Basic properties
Modulus: | \(89\) | |
Conductor: | \(89\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 89.h
\(\chi_{89}(3,\cdot)\) \(\chi_{89}(6,\cdot)\) \(\chi_{89}(7,\cdot)\) \(\chi_{89}(13,\cdot)\) \(\chi_{89}(14,\cdot)\) \(\chi_{89}(15,\cdot)\) \(\chi_{89}(19,\cdot)\) \(\chi_{89}(23,\cdot)\) \(\chi_{89}(24,\cdot)\) \(\chi_{89}(26,\cdot)\) \(\chi_{89}(27,\cdot)\) \(\chi_{89}(28,\cdot)\) \(\chi_{89}(29,\cdot)\) \(\chi_{89}(30,\cdot)\) \(\chi_{89}(31,\cdot)\) \(\chi_{89}(33,\cdot)\) \(\chi_{89}(35,\cdot)\) \(\chi_{89}(38,\cdot)\) \(\chi_{89}(41,\cdot)\) \(\chi_{89}(43,\cdot)\) \(\chi_{89}(46,\cdot)\) \(\chi_{89}(48,\cdot)\) \(\chi_{89}(51,\cdot)\) \(\chi_{89}(54,\cdot)\) \(\chi_{89}(56,\cdot)\) \(\chi_{89}(58,\cdot)\) \(\chi_{89}(59,\cdot)\) \(\chi_{89}(60,\cdot)\) \(\chi_{89}(61,\cdot)\) \(\chi_{89}(62,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\(3\) → \(e\left(\frac{67}{88}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 89 }(76, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |