Basic properties
Modulus: | \(1033\) | |
Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(43\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.i
\(\chi_{1033}(64,\cdot)\) \(\chi_{1033}(113,\cdot)\) \(\chi_{1033}(115,\cdot)\) \(\chi_{1033}(129,\cdot)\) \(\chi_{1033}(263,\cdot)\) \(\chi_{1033}(288,\cdot)\) \(\chi_{1033}(296,\cdot)\) \(\chi_{1033}(299,\cdot)\) \(\chi_{1033}(300,\cdot)\) \(\chi_{1033}(304,\cdot)\) \(\chi_{1033}(317,\cdot)\) \(\chi_{1033}(335,\cdot)\) \(\chi_{1033}(336,\cdot)\) \(\chi_{1033}(350,\cdot)\) \(\chi_{1033}(373,\cdot)\) \(\chi_{1033}(392,\cdot)\) \(\chi_{1033}(411,\cdot)\) \(\chi_{1033}(419,\cdot)\) \(\chi_{1033}(479,\cdot)\) \(\chi_{1033}(521,\cdot)\) \(\chi_{1033}(542,\cdot)\) \(\chi_{1033}(563,\cdot)\) \(\chi_{1033}(599,\cdot)\) \(\chi_{1033}(606,\cdot)\) \(\chi_{1033}(661,\cdot)\) \(\chi_{1033}(667,\cdot)\) \(\chi_{1033}(699,\cdot)\) \(\chi_{1033}(707,\cdot)\) \(\chi_{1033}(731,\cdot)\) \(\chi_{1033}(780,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{43})$ |
Fixed field: | Number field defined by a degree 43 polynomial |
Values on generators
\(5\) → \(e\left(\frac{19}{43}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1033 }(129, a) \) | \(1\) | \(1\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{12}{43}\right)\) | \(e\left(\frac{28}{43}\right)\) |