Basic properties
Modulus: | \(3520\) | |
Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{704}(141,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3520.fh
\(\chi_{3520}(141,\cdot)\) \(\chi_{3520}(181,\cdot)\) \(\chi_{3520}(301,\cdot)\) \(\chi_{3520}(421,\cdot)\) \(\chi_{3520}(581,\cdot)\) \(\chi_{3520}(621,\cdot)\) \(\chi_{3520}(741,\cdot)\) \(\chi_{3520}(861,\cdot)\) \(\chi_{3520}(1021,\cdot)\) \(\chi_{3520}(1061,\cdot)\) \(\chi_{3520}(1181,\cdot)\) \(\chi_{3520}(1301,\cdot)\) \(\chi_{3520}(1461,\cdot)\) \(\chi_{3520}(1501,\cdot)\) \(\chi_{3520}(1621,\cdot)\) \(\chi_{3520}(1741,\cdot)\) \(\chi_{3520}(1901,\cdot)\) \(\chi_{3520}(1941,\cdot)\) \(\chi_{3520}(2061,\cdot)\) \(\chi_{3520}(2181,\cdot)\) \(\chi_{3520}(2341,\cdot)\) \(\chi_{3520}(2381,\cdot)\) \(\chi_{3520}(2501,\cdot)\) \(\chi_{3520}(2621,\cdot)\) \(\chi_{3520}(2781,\cdot)\) \(\chi_{3520}(2821,\cdot)\) \(\chi_{3520}(2941,\cdot)\) \(\chi_{3520}(3061,\cdot)\) \(\chi_{3520}(3221,\cdot)\) \(\chi_{3520}(3261,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((1,e\left(\frac{15}{16}\right),1,e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3520 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) |