Basic properties
| Modulus: | \(226\) | |
| Conductor: | \(113\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{113}(110,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 226.j
\(\chi_{226}(3,\cdot)\) \(\chi_{226}(5,\cdot)\) \(\chi_{226}(17,\cdot)\) \(\chi_{226}(19,\cdot)\) \(\chi_{226}(21,\cdot)\) \(\chi_{226}(23,\cdot)\) \(\chi_{226}(27,\cdot)\) \(\chi_{226}(29,\cdot)\) \(\chi_{226}(33,\cdot)\) \(\chi_{226}(37,\cdot)\) \(\chi_{226}(39,\cdot)\) \(\chi_{226}(43,\cdot)\) \(\chi_{226}(45,\cdot)\) \(\chi_{226}(47,\cdot)\) \(\chi_{226}(55,\cdot)\) \(\chi_{226}(59,\cdot)\) \(\chi_{226}(67,\cdot)\) \(\chi_{226}(75,\cdot)\) \(\chi_{226}(79,\cdot)\) \(\chi_{226}(89,\cdot)\) \(\chi_{226}(93,\cdot)\) \(\chi_{226}(101,\cdot)\) \(\chi_{226}(103,\cdot)\) \(\chi_{226}(107,\cdot)\) \(\chi_{226}(119,\cdot)\) \(\chi_{226}(123,\cdot)\) \(\chi_{226}(125,\cdot)\) \(\chi_{226}(133,\cdot)\) \(\chi_{226}(137,\cdot)\) \(\chi_{226}(147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{57}{112}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 226 }(223, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{27}{112}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(-i\) | \(e\left(\frac{61}{112}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{65}{112}\right)\) |