Basic properties
| Modulus: | \(3520\) | |
| Conductor: | \(3520\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.fm
\(\chi_{3520}(13,\cdot)\) \(\chi_{3520}(117,\cdot)\) \(\chi_{3520}(173,\cdot)\) \(\chi_{3520}(277,\cdot)\) \(\chi_{3520}(413,\cdot)\) \(\chi_{3520}(437,\cdot)\) \(\chi_{3520}(677,\cdot)\) \(\chi_{3520}(733,\cdot)\) \(\chi_{3520}(893,\cdot)\) \(\chi_{3520}(997,\cdot)\) \(\chi_{3520}(1053,\cdot)\) \(\chi_{3520}(1157,\cdot)\) \(\chi_{3520}(1293,\cdot)\) \(\chi_{3520}(1317,\cdot)\) \(\chi_{3520}(1557,\cdot)\) \(\chi_{3520}(1613,\cdot)\) \(\chi_{3520}(1773,\cdot)\) \(\chi_{3520}(1877,\cdot)\) \(\chi_{3520}(1933,\cdot)\) \(\chi_{3520}(2037,\cdot)\) \(\chi_{3520}(2173,\cdot)\) \(\chi_{3520}(2197,\cdot)\) \(\chi_{3520}(2437,\cdot)\) \(\chi_{3520}(2493,\cdot)\) \(\chi_{3520}(2653,\cdot)\) \(\chi_{3520}(2757,\cdot)\) \(\chi_{3520}(2813,\cdot)\) \(\chi_{3520}(2917,\cdot)\) \(\chi_{3520}(3053,\cdot)\) \(\chi_{3520}(3077,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((1,e\left(\frac{9}{16}\right),i,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3520 }(1317, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) |