Basic properties
| Modulus: | \(3872\) | |
| Conductor: | \(968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{968}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3872.bx
\(\chi_{3872}(15,\cdot)\) \(\chi_{3872}(47,\cdot)\) \(\chi_{3872}(207,\cdot)\) \(\chi_{3872}(335,\cdot)\) \(\chi_{3872}(367,\cdot)\) \(\chi_{3872}(399,\cdot)\) \(\chi_{3872}(559,\cdot)\) \(\chi_{3872}(687,\cdot)\) \(\chi_{3872}(719,\cdot)\) \(\chi_{3872}(751,\cdot)\) \(\chi_{3872}(911,\cdot)\) \(\chi_{3872}(1039,\cdot)\) \(\chi_{3872}(1071,\cdot)\) \(\chi_{3872}(1103,\cdot)\) \(\chi_{3872}(1263,\cdot)\) \(\chi_{3872}(1391,\cdot)\) \(\chi_{3872}(1423,\cdot)\) \(\chi_{3872}(1615,\cdot)\) \(\chi_{3872}(1743,\cdot)\) \(\chi_{3872}(1807,\cdot)\) \(\chi_{3872}(1967,\cdot)\) \(\chi_{3872}(2095,\cdot)\) \(\chi_{3872}(2127,\cdot)\) \(\chi_{3872}(2159,\cdot)\) \(\chi_{3872}(2319,\cdot)\) \(\chi_{3872}(2479,\cdot)\) \(\chi_{3872}(2511,\cdot)\) \(\chi_{3872}(2799,\cdot)\) \(\chi_{3872}(2831,\cdot)\) \(\chi_{3872}(2863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,485,2785)\) → \((-1,-1,e\left(\frac{17}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3872 }(3503, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |