Basic properties
Modulus: | \(1601\) | |
Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(200\) | 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 1601.q
\(\chi_{1601}(4,\cdot)\) \(\chi_{1601}(10,\cdot)\) \(\chi_{1601}(25,\cdot)\) \(\chi_{1601}(29,\cdot)\) \(\chi_{1601}(64,\cdot)\) \(\chi_{1601}(76,\cdot)\) \(\chi_{1601}(124,\cdot)\) \(\chi_{1601}(154,\cdot)\) \(\chi_{1601}(157,\cdot)\) \(\chi_{1601}(160,\cdot)\) \(\chi_{1601}(162,\cdot)\) \(\chi_{1601}(167,\cdot)\) \(\chi_{1601}(168,\cdot)\) \(\chi_{1601}(190,\cdot)\) \(\chi_{1601}(244,\cdot)\) \(\chi_{1601}(253,\cdot)\) \(\chi_{1601}(276,\cdot)\) \(\chi_{1601}(302,\cdot)\) \(\chi_{1601}(316,\cdot)\) \(\chi_{1601}(374,\cdot)\) \(\chi_{1601}(383,\cdot)\) \(\chi_{1601}(385,\cdot)\) \(\chi_{1601}(387,\cdot)\) \(\chi_{1601}(400,\cdot)\) \(\chi_{1601}(405,\cdot)\) \(\chi_{1601}(420,\cdot)\) \(\chi_{1601}(441,\cdot)\) \(\chi_{1601}(464,\cdot)\) \(\chi_{1601}(514,\cdot)\) \(\chi_{1601}(530,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{97}{200}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1601 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{97}{200}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{141}{200}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{1}{200}\right)\) |