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
\((189,898)\) → \((e\left(\frac{15}{22}\right),e\left(\frac{45}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1081 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{131}{506}\right)\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{240}{253}\right)\) | \(e\left(\frac{160}{253}\right)\) | \(e\left(\frac{249}{253}\right)\) |