Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(1680\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8041.gb
\(\chi_{8041}(14,\cdot)\) \(\chi_{8041}(31,\cdot)\) \(\chi_{8041}(58,\cdot)\) \(\chi_{8041}(124,\cdot)\) \(\chi_{8041}(126,\cdot)\) \(\chi_{8041}(146,\cdot)\) \(\chi_{8041}(181,\cdot)\) \(\chi_{8041}(224,\cdot)\) \(\chi_{8041}(267,\cdot)\) \(\chi_{8041}(311,\cdot)\) \(\chi_{8041}(367,\cdot)\) \(\chi_{8041}(368,\cdot)\) \(\chi_{8041}(401,\cdot)\) \(\chi_{8041}(411,\cdot)\) \(\chi_{8041}(445,\cdot)\) \(\chi_{8041}(454,\cdot)\) \(\chi_{8041}(482,\cdot)\) \(\chi_{8041}(487,\cdot)\) \(\chi_{8041}(488,\cdot)\) \(\chi_{8041}(498,\cdot)\) \(\chi_{8041}(504,\cdot)\) \(\chi_{8041}(533,\cdot)\) \(\chi_{8041}(554,\cdot)\) \(\chi_{8041}(619,\cdot)\) \(\chi_{8041}(658,\cdot)\) \(\chi_{8041}(669,\cdot)\) \(\chi_{8041}(685,\cdot)\) \(\chi_{8041}(702,\cdot)\) \(\chi_{8041}(719,\cdot)\) \(\chi_{8041}(741,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1680})$ |
Fixed field: | Number field defined by a degree 1680 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{9}{16}\right),e\left(\frac{10}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{280}\right)\) | \(e\left(\frac{737}{1680}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{1541}{1680}\right)\) | \(e\left(\frac{233}{240}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{167}{280}\right)\) | \(e\left(\frac{737}{840}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{169}{336}\right)\) |