Basic properties
| Modulus: | \(1303\) | |
| Conductor: | \(1303\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1302\) | 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 1303.p
\(\chi_{1303}(6,\cdot)\) \(\chi_{1303}(7,\cdot)\) \(\chi_{1303}(10,\cdot)\) \(\chi_{1303}(12,\cdot)\) \(\chi_{1303}(14,\cdot)\) \(\chi_{1303}(20,\cdot)\) \(\chi_{1303}(22,\cdot)\) \(\chi_{1303}(29,\cdot)\) \(\chi_{1303}(31,\cdot)\) \(\chi_{1303}(34,\cdot)\) \(\chi_{1303}(37,\cdot)\) \(\chi_{1303}(38,\cdot)\) \(\chi_{1303}(39,\cdot)\) \(\chi_{1303}(44,\cdot)\) \(\chi_{1303}(48,\cdot)\) \(\chi_{1303}(53,\cdot)\) \(\chi_{1303}(56,\cdot)\) \(\chi_{1303}(58,\cdot)\) \(\chi_{1303}(59,\cdot)\) \(\chi_{1303}(63,\cdot)\) \(\chi_{1303}(69,\cdot)\) \(\chi_{1303}(71,\cdot)\) \(\chi_{1303}(73,\cdot)\) \(\chi_{1303}(78,\cdot)\) \(\chi_{1303}(80,\cdot)\) \(\chi_{1303}(86,\cdot)\) \(\chi_{1303}(90,\cdot)\) \(\chi_{1303}(91,\cdot)\) \(\chi_{1303}(94,\cdot)\) \(\chi_{1303}(97,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{651})$ |
| Fixed field: | Number field defined by a degree 1302 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{271}{1302}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1303 }(1301, a) \) | \(-1\) | \(1\) | \(e\left(\frac{590}{651}\right)\) | \(e\left(\frac{131}{434}\right)\) | \(e\left(\frac{529}{651}\right)\) | \(e\left(\frac{47}{62}\right)\) | \(e\left(\frac{271}{1302}\right)\) | \(e\left(\frac{433}{1302}\right)\) | \(e\left(\frac{156}{217}\right)\) | \(e\left(\frac{131}{217}\right)\) | \(e\left(\frac{865}{1302}\right)\) | \(e\left(\frac{3}{62}\right)\) |