Basic properties
Modulus: | \(2183\) | |
Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(522\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2183.bh
\(\chi_{2183}(3,\cdot)\) \(\chi_{2183}(4,\cdot)\) \(\chi_{2183}(21,\cdot)\) \(\chi_{2183}(25,\cdot)\) \(\chi_{2183}(28,\cdot)\) \(\chi_{2183}(41,\cdot)\) \(\chi_{2183}(62,\cdot)\) \(\chi_{2183}(78,\cdot)\) \(\chi_{2183}(95,\cdot)\) \(\chi_{2183}(104,\cdot)\) \(\chi_{2183}(139,\cdot)\) \(\chi_{2183}(169,\cdot)\) \(\chi_{2183}(189,\cdot)\) \(\chi_{2183}(206,\cdot)\) \(\chi_{2183}(213,\cdot)\) \(\chi_{2183}(225,\cdot)\) \(\chi_{2183}(226,\cdot)\) \(\chi_{2183}(243,\cdot)\) \(\chi_{2183}(252,\cdot)\) \(\chi_{2183}(262,\cdot)\) \(\chi_{2183}(263,\cdot)\) \(\chi_{2183}(284,\cdot)\) \(\chi_{2183}(287,\cdot)\) \(\chi_{2183}(289,\cdot)\) \(\chi_{2183}(299,\cdot)\) \(\chi_{2183}(300,\cdot)\) \(\chi_{2183}(317,\cdot)\) \(\chi_{2183}(321,\cdot)\) \(\chi_{2183}(324,\cdot)\) \(\chi_{2183}(336,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{261})$ |
Fixed field: | Number field defined by a degree 522 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{1}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2183 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{47}{261}\right)\) | \(e\left(\frac{253}{522}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{104}{261}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{88}{261}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{46}{87}\right)\) |