Basic properties
| Modulus: | \(1081\) | |
| Conductor: | \(1081\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(253\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1081.m
\(\chi_{1081}(2,\cdot)\) \(\chi_{1081}(3,\cdot)\) \(\chi_{1081}(4,\cdot)\) \(\chi_{1081}(6,\cdot)\) \(\chi_{1081}(8,\cdot)\) \(\chi_{1081}(9,\cdot)\) \(\chi_{1081}(12,\cdot)\) \(\chi_{1081}(16,\cdot)\) \(\chi_{1081}(18,\cdot)\) \(\chi_{1081}(25,\cdot)\) \(\chi_{1081}(27,\cdot)\) \(\chi_{1081}(32,\cdot)\) \(\chi_{1081}(36,\cdot)\) \(\chi_{1081}(49,\cdot)\) \(\chi_{1081}(50,\cdot)\) \(\chi_{1081}(54,\cdot)\) \(\chi_{1081}(55,\cdot)\) \(\chi_{1081}(59,\cdot)\) \(\chi_{1081}(64,\cdot)\) \(\chi_{1081}(71,\cdot)\) \(\chi_{1081}(72,\cdot)\) \(\chi_{1081}(75,\cdot)\) \(\chi_{1081}(81,\cdot)\) \(\chi_{1081}(96,\cdot)\) \(\chi_{1081}(98,\cdot)\) \(\chi_{1081}(100,\cdot)\) \(\chi_{1081}(101,\cdot)\) \(\chi_{1081}(108,\cdot)\) \(\chi_{1081}(110,\cdot)\) \(\chi_{1081}(118,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\((189,898)\) → \((e\left(\frac{1}{11}\right),e\left(\frac{9}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1081 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{253}\right)\) | \(e\left(\frac{71}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{63}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) | \(e\left(\frac{142}{253}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{141}{253}\right)\) |