Basic properties
Modulus: | \(4023\) | |
Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(666\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 4023.bh
\(\chi_{4023}(20,\cdot)\) \(\chi_{4023}(47,\cdot)\) \(\chi_{4023}(68,\cdot)\) \(\chi_{4023}(86,\cdot)\) \(\chi_{4023}(110,\cdot)\) \(\chi_{4023}(113,\cdot)\) \(\chi_{4023}(119,\cdot)\) \(\chi_{4023}(158,\cdot)\) \(\chi_{4023}(173,\cdot)\) \(\chi_{4023}(191,\cdot)\) \(\chi_{4023}(194,\cdot)\) \(\chi_{4023}(203,\cdot)\) \(\chi_{4023}(218,\cdot)\) \(\chi_{4023}(281,\cdot)\) \(\chi_{4023}(293,\cdot)\) \(\chi_{4023}(302,\cdot)\) \(\chi_{4023}(320,\cdot)\) \(\chi_{4023}(362,\cdot)\) \(\chi_{4023}(374,\cdot)\) \(\chi_{4023}(380,\cdot)\) \(\chi_{4023}(398,\cdot)\) \(\chi_{4023}(401,\cdot)\) \(\chi_{4023}(410,\cdot)\) \(\chi_{4023}(416,\cdot)\) \(\chi_{4023}(419,\cdot)\) \(\chi_{4023}(428,\cdot)\) \(\chi_{4023}(473,\cdot)\) \(\chi_{4023}(482,\cdot)\) \(\chi_{4023}(500,\cdot)\) \(\chi_{4023}(515,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{333})$ |
Fixed field: | Number field defined by a degree 666 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{53}{74}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4023 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{333}\right)\) | \(e\left(\frac{70}{333}\right)\) | \(e\left(\frac{287}{666}\right)\) | \(e\left(\frac{308}{333}\right)\) | \(e\left(\frac{35}{111}\right)\) | \(e\left(\frac{119}{222}\right)\) | \(e\left(\frac{41}{333}\right)\) | \(e\left(\frac{47}{666}\right)\) | \(e\left(\frac{10}{333}\right)\) | \(e\left(\frac{140}{333}\right)\) |