Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.gc
\(\chi_{8041}(24,\cdot)\) \(\chi_{8041}(40,\cdot)\) \(\chi_{8041}(57,\cdot)\) \(\chi_{8041}(74,\cdot)\) \(\chi_{8041}(95,\cdot)\) \(\chi_{8041}(96,\cdot)\) \(\chi_{8041}(139,\cdot)\) \(\chi_{8041}(160,\cdot)\) \(\chi_{8041}(167,\cdot)\) \(\chi_{8041}(182,\cdot)\) \(\chi_{8041}(228,\cdot)\) \(\chi_{8041}(282,\cdot)\) \(\chi_{8041}(283,\cdot)\) \(\chi_{8041}(316,\cdot)\) \(\chi_{8041}(326,\cdot)\) \(\chi_{8041}(354,\cdot)\) \(\chi_{8041}(369,\cdot)\) \(\chi_{8041}(402,\cdot)\) \(\chi_{8041}(447,\cdot)\) \(\chi_{8041}(453,\cdot)\) \(\chi_{8041}(470,\cdot)\) \(\chi_{8041}(486,\cdot)\) \(\chi_{8041}(490,\cdot)\) \(\chi_{8041}(513,\cdot)\) \(\chi_{8041}(530,\cdot)\) \(\chi_{8041}(541,\cdot)\) \(\chi_{8041}(547,\cdot)\) \(\chi_{8041}(556,\cdot)\) \(\chi_{8041}(568,\cdot)\) \(\chi_{8041}(590,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1680})$ |
Fixed field: | Number field defined by a degree 1680 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{1}{16}\right),e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(513, a) \) | \(1\) | \(1\) | \(e\left(\frac{201}{280}\right)\) | \(e\left(\frac{313}{1680}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{349}{1680}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{43}{280}\right)\) | \(e\left(\frac{313}{840}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{209}{336}\right)\) |