Basic properties
| Modulus: | \(113\) | |
| Conductor: | \(113\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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 113.j
\(\chi_{113}(3,\cdot)\) \(\chi_{113}(5,\cdot)\) \(\chi_{113}(6,\cdot)\) \(\chi_{113}(10,\cdot)\) \(\chi_{113}(12,\cdot)\) \(\chi_{113}(17,\cdot)\) \(\chi_{113}(19,\cdot)\) \(\chi_{113}(20,\cdot)\) \(\chi_{113}(21,\cdot)\) \(\chi_{113}(23,\cdot)\) \(\chi_{113}(24,\cdot)\) \(\chi_{113}(27,\cdot)\) \(\chi_{113}(29,\cdot)\) \(\chi_{113}(33,\cdot)\) \(\chi_{113}(34,\cdot)\) \(\chi_{113}(37,\cdot)\) \(\chi_{113}(38,\cdot)\) \(\chi_{113}(39,\cdot)\) \(\chi_{113}(43,\cdot)\) \(\chi_{113}(45,\cdot)\) \(\chi_{113}(46,\cdot)\) \(\chi_{113}(47,\cdot)\) \(\chi_{113}(54,\cdot)\) \(\chi_{113}(55,\cdot)\) \(\chi_{113}(58,\cdot)\) \(\chi_{113}(59,\cdot)\) \(\chi_{113}(66,\cdot)\) \(\chi_{113}(67,\cdot)\) \(\chi_{113}(68,\cdot)\) \(\chi_{113}(70,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{83}{112}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 113 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{83}{112}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{71}{112}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{45}{112}\right)\) | \(e\left(\frac{47}{56}\right)\) |