Basic properties
| Modulus: | \(227\) | |
| Conductor: | \(227\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(226\) | 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 227.d
\(\chi_{227}(2,\cdot)\) \(\chi_{227}(5,\cdot)\) \(\chi_{227}(6,\cdot)\) \(\chi_{227}(8,\cdot)\) \(\chi_{227}(13,\cdot)\) \(\chi_{227}(14,\cdot)\) \(\chi_{227}(15,\cdot)\) \(\chi_{227}(17,\cdot)\) \(\chi_{227}(18,\cdot)\) \(\chi_{227}(20,\cdot)\) \(\chi_{227}(22,\cdot)\) \(\chi_{227}(24,\cdot)\) \(\chi_{227}(31,\cdot)\) \(\chi_{227}(32,\cdot)\) \(\chi_{227}(35,\cdot)\) \(\chi_{227}(37,\cdot)\) \(\chi_{227}(38,\cdot)\) \(\chi_{227}(39,\cdot)\) \(\chi_{227}(41,\cdot)\) \(\chi_{227}(42,\cdot)\) \(\chi_{227}(45,\cdot)\) \(\chi_{227}(46,\cdot)\) \(\chi_{227}(50,\cdot)\) \(\chi_{227}(51,\cdot)\) \(\chi_{227}(52,\cdot)\) \(\chi_{227}(54,\cdot)\) \(\chi_{227}(55,\cdot)\) \(\chi_{227}(56,\cdot)\) \(\chi_{227}(58,\cdot)\) \(\chi_{227}(60,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{113})$ |
| Fixed field: | Number field defined by a degree 226 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{159}{226}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 227 }(224, a) \) | \(-1\) | \(1\) | \(e\left(\frac{159}{226}\right)\) | \(e\left(\frac{41}{113}\right)\) | \(e\left(\frac{46}{113}\right)\) | \(e\left(\frac{167}{226}\right)\) | \(e\left(\frac{15}{226}\right)\) | \(e\left(\frac{39}{113}\right)\) | \(e\left(\frac{25}{226}\right)\) | \(e\left(\frac{82}{113}\right)\) | \(e\left(\frac{50}{113}\right)\) | \(e\left(\frac{79}{113}\right)\) |