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 \(\chi_{3040}(2923,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.hq
\(\chi_{6080}(263,\cdot)\) \(\chi_{6080}(423,\cdot)\) \(\chi_{6080}(567,\cdot)\) \(\chi_{6080}(727,\cdot)\) \(\chi_{6080}(1543,\cdot)\) \(\chi_{6080}(1847,\cdot)\) \(\chi_{6080}(2023,\cdot)\) \(\chi_{6080}(2183,\cdot)\) \(\chi_{6080}(2327,\cdot)\) \(\chi_{6080}(2343,\cdot)\) \(\chi_{6080}(2487,\cdot)\) \(\chi_{6080}(2647,\cdot)\) \(\chi_{6080}(3303,\cdot)\) \(\chi_{6080}(3463,\cdot)\) \(\chi_{6080}(3607,\cdot)\) \(\chi_{6080}(3767,\cdot)\) \(\chi_{6080}(4583,\cdot)\) \(\chi_{6080}(4887,\cdot)\) \(\chi_{6080}(5063,\cdot)\) \(\chi_{6080}(5223,\cdot)\) \(\chi_{6080}(5367,\cdot)\) \(\chi_{6080}(5383,\cdot)\) \(\chi_{6080}(5527,\cdot)\) \(\chi_{6080}(5687,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{5}{8}\right),-i,e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(263, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{72}\right)\) |