Basic properties
| Modulus: | \(3520\) | |
| Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{704}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3520.fd
\(\chi_{3520}(51,\cdot)\) \(\chi_{3520}(171,\cdot)\) \(\chi_{3520}(211,\cdot)\) \(\chi_{3520}(371,\cdot)\) \(\chi_{3520}(491,\cdot)\) \(\chi_{3520}(611,\cdot)\) \(\chi_{3520}(651,\cdot)\) \(\chi_{3520}(811,\cdot)\) \(\chi_{3520}(931,\cdot)\) \(\chi_{3520}(1051,\cdot)\) \(\chi_{3520}(1091,\cdot)\) \(\chi_{3520}(1251,\cdot)\) \(\chi_{3520}(1371,\cdot)\) \(\chi_{3520}(1491,\cdot)\) \(\chi_{3520}(1531,\cdot)\) \(\chi_{3520}(1691,\cdot)\) \(\chi_{3520}(1811,\cdot)\) \(\chi_{3520}(1931,\cdot)\) \(\chi_{3520}(1971,\cdot)\) \(\chi_{3520}(2131,\cdot)\) \(\chi_{3520}(2251,\cdot)\) \(\chi_{3520}(2371,\cdot)\) \(\chi_{3520}(2411,\cdot)\) \(\chi_{3520}(2571,\cdot)\) \(\chi_{3520}(2691,\cdot)\) \(\chi_{3520}(2811,\cdot)\) \(\chi_{3520}(2851,\cdot)\) \(\chi_{3520}(3011,\cdot)\) \(\chi_{3520}(3131,\cdot)\) \(\chi_{3520}(3251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((-1,e\left(\frac{15}{16}\right),1,e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3520 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) |