Basic properties
Modulus: | \(4021\) | |
Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(335\) | 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 4021.q
\(\chi_{4021}(27,\cdot)\) \(\chi_{4021}(38,\cdot)\) \(\chi_{4021}(42,\cdot)\) \(\chi_{4021}(45,\cdot)\) \(\chi_{4021}(48,\cdot)\) \(\chi_{4021}(70,\cdot)\) \(\chi_{4021}(71,\cdot)\) \(\chi_{4021}(75,\cdot)\) \(\chi_{4021}(80,\cdot)\) \(\chi_{4021}(86,\cdot)\) \(\chi_{4021}(94,\cdot)\) \(\chi_{4021}(101,\cdot)\) \(\chi_{4021}(125,\cdot)\) \(\chi_{4021}(209,\cdot)\) \(\chi_{4021}(221,\cdot)\) \(\chi_{4021}(231,\cdot)\) \(\chi_{4021}(244,\cdot)\) \(\chi_{4021}(264,\cdot)\) \(\chi_{4021}(269,\cdot)\) \(\chi_{4021}(289,\cdot)\) \(\chi_{4021}(333,\cdot)\) \(\chi_{4021}(346,\cdot)\) \(\chi_{4021}(356,\cdot)\) \(\chi_{4021}(359,\cdot)\) \(\chi_{4021}(385,\cdot)\) \(\chi_{4021}(440,\cdot)\) \(\chi_{4021}(473,\cdot)\) \(\chi_{4021}(491,\cdot)\) \(\chi_{4021}(517,\cdot)\) \(\chi_{4021}(518,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{335})$ |
Fixed field: | Number field defined by a degree 335 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{76}{335}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4021 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{335}\right)\) | \(e\left(\frac{324}{335}\right)\) | \(e\left(\frac{152}{335}\right)\) | \(e\left(\frac{294}{335}\right)\) | \(e\left(\frac{13}{67}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{228}{335}\right)\) | \(e\left(\frac{313}{335}\right)\) | \(e\left(\frac{7}{67}\right)\) | \(e\left(\frac{32}{335}\right)\) |