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.fe
\(\chi_{3520}(19,\cdot)\) \(\chi_{3520}(139,\cdot)\) \(\chi_{3520}(259,\cdot)\) \(\chi_{3520}(299,\cdot)\) \(\chi_{3520}(459,\cdot)\) \(\chi_{3520}(579,\cdot)\) \(\chi_{3520}(699,\cdot)\) \(\chi_{3520}(739,\cdot)\) \(\chi_{3520}(899,\cdot)\) \(\chi_{3520}(1019,\cdot)\) \(\chi_{3520}(1139,\cdot)\) \(\chi_{3520}(1179,\cdot)\) \(\chi_{3520}(1339,\cdot)\) \(\chi_{3520}(1459,\cdot)\) \(\chi_{3520}(1579,\cdot)\) \(\chi_{3520}(1619,\cdot)\) \(\chi_{3520}(1779,\cdot)\) \(\chi_{3520}(1899,\cdot)\) \(\chi_{3520}(2019,\cdot)\) \(\chi_{3520}(2059,\cdot)\) \(\chi_{3520}(2219,\cdot)\) \(\chi_{3520}(2339,\cdot)\) \(\chi_{3520}(2459,\cdot)\) \(\chi_{3520}(2499,\cdot)\) \(\chi_{3520}(2659,\cdot)\) \(\chi_{3520}(2779,\cdot)\) \(\chi_{3520}(2899,\cdot)\) \(\chi_{3520}(2939,\cdot)\) \(\chi_{3520}(3099,\cdot)\) \(\chi_{3520}(3219,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((-1,e\left(\frac{15}{16}\right),-1,e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3520 }(1139, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) |