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.fb
\(\chi_{3520}(237,\cdot)\) \(\chi_{3520}(293,\cdot)\) \(\chi_{3520}(453,\cdot)\) \(\chi_{3520}(557,\cdot)\) \(\chi_{3520}(613,\cdot)\) \(\chi_{3520}(717,\cdot)\) \(\chi_{3520}(853,\cdot)\) \(\chi_{3520}(877,\cdot)\) \(\chi_{3520}(1117,\cdot)\) \(\chi_{3520}(1173,\cdot)\) \(\chi_{3520}(1333,\cdot)\) \(\chi_{3520}(1437,\cdot)\) \(\chi_{3520}(1493,\cdot)\) \(\chi_{3520}(1597,\cdot)\) \(\chi_{3520}(1733,\cdot)\) \(\chi_{3520}(1757,\cdot)\) \(\chi_{3520}(1997,\cdot)\) \(\chi_{3520}(2053,\cdot)\) \(\chi_{3520}(2213,\cdot)\) \(\chi_{3520}(2317,\cdot)\) \(\chi_{3520}(2373,\cdot)\) \(\chi_{3520}(2477,\cdot)\) \(\chi_{3520}(2613,\cdot)\) \(\chi_{3520}(2637,\cdot)\) \(\chi_{3520}(2877,\cdot)\) \(\chi_{3520}(2933,\cdot)\) \(\chi_{3520}(3093,\cdot)\) \(\chi_{3520}(3197,\cdot)\) \(\chi_{3520}(3253,\cdot)\) \(\chi_{3520}(3357,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((1,e\left(\frac{3}{16}\right),i,e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3520 }(1597, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) |