\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(111\) | 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 223.g
\(\chi_{223}(9,\cdot)\) \(\chi_{223}(18,\cdot)\) \(\chi_{223}(19,\cdot)\) \(\chi_{223}(25,\cdot)\) \(\chi_{223}(29,\cdot)\) \(\chi_{223}(31,\cdot)\) \(\chi_{223}(36,\cdot)\) \(\chi_{223}(37,\cdot)\) \(\chi_{223}(38,\cdot)\) \(\chi_{223}(43,\cdot)\) \(\chi_{223}(47,\cdot)\) \(\chi_{223}(50,\cdot)\) \(\chi_{223}(53,\cdot)\) \(\chi_{223}(55,\cdot)\) \(\chi_{223}(58,\cdot)\) \(\chi_{223}(62,\cdot)\) \(\chi_{223}(63,\cdot)\) \(\chi_{223}(65,\cdot)\) \(\chi_{223}(69,\cdot)\) \(\chi_{223}(72,\cdot)\) \(\chi_{223}(73,\cdot)\) \(\chi_{223}(74,\cdot)\) \(\chi_{223}(76,\cdot)\) \(\chi_{223}(78,\cdot)\) \(\chi_{223}(81,\cdot)\) \(\chi_{223}(83,\cdot)\) \(\chi_{223}(86,\cdot)\) \(\chi_{223}(89,\cdot)\) \(\chi_{223}(94,\cdot)\) \(\chi_{223}(100,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{56}{111}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 223 }(220, a) \) | \(1\) | \(1\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{56}{111}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{100}{111}\right)\) | \(e\left(\frac{35}{111}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{1}{111}\right)\) | \(e\left(\frac{79}{111}\right)\) | \(e\left(\frac{109}{111}\right)\) |