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 \(\chi_{968}(387,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3872.by
\(\chi_{3872}(79,\cdot)\) \(\chi_{3872}(271,\cdot)\) \(\chi_{3872}(303,\cdot)\) \(\chi_{3872}(431,\cdot)\) \(\chi_{3872}(591,\cdot)\) \(\chi_{3872}(623,\cdot)\) \(\chi_{3872}(655,\cdot)\) \(\chi_{3872}(783,\cdot)\) \(\chi_{3872}(943,\cdot)\) \(\chi_{3872}(975,\cdot)\) \(\chi_{3872}(1007,\cdot)\) \(\chi_{3872}(1135,\cdot)\) \(\chi_{3872}(1295,\cdot)\) \(\chi_{3872}(1327,\cdot)\) \(\chi_{3872}(1359,\cdot)\) \(\chi_{3872}(1487,\cdot)\) \(\chi_{3872}(1647,\cdot)\) \(\chi_{3872}(1679,\cdot)\) \(\chi_{3872}(1711,\cdot)\) \(\chi_{3872}(1839,\cdot)\) \(\chi_{3872}(1999,\cdot)\) \(\chi_{3872}(2031,\cdot)\) \(\chi_{3872}(2063,\cdot)\) \(\chi_{3872}(2191,\cdot)\) \(\chi_{3872}(2351,\cdot)\) \(\chi_{3872}(2383,\cdot)\) \(\chi_{3872}(2415,\cdot)\) \(\chi_{3872}(2543,\cdot)\) \(\chi_{3872}(2703,\cdot)\) \(\chi_{3872}(2735,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,485,2785)\) → \((-1,-1,e\left(\frac{91}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3872 }(1839, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) |