Basic properties
| Modulus: | \(1277\) | |
| Conductor: | \(1277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1276\) | 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 1277.l
\(\chi_{1277}(2,\cdot)\) \(\chi_{1277}(3,\cdot)\) \(\chi_{1277}(5,\cdot)\) \(\chi_{1277}(7,\cdot)\) \(\chi_{1277}(8,\cdot)\) \(\chi_{1277}(18,\cdot)\) \(\chi_{1277}(20,\cdot)\) \(\chi_{1277}(22,\cdot)\) \(\chi_{1277}(26,\cdot)\) \(\chi_{1277}(27,\cdot)\) \(\chi_{1277}(28,\cdot)\) \(\chi_{1277}(31,\cdot)\) \(\chi_{1277}(32,\cdot)\) \(\chi_{1277}(34,\cdot)\) \(\chi_{1277}(38,\cdot)\) \(\chi_{1277}(39,\cdot)\) \(\chi_{1277}(42,\cdot)\) \(\chi_{1277}(43,\cdot)\) \(\chi_{1277}(45,\cdot)\) \(\chi_{1277}(46,\cdot)\) \(\chi_{1277}(48,\cdot)\) \(\chi_{1277}(50,\cdot)\) \(\chi_{1277}(51,\cdot)\) \(\chi_{1277}(55,\cdot)\) \(\chi_{1277}(57,\cdot)\) \(\chi_{1277}(58,\cdot)\) \(\chi_{1277}(63,\cdot)\) \(\chi_{1277}(65,\cdot)\) \(\chi_{1277}(70,\cdot)\) \(\chi_{1277}(71,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1276})$ |
| Fixed field: | Number field defined by a degree 1276 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{639}{1276}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1277 }(1275, a) \) | \(-1\) | \(1\) | \(e\left(\frac{639}{1276}\right)\) | \(e\left(\frac{31}{1276}\right)\) | \(e\left(\frac{1}{638}\right)\) | \(e\left(\frac{23}{1276}\right)\) | \(e\left(\frac{335}{638}\right)\) | \(e\left(\frac{475}{1276}\right)\) | \(e\left(\frac{641}{1276}\right)\) | \(e\left(\frac{31}{638}\right)\) | \(e\left(\frac{331}{638}\right)\) | \(e\left(\frac{61}{319}\right)\) |