Basic properties
| Modulus: | \(3680\) | |
| Conductor: | \(3680\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | 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 3680.eg
\(\chi_{3680}(123,\cdot)\) \(\chi_{3680}(147,\cdot)\) \(\chi_{3680}(307,\cdot)\) \(\chi_{3680}(363,\cdot)\) \(\chi_{3680}(443,\cdot)\) \(\chi_{3680}(547,\cdot)\) \(\chi_{3680}(627,\cdot)\) \(\chi_{3680}(683,\cdot)\) \(\chi_{3680}(763,\cdot)\) \(\chi_{3680}(867,\cdot)\) \(\chi_{3680}(923,\cdot)\) \(\chi_{3680}(947,\cdot)\) \(\chi_{3680}(1083,\cdot)\) \(\chi_{3680}(1107,\cdot)\) \(\chi_{3680}(1163,\cdot)\) \(\chi_{3680}(1267,\cdot)\) \(\chi_{3680}(1323,\cdot)\) \(\chi_{3680}(1347,\cdot)\) \(\chi_{3680}(1507,\cdot)\) \(\chi_{3680}(1803,\cdot)\) \(\chi_{3680}(1963,\cdot)\) \(\chi_{3680}(1987,\cdot)\) \(\chi_{3680}(2147,\cdot)\) \(\chi_{3680}(2203,\cdot)\) \(\chi_{3680}(2283,\cdot)\) \(\chi_{3680}(2387,\cdot)\) \(\chi_{3680}(2467,\cdot)\) \(\chi_{3680}(2523,\cdot)\) \(\chi_{3680}(2603,\cdot)\) \(\chi_{3680}(2707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,1381,737,3041)\) → \((-1,e\left(\frac{3}{8}\right),i,e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 3680 }(2467, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{31}{88}\right)\) |