Basic properties
Modulus: | \(6011\) | |
Conductor: | \(6011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(601\) | 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 6011.e
\(\chi_{6011}(3,\cdot)\) \(\chi_{6011}(9,\cdot)\) \(\chi_{6011}(20,\cdot)\) \(\chi_{6011}(27,\cdot)\) \(\chi_{6011}(46,\cdot)\) \(\chi_{6011}(58,\cdot)\) \(\chi_{6011}(60,\cdot)\) \(\chi_{6011}(81,\cdot)\) \(\chi_{6011}(112,\cdot)\) \(\chi_{6011}(136,\cdot)\) \(\chi_{6011}(138,\cdot)\) \(\chi_{6011}(154,\cdot)\) \(\chi_{6011}(174,\cdot)\) \(\chi_{6011}(180,\cdot)\) \(\chi_{6011}(182,\cdot)\) \(\chi_{6011}(187,\cdot)\) \(\chi_{6011}(205,\cdot)\) \(\chi_{6011}(221,\cdot)\) \(\chi_{6011}(236,\cdot)\) \(\chi_{6011}(243,\cdot)\) \(\chi_{6011}(245,\cdot)\) \(\chi_{6011}(248,\cdot)\) \(\chi_{6011}(251,\cdot)\) \(\chi_{6011}(278,\cdot)\) \(\chi_{6011}(284,\cdot)\) \(\chi_{6011}(292,\cdot)\) \(\chi_{6011}(301,\cdot)\) \(\chi_{6011}(326,\cdot)\) \(\chi_{6011}(336,\cdot)\) \(\chi_{6011}(337,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{601})$ |
Fixed field: | Number field defined by a degree 601 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{474}{601}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6011 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{474}{601}\right)\) | \(e\left(\frac{255}{601}\right)\) | \(e\left(\frac{347}{601}\right)\) | \(e\left(\frac{484}{601}\right)\) | \(e\left(\frac{128}{601}\right)\) | \(e\left(\frac{380}{601}\right)\) | \(e\left(\frac{220}{601}\right)\) | \(e\left(\frac{510}{601}\right)\) | \(e\left(\frac{357}{601}\right)\) | \(e\left(\frac{598}{601}\right)\) |