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.hz
\(\chi_{6080}(187,\cdot)\) \(\chi_{6080}(347,\cdot)\) \(\chi_{6080}(403,\cdot)\) \(\chi_{6080}(427,\cdot)\) \(\chi_{6080}(587,\cdot)\) \(\chi_{6080}(643,\cdot)\) \(\chi_{6080}(747,\cdot)\) \(\chi_{6080}(803,\cdot)\) \(\chi_{6080}(883,\cdot)\) \(\chi_{6080}(1043,\cdot)\) \(\chi_{6080}(1203,\cdot)\) \(\chi_{6080}(1467,\cdot)\) \(\chi_{6080}(1707,\cdot)\) \(\chi_{6080}(1867,\cdot)\) \(\chi_{6080}(1923,\cdot)\) \(\chi_{6080}(1947,\cdot)\) \(\chi_{6080}(2107,\cdot)\) \(\chi_{6080}(2163,\cdot)\) \(\chi_{6080}(2267,\cdot)\) \(\chi_{6080}(2323,\cdot)\) \(\chi_{6080}(2403,\cdot)\) \(\chi_{6080}(2563,\cdot)\) \(\chi_{6080}(2723,\cdot)\) \(\chi_{6080}(2987,\cdot)\) \(\chi_{6080}(3227,\cdot)\) \(\chi_{6080}(3387,\cdot)\) \(\chi_{6080}(3443,\cdot)\) \(\chi_{6080}(3467,\cdot)\) \(\chi_{6080}(3627,\cdot)\) \(\chi_{6080}(3683,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{1}{16}\right),i,e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{115}{144}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{144}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{139}{144}\right)\) |