Basic properties
Modulus: | \(4021\) | |
Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(402\) | 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)
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Galois orbit 4021.r
\(\chi_{4021}(53,\cdot)\) \(\chi_{4021}(147,\cdot)\) \(\chi_{4021}(153,\cdot)\) \(\chi_{4021}(168,\cdot)\) \(\chi_{4021}(174,\cdot)\) \(\chi_{4021}(192,\cdot)\) \(\chi_{4021}(245,\cdot)\) \(\chi_{4021}(249,\cdot)\) \(\chi_{4021}(251,\cdot)\) \(\chi_{4021}(255,\cdot)\) \(\chi_{4021}(280,\cdot)\) \(\chi_{4021}(287,\cdot)\) \(\chi_{4021}(290,\cdot)\) \(\chi_{4021}(298,\cdot)\) \(\chi_{4021}(320,\cdot)\) \(\chi_{4021}(328,\cdot)\) \(\chi_{4021}(331,\cdot)\) \(\chi_{4021}(341,\cdot)\) \(\chi_{4021}(381,\cdot)\) \(\chi_{4021}(415,\cdot)\) \(\chi_{4021}(425,\cdot)\) \(\chi_{4021}(439,\cdot)\) \(\chi_{4021}(543,\cdot)\) \(\chi_{4021}(549,\cdot)\) \(\chi_{4021}(557,\cdot)\) \(\chi_{4021}(594,\cdot)\) \(\chi_{4021}(599,\cdot)\) \(\chi_{4021}(635,\cdot)\) \(\chi_{4021}(678,\cdot)\) \(\chi_{4021}(686,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{201})$ |
Fixed field: | Number field defined by a degree 402 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{35}{402}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4021 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{402}\right)\) | \(e\left(\frac{161}{201}\right)\) | \(e\left(\frac{35}{201}\right)\) | \(e\left(\frac{125}{201}\right)\) | \(e\left(\frac{119}{134}\right)\) | \(-1\) | \(e\left(\frac{35}{134}\right)\) | \(e\left(\frac{121}{201}\right)\) | \(e\left(\frac{95}{134}\right)\) | \(e\left(\frac{251}{402}\right)\) |