Basic properties
| Modulus: | \(1081\) | |
| Conductor: | \(1081\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(506\) | 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 1081.n
\(\chi_{1081}(7,\cdot)\) \(\chi_{1081}(14,\cdot)\) \(\chi_{1081}(17,\cdot)\) \(\chi_{1081}(21,\cdot)\) \(\chi_{1081}(28,\cdot)\) \(\chi_{1081}(34,\cdot)\) \(\chi_{1081}(37,\cdot)\) \(\chi_{1081}(42,\cdot)\) \(\chi_{1081}(51,\cdot)\) \(\chi_{1081}(53,\cdot)\) \(\chi_{1081}(56,\cdot)\) \(\chi_{1081}(61,\cdot)\) \(\chi_{1081}(63,\cdot)\) \(\chi_{1081}(65,\cdot)\) \(\chi_{1081}(74,\cdot)\) \(\chi_{1081}(79,\cdot)\) \(\chi_{1081}(83,\cdot)\) \(\chi_{1081}(84,\cdot)\) \(\chi_{1081}(89,\cdot)\) \(\chi_{1081}(97,\cdot)\) \(\chi_{1081}(102,\cdot)\) \(\chi_{1081}(103,\cdot)\) \(\chi_{1081}(106,\cdot)\) \(\chi_{1081}(111,\cdot)\) \(\chi_{1081}(112,\cdot)\) \(\chi_{1081}(122,\cdot)\) \(\chi_{1081}(126,\cdot)\) \(\chi_{1081}(130,\cdot)\) \(\chi_{1081}(136,\cdot)\) \(\chi_{1081}(143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\((189,898)\) → \((e\left(\frac{13}{22}\right),e\left(\frac{3}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1081 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{134}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{365}{506}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{203}{506}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{127}{506}\right)\) | \(e\left(\frac{117}{506}\right)\) |