Basic properties
Modulus: | \(3520\) | |
Conductor: | \(3520\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 3520.fk
\(\chi_{3520}(147,\cdot)\) \(\chi_{3520}(203,\cdot)\) \(\chi_{3520}(443,\cdot)\) \(\chi_{3520}(467,\cdot)\) \(\chi_{3520}(603,\cdot)\) \(\chi_{3520}(707,\cdot)\) \(\chi_{3520}(763,\cdot)\) \(\chi_{3520}(867,\cdot)\) \(\chi_{3520}(1027,\cdot)\) \(\chi_{3520}(1083,\cdot)\) \(\chi_{3520}(1323,\cdot)\) \(\chi_{3520}(1347,\cdot)\) \(\chi_{3520}(1483,\cdot)\) \(\chi_{3520}(1587,\cdot)\) \(\chi_{3520}(1643,\cdot)\) \(\chi_{3520}(1747,\cdot)\) \(\chi_{3520}(1907,\cdot)\) \(\chi_{3520}(1963,\cdot)\) \(\chi_{3520}(2203,\cdot)\) \(\chi_{3520}(2227,\cdot)\) \(\chi_{3520}(2363,\cdot)\) \(\chi_{3520}(2467,\cdot)\) \(\chi_{3520}(2523,\cdot)\) \(\chi_{3520}(2627,\cdot)\) \(\chi_{3520}(2787,\cdot)\) \(\chi_{3520}(2843,\cdot)\) \(\chi_{3520}(3083,\cdot)\) \(\chi_{3520}(3107,\cdot)\) \(\chi_{3520}(3243,\cdot)\) \(\chi_{3520}(3347,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((-1,e\left(\frac{3}{16}\right),i,e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3520 }(1347, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) |