Basic properties
| Modulus: | \(6080\) | |
| Conductor: | \(6080\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.ht
\(\chi_{6080}(43,\cdot)\) \(\chi_{6080}(123,\cdot)\) \(\chi_{6080}(283,\cdot)\) \(\chi_{6080}(443,\cdot)\) \(\chi_{6080}(707,\cdot)\) \(\chi_{6080}(947,\cdot)\) \(\chi_{6080}(1107,\cdot)\) \(\chi_{6080}(1163,\cdot)\) \(\chi_{6080}(1187,\cdot)\) \(\chi_{6080}(1347,\cdot)\) \(\chi_{6080}(1403,\cdot)\) \(\chi_{6080}(1507,\cdot)\) \(\chi_{6080}(1563,\cdot)\) \(\chi_{6080}(1643,\cdot)\) \(\chi_{6080}(1803,\cdot)\) \(\chi_{6080}(1963,\cdot)\) \(\chi_{6080}(2227,\cdot)\) \(\chi_{6080}(2467,\cdot)\) \(\chi_{6080}(2627,\cdot)\) \(\chi_{6080}(2683,\cdot)\) \(\chi_{6080}(2707,\cdot)\) \(\chi_{6080}(2867,\cdot)\) \(\chi_{6080}(2923,\cdot)\) \(\chi_{6080}(3027,\cdot)\) \(\chi_{6080}(3083,\cdot)\) \(\chi_{6080}(3163,\cdot)\) \(\chi_{6080}(3323,\cdot)\) \(\chi_{6080}(3483,\cdot)\) \(\chi_{6080}(3747,\cdot)\) \(\chi_{6080}(3987,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{13}{16}\right),-i,e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{127}{144}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{79}{144}\right)\) |