Basic properties
Modulus: | \(1033\) | |
Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(172\) | 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 1033.l
\(\chi_{1033}(6,\cdot)\) \(\chi_{1033}(7,\cdot)\) \(\chi_{1033}(27,\cdot)\) \(\chi_{1033}(34,\cdot)\) \(\chi_{1033}(48,\cdot)\) \(\chi_{1033}(50,\cdot)\) \(\chi_{1033}(56,\cdot)\) \(\chi_{1033}(61,\cdot)\) \(\chi_{1033}(62,\cdot)\) \(\chi_{1033}(101,\cdot)\) \(\chi_{1033}(110,\cdot)\) \(\chi_{1033}(130,\cdot)\) \(\chi_{1033}(153,\cdot)\) \(\chi_{1033}(164,\cdot)\) \(\chi_{1033}(166,\cdot)\) \(\chi_{1033}(172,\cdot)\) \(\chi_{1033}(191,\cdot)\) \(\chi_{1033}(216,\cdot)\) \(\chi_{1033}(222,\cdot)\) \(\chi_{1033}(225,\cdot)\) \(\chi_{1033}(228,\cdot)\) \(\chi_{1033}(242,\cdot)\) \(\chi_{1033}(252,\cdot)\) \(\chi_{1033}(254,\cdot)\) \(\chi_{1033}(259,\cdot)\) \(\chi_{1033}(266,\cdot)\) \(\chi_{1033}(272,\cdot)\) \(\chi_{1033}(279,\cdot)\) \(\chi_{1033}(286,\cdot)\) \(\chi_{1033}(290,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{172})$ |
Fixed field: | Number field defined by a degree 172 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{93}{172}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1033 }(1006, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{49}{86}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{93}{172}\right)\) | \(e\left(\frac{33}{86}\right)\) | \(e\left(\frac{59}{86}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{61}{172}\right)\) | \(e\left(\frac{85}{172}\right)\) |