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 \(\chi_{3040}(1203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.hf
\(\chi_{6080}(23,\cdot)\) \(\chi_{6080}(327,\cdot)\) \(\chi_{6080}(503,\cdot)\) \(\chi_{6080}(663,\cdot)\) \(\chi_{6080}(807,\cdot)\) \(\chi_{6080}(823,\cdot)\) \(\chi_{6080}(967,\cdot)\) \(\chi_{6080}(1127,\cdot)\) \(\chi_{6080}(1783,\cdot)\) \(\chi_{6080}(1943,\cdot)\) \(\chi_{6080}(2087,\cdot)\) \(\chi_{6080}(2247,\cdot)\) \(\chi_{6080}(3063,\cdot)\) \(\chi_{6080}(3367,\cdot)\) \(\chi_{6080}(3543,\cdot)\) \(\chi_{6080}(3703,\cdot)\) \(\chi_{6080}(3847,\cdot)\) \(\chi_{6080}(3863,\cdot)\) \(\chi_{6080}(4007,\cdot)\) \(\chi_{6080}(4167,\cdot)\) \(\chi_{6080}(4823,\cdot)\) \(\chi_{6080}(4983,\cdot)\) \(\chi_{6080}(5127,\cdot)\) \(\chi_{6080}(5287,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{7}{8}\right),-i,e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(3863, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{25}{72}\right)\) |