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.dv
\(\chi_{3680}(3,\cdot)\) \(\chi_{3680}(27,\cdot)\) \(\chi_{3680}(163,\cdot)\) \(\chi_{3680}(187,\cdot)\) \(\chi_{3680}(243,\cdot)\) \(\chi_{3680}(347,\cdot)\) \(\chi_{3680}(403,\cdot)\) \(\chi_{3680}(427,\cdot)\) \(\chi_{3680}(587,\cdot)\) \(\chi_{3680}(883,\cdot)\) \(\chi_{3680}(1043,\cdot)\) \(\chi_{3680}(1067,\cdot)\) \(\chi_{3680}(1227,\cdot)\) \(\chi_{3680}(1283,\cdot)\) \(\chi_{3680}(1363,\cdot)\) \(\chi_{3680}(1467,\cdot)\) \(\chi_{3680}(1547,\cdot)\) \(\chi_{3680}(1603,\cdot)\) \(\chi_{3680}(1683,\cdot)\) \(\chi_{3680}(1787,\cdot)\) \(\chi_{3680}(1843,\cdot)\) \(\chi_{3680}(1867,\cdot)\) \(\chi_{3680}(2003,\cdot)\) \(\chi_{3680}(2027,\cdot)\) \(\chi_{3680}(2083,\cdot)\) \(\chi_{3680}(2187,\cdot)\) \(\chi_{3680}(2243,\cdot)\) \(\chi_{3680}(2267,\cdot)\) \(\chi_{3680}(2427,\cdot)\) \(\chi_{3680}(2723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,1381,737,3041)\) → \((-1,e\left(\frac{5}{8}\right),i,e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 3680 }(2187, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{1}{88}\right)\) |