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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1081.p
\(\chi_{1081}(5,\cdot)\) \(\chi_{1081}(10,\cdot)\) \(\chi_{1081}(11,\cdot)\) \(\chi_{1081}(15,\cdot)\) \(\chi_{1081}(19,\cdot)\) \(\chi_{1081}(20,\cdot)\) \(\chi_{1081}(30,\cdot)\) \(\chi_{1081}(33,\cdot)\) \(\chi_{1081}(38,\cdot)\) \(\chi_{1081}(40,\cdot)\) \(\chi_{1081}(43,\cdot)\) \(\chi_{1081}(44,\cdot)\) \(\chi_{1081}(57,\cdot)\) \(\chi_{1081}(60,\cdot)\) \(\chi_{1081}(66,\cdot)\) \(\chi_{1081}(67,\cdot)\) \(\chi_{1081}(76,\cdot)\) \(\chi_{1081}(80,\cdot)\) \(\chi_{1081}(86,\cdot)\) \(\chi_{1081}(88,\cdot)\) \(\chi_{1081}(90,\cdot)\) \(\chi_{1081}(99,\cdot)\) \(\chi_{1081}(107,\cdot)\) \(\chi_{1081}(109,\cdot)\) \(\chi_{1081}(113,\cdot)\) \(\chi_{1081}(120,\cdot)\) \(\chi_{1081}(125,\cdot)\) \(\chi_{1081}(129,\cdot)\) \(\chi_{1081}(132,\cdot)\) \(\chi_{1081}(134,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\((189,898)\) → \((e\left(\frac{17}{22}\right),e\left(\frac{21}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1081 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{253}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{58}{253}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) |