Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(560\) | 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.ft
\(\chi_{8041}(27,\cdot)\) \(\chi_{8041}(75,\cdot)\) \(\chi_{8041}(82,\cdot)\) \(\chi_{8041}(108,\cdot)\) \(\chi_{8041}(113,\cdot)\) \(\chi_{8041}(125,\cdot)\) \(\chi_{8041}(180,\cdot)\) \(\chi_{8041}(328,\cdot)\) \(\chi_{8041}(333,\cdot)\) \(\chi_{8041}(346,\cdot)\) \(\chi_{8041}(432,\cdot)\) \(\chi_{8041}(500,\cdot)\) \(\chi_{8041}(555,\cdot)\) \(\chi_{8041}(581,\cdot)\) \(\chi_{8041}(598,\cdot)\) \(\chi_{8041}(641,\cdot)\) \(\chi_{8041}(653,\cdot)\) \(\chi_{8041}(720,\cdot)\) \(\chi_{8041}(753,\cdot)\) \(\chi_{8041}(796,\cdot)\) \(\chi_{8041}(806,\cdot)\) \(\chi_{8041}(819,\cdot)\) \(\chi_{8041}(839,\cdot)\) \(\chi_{8041}(856,\cdot)\) \(\chi_{8041}(862,\cdot)\) \(\chi_{8041}(911,\cdot)\) \(\chi_{8041}(1059,\cdot)\) \(\chi_{8041}(1083,\cdot)\) \(\chi_{8041}(1193,\cdot)\) \(\chi_{8041}(1236,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{560})$ |
Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{3}{16}\right),e\left(\frac{13}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(911, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{280}\right)\) | \(e\left(\frac{513}{560}\right)\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{309}{560}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{249}{280}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{95}{112}\right)\) | \(e\left(\frac{57}{112}\right)\) |