Basic properties
| Modulus: | \(1249\) | |
| Conductor: | \(1249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1248\) | 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 1249.x
\(\chi_{1249}(7,\cdot)\) \(\chi_{1249}(11,\cdot)\) \(\chi_{1249}(14,\cdot)\) \(\chi_{1249}(19,\cdot)\) \(\chi_{1249}(21,\cdot)\) \(\chi_{1249}(29,\cdot)\) \(\chi_{1249}(33,\cdot)\) \(\chi_{1249}(41,\cdot)\) \(\chi_{1249}(42,\cdot)\) \(\chi_{1249}(43,\cdot)\) \(\chi_{1249}(44,\cdot)\) \(\chi_{1249}(55,\cdot)\) \(\chi_{1249}(56,\cdot)\) \(\chi_{1249}(59,\cdot)\) \(\chi_{1249}(61,\cdot)\) \(\chi_{1249}(63,\cdot)\) \(\chi_{1249}(67,\cdot)\) \(\chi_{1249}(70,\cdot)\) \(\chi_{1249}(71,\cdot)\) \(\chi_{1249}(87,\cdot)\) \(\chi_{1249}(88,\cdot)\) \(\chi_{1249}(89,\cdot)\) \(\chi_{1249}(91,\cdot)\) \(\chi_{1249}(92,\cdot)\) \(\chi_{1249}(95,\cdot)\) \(\chi_{1249}(99,\cdot)\) \(\chi_{1249}(106,\cdot)\) \(\chi_{1249}(107,\cdot)\) \(\chi_{1249}(110,\cdot)\) \(\chi_{1249}(112,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1248})$ |
| Fixed field: | Number field defined by a degree 1248 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{1}{1248}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1249 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{125}{208}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{361}{624}\right)\) | \(e\left(\frac{179}{624}\right)\) | \(e\left(\frac{1}{1248}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{55}{208}\right)\) | \(e\left(\frac{191}{1248}\right)\) |