Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(966\) | 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 4031.bt
\(\chi_{4031}(4,\cdot)\) \(\chi_{4031}(5,\cdot)\) \(\chi_{4031}(9,\cdot)\) \(\chi_{4031}(13,\cdot)\) \(\chi_{4031}(35,\cdot)\) \(\chi_{4031}(38,\cdot)\) \(\chi_{4031}(51,\cdot)\) \(\chi_{4031}(67,\cdot)\) \(\chi_{4031}(71,\cdot)\) \(\chi_{4031}(120,\cdot)\) \(\chi_{4031}(121,\cdot)\) \(\chi_{4031}(122,\cdot)\) \(\chi_{4031}(150,\cdot)\) \(\chi_{4031}(167,\cdot)\) \(\chi_{4031}(180,\cdot)\) \(\chi_{4031}(208,\cdot)\) \(\chi_{4031}(225,\cdot)\) \(\chi_{4031}(238,\cdot)\) \(\chi_{4031}(266,\cdot)\) \(\chi_{4031}(283,\cdot)\) \(\chi_{4031}(294,\cdot)\) \(\chi_{4031}(303,\cdot)\) \(\chi_{4031}(324,\cdot)\) \(\chi_{4031}(325,\cdot)\) \(\chi_{4031}(332,\cdot)\) \(\chi_{4031}(361,\cdot)\) \(\chi_{4031}(399,\cdot)\) \(\chi_{4031}(415,\cdot)\) \(\chi_{4031}(428,\cdot)\) \(\chi_{4031}(441,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{62}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(332, a) \) | \(1\) | \(1\) | \(e\left(\frac{523}{966}\right)\) | \(e\left(\frac{53}{966}\right)\) | \(e\left(\frac{40}{483}\right)\) | \(e\left(\frac{202}{483}\right)\) | \(e\left(\frac{96}{161}\right)\) | \(e\left(\frac{310}{483}\right)\) | \(e\left(\frac{201}{322}\right)\) | \(e\left(\frac{53}{483}\right)\) | \(e\left(\frac{309}{322}\right)\) | \(e\left(\frac{349}{966}\right)\) |