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
\((189,898)\) → \((e\left(\frac{21}{22}\right),e\left(\frac{2}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1081 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{240}{253}\right)\) | \(e\left(\frac{21}{506}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{465}{506}\right)\) | \(e\left(\frac{107}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{261}{506}\right)\) | \(e\left(\frac{101}{506}\right)\) |