Basic properties
| Modulus: | \(223\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | 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 223.h
\(\chi_{223}(3,\cdot)\) \(\chi_{223}(5,\cdot)\) \(\chi_{223}(6,\cdot)\) \(\chi_{223}(10,\cdot)\) \(\chi_{223}(11,\cdot)\) \(\chi_{223}(12,\cdot)\) \(\chi_{223}(20,\cdot)\) \(\chi_{223}(21,\cdot)\) \(\chi_{223}(22,\cdot)\) \(\chi_{223}(23,\cdot)\) \(\chi_{223}(24,\cdot)\) \(\chi_{223}(35,\cdot)\) \(\chi_{223}(42,\cdot)\) \(\chi_{223}(44,\cdot)\) \(\chi_{223}(45,\cdot)\) \(\chi_{223}(46,\cdot)\) \(\chi_{223}(48,\cdot)\) \(\chi_{223}(51,\cdot)\) \(\chi_{223}(57,\cdot)\) \(\chi_{223}(61,\cdot)\) \(\chi_{223}(67,\cdot)\) \(\chi_{223}(70,\cdot)\) \(\chi_{223}(71,\cdot)\) \(\chi_{223}(75,\cdot)\) \(\chi_{223}(77,\cdot)\) \(\chi_{223}(79,\cdot)\) \(\chi_{223}(80,\cdot)\) \(\chi_{223}(84,\cdot)\) \(\chi_{223}(85,\cdot)\) \(\chi_{223}(88,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{47}{222}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 223 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{47}{222}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{187}{222}\right)\) | \(e\left(\frac{71}{222}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{47}{111}\right)\) | \(e\left(\frac{211}{222}\right)\) | \(e\left(\frac{145}{222}\right)\) |