Basic properties
| Modulus: | \(81120\) | |
| Conductor: | \(81120\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | 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 81120.bfw
\(\chi_{81120}(59,\cdot)\) \(\chi_{81120}(899,\cdot)\) \(\chi_{81120}(1259,\cdot)\) \(\chi_{81120}(2099,\cdot)\) \(\chi_{81120}(3179,\cdot)\) \(\chi_{81120}(4019,\cdot)\) \(\chi_{81120}(4379,\cdot)\) \(\chi_{81120}(5219,\cdot)\) \(\chi_{81120}(6299,\cdot)\) \(\chi_{81120}(7139,\cdot)\) \(\chi_{81120}(7499,\cdot)\) \(\chi_{81120}(8339,\cdot)\) \(\chi_{81120}(9419,\cdot)\) \(\chi_{81120}(10259,\cdot)\) \(\chi_{81120}(10619,\cdot)\) \(\chi_{81120}(11459,\cdot)\) \(\chi_{81120}(12539,\cdot)\) \(\chi_{81120}(13379,\cdot)\) \(\chi_{81120}(13739,\cdot)\) \(\chi_{81120}(14579,\cdot)\) \(\chi_{81120}(15659,\cdot)\) \(\chi_{81120}(16499,\cdot)\) \(\chi_{81120}(16859,\cdot)\) \(\chi_{81120}(17699,\cdot)\) \(\chi_{81120}(18779,\cdot)\) \(\chi_{81120}(19619,\cdot)\) \(\chi_{81120}(19979,\cdot)\) \(\chi_{81120}(20819,\cdot)\) \(\chi_{81120}(21899,\cdot)\) \(\chi_{81120}(22739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((45631,70981,27041,64897,12001)\) → \((-1,e\left(\frac{3}{8}\right),-1,-1,e\left(\frac{37}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 81120 }(75779, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{95}{312}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{35}{312}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{215}{312}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{253}{312}\right)\) |