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.o
\(\chi_{1081}(13,\cdot)\) \(\chi_{1081}(26,\cdot)\) \(\chi_{1081}(29,\cdot)\) \(\chi_{1081}(31,\cdot)\) \(\chi_{1081}(35,\cdot)\) \(\chi_{1081}(39,\cdot)\) \(\chi_{1081}(41,\cdot)\) \(\chi_{1081}(52,\cdot)\) \(\chi_{1081}(58,\cdot)\) \(\chi_{1081}(62,\cdot)\) \(\chi_{1081}(73,\cdot)\) \(\chi_{1081}(77,\cdot)\) \(\chi_{1081}(78,\cdot)\) \(\chi_{1081}(82,\cdot)\) \(\chi_{1081}(85,\cdot)\) \(\chi_{1081}(87,\cdot)\) \(\chi_{1081}(104,\cdot)\) \(\chi_{1081}(105,\cdot)\) \(\chi_{1081}(117,\cdot)\) \(\chi_{1081}(123,\cdot)\) \(\chi_{1081}(124,\cdot)\) \(\chi_{1081}(127,\cdot)\) \(\chi_{1081}(133,\cdot)\) \(\chi_{1081}(146,\cdot)\) \(\chi_{1081}(151,\cdot)\) \(\chi_{1081}(154,\cdot)\) \(\chi_{1081}(156,\cdot)\) \(\chi_{1081}(163,\cdot)\) \(\chi_{1081}(164,\cdot)\) \(\chi_{1081}(167,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\((189,898)\) → \((e\left(\frac{7}{11}\right),e\left(\frac{11}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1081 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{146}{253}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{188}{253}\right)\) | \(e\left(\frac{185}{253}\right)\) | \(e\left(\frac{235}{253}\right)\) | \(e\left(\frac{229}{506}\right)\) | \(e\left(\frac{203}{506}\right)\) |