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.dx
\(\chi_{3680}(29,\cdot)\) \(\chi_{3680}(269,\cdot)\) \(\chi_{3680}(349,\cdot)\) \(\chi_{3680}(469,\cdot)\) \(\chi_{3680}(509,\cdot)\) \(\chi_{3680}(629,\cdot)\) \(\chi_{3680}(669,\cdot)\) \(\chi_{3680}(749,\cdot)\) \(\chi_{3680}(869,\cdot)\) \(\chi_{3680}(909,\cdot)\) \(\chi_{3680}(949,\cdot)\) \(\chi_{3680}(1189,\cdot)\) \(\chi_{3680}(1269,\cdot)\) \(\chi_{3680}(1389,\cdot)\) \(\chi_{3680}(1429,\cdot)\) \(\chi_{3680}(1549,\cdot)\) \(\chi_{3680}(1589,\cdot)\) \(\chi_{3680}(1669,\cdot)\) \(\chi_{3680}(1789,\cdot)\) \(\chi_{3680}(1829,\cdot)\) \(\chi_{3680}(1869,\cdot)\) \(\chi_{3680}(2109,\cdot)\) \(\chi_{3680}(2189,\cdot)\) \(\chi_{3680}(2309,\cdot)\) \(\chi_{3680}(2349,\cdot)\) \(\chi_{3680}(2469,\cdot)\) \(\chi_{3680}(2509,\cdot)\) \(\chi_{3680}(2589,\cdot)\) \(\chi_{3680}(2709,\cdot)\) \(\chi_{3680}(2749,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,1381,737,3041)\) → \((1,e\left(\frac{1}{8}\right),-1,e\left(\frac{6}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 3680 }(869, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{17}{88}\right)\) |