Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
Conductor | = | 89 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
Order | = | 88 |
Real | = | No |
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
Primitive | = | Yes |
sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
Parity | = | Odd |
Orbit label | = | 89.h |
Orbit index | = | 8 |
Galois orbit
\(\chi_{89}(3,\cdot)\) \(\chi_{89}(6,\cdot)\) \(\chi_{89}(7,\cdot)\) \(\chi_{89}(13,\cdot)\) \(\chi_{89}(14,\cdot)\) \(\chi_{89}(15,\cdot)\) \(\chi_{89}(19,\cdot)\) \(\chi_{89}(23,\cdot)\) \(\chi_{89}(24,\cdot)\) \(\chi_{89}(26,\cdot)\) \(\chi_{89}(27,\cdot)\) \(\chi_{89}(28,\cdot)\) \(\chi_{89}(29,\cdot)\) \(\chi_{89}(30,\cdot)\) \(\chi_{89}(31,\cdot)\) \(\chi_{89}(33,\cdot)\) \(\chi_{89}(35,\cdot)\) \(\chi_{89}(38,\cdot)\) \(\chi_{89}(41,\cdot)\) \(\chi_{89}(43,\cdot)\) \(\chi_{89}(46,\cdot)\) \(\chi_{89}(48,\cdot)\) \(\chi_{89}(51,\cdot)\) \(\chi_{89}(54,\cdot)\) \(\chi_{89}(56,\cdot)\) \(\chi_{89}(58,\cdot)\) \(\chi_{89}(59,\cdot)\) \(\chi_{89}(60,\cdot)\) \(\chi_{89}(61,\cdot)\) \(\chi_{89}(62,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{59}{88}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{88})\) |