Basic properties
| Modulus: | \(1217\) | |
| Conductor: | \(1217\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1216\) | 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 1217.n
\(\chi_{1217}(3,\cdot)\) \(\chi_{1217}(5,\cdot)\) \(\chi_{1217}(6,\cdot)\) \(\chi_{1217}(7,\cdot)\) \(\chi_{1217}(10,\cdot)\) \(\chi_{1217}(11,\cdot)\) \(\chi_{1217}(12,\cdot)\) \(\chi_{1217}(13,\cdot)\) \(\chi_{1217}(14,\cdot)\) \(\chi_{1217}(17,\cdot)\) \(\chi_{1217}(20,\cdot)\) \(\chi_{1217}(22,\cdot)\) \(\chi_{1217}(23,\cdot)\) \(\chi_{1217}(24,\cdot)\) \(\chi_{1217}(26,\cdot)\) \(\chi_{1217}(27,\cdot)\) \(\chi_{1217}(28,\cdot)\) \(\chi_{1217}(34,\cdot)\) \(\chi_{1217}(40,\cdot)\) \(\chi_{1217}(41,\cdot)\) \(\chi_{1217}(44,\cdot)\) \(\chi_{1217}(45,\cdot)\) \(\chi_{1217}(46,\cdot)\) \(\chi_{1217}(48,\cdot)\) \(\chi_{1217}(52,\cdot)\) \(\chi_{1217}(53,\cdot)\) \(\chi_{1217}(54,\cdot)\) \(\chi_{1217}(56,\cdot)\) \(\chi_{1217}(57,\cdot)\) \(\chi_{1217}(59,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1216})$ |
| Fixed field: | Number field defined by a degree 1216 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{609}{1216}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1217 }(1214, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{152}\right)\) | \(e\left(\frac{609}{1216}\right)\) | \(e\left(\frac{27}{76}\right)\) | \(e\left(\frac{211}{1216}\right)\) | \(e\left(\frac{825}{1216}\right)\) | \(e\left(\frac{721}{1216}\right)\) | \(e\left(\frac{81}{152}\right)\) | \(e\left(\frac{1}{608}\right)\) | \(e\left(\frac{427}{1216}\right)\) | \(e\left(\frac{451}{1216}\right)\) |