Basic properties
| Modulus: | \(127\) | |
| Conductor: | \(127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 127.l
\(\chi_{127}(3,\cdot)\) \(\chi_{127}(6,\cdot)\) \(\chi_{127}(7,\cdot)\) \(\chi_{127}(12,\cdot)\) \(\chi_{127}(14,\cdot)\) \(\chi_{127}(23,\cdot)\) \(\chi_{127}(29,\cdot)\) \(\chi_{127}(39,\cdot)\) \(\chi_{127}(43,\cdot)\) \(\chi_{127}(45,\cdot)\) \(\chi_{127}(46,\cdot)\) \(\chi_{127}(48,\cdot)\) \(\chi_{127}(53,\cdot)\) \(\chi_{127}(55,\cdot)\) \(\chi_{127}(56,\cdot)\) \(\chi_{127}(57,\cdot)\) \(\chi_{127}(58,\cdot)\) \(\chi_{127}(65,\cdot)\) \(\chi_{127}(67,\cdot)\) \(\chi_{127}(78,\cdot)\) \(\chi_{127}(83,\cdot)\) \(\chi_{127}(85,\cdot)\) \(\chi_{127}(86,\cdot)\) \(\chi_{127}(91,\cdot)\) \(\chi_{127}(92,\cdot)\) \(\chi_{127}(93,\cdot)\) \(\chi_{127}(96,\cdot)\) \(\chi_{127}(97,\cdot)\) \(\chi_{127}(101,\cdot)\) \(\chi_{127}(106,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{65}{126}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 127 }(118, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{63}\right)\) |