Basic properties
| Modulus: | \(6080\) | |
| Conductor: | \(3040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3040}(659,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.hh
\(\chi_{6080}(279,\cdot)\) \(\chi_{6080}(439,\cdot)\) \(\chi_{6080}(599,\cdot)\) \(\chi_{6080}(679,\cdot)\) \(\chi_{6080}(839,\cdot)\) \(\chi_{6080}(1079,\cdot)\) \(\chi_{6080}(1799,\cdot)\) \(\chi_{6080}(1959,\cdot)\) \(\chi_{6080}(2119,\cdot)\) \(\chi_{6080}(2199,\cdot)\) \(\chi_{6080}(2359,\cdot)\) \(\chi_{6080}(2599,\cdot)\) \(\chi_{6080}(3319,\cdot)\) \(\chi_{6080}(3479,\cdot)\) \(\chi_{6080}(3639,\cdot)\) \(\chi_{6080}(3719,\cdot)\) \(\chi_{6080}(3879,\cdot)\) \(\chi_{6080}(4119,\cdot)\) \(\chi_{6080}(4839,\cdot)\) \(\chi_{6080}(4999,\cdot)\) \(\chi_{6080}(5159,\cdot)\) \(\chi_{6080}(5239,\cdot)\) \(\chi_{6080}(5399,\cdot)\) \(\chi_{6080}(5639,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{7}{8}\right),-1,e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(279, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{72}\right)\) |