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 \(\chi_{3040}(2693,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.he
\(\chi_{6080}(793,\cdot)\) \(\chi_{6080}(953,\cdot)\) \(\chi_{6080}(1097,\cdot)\) \(\chi_{6080}(1257,\cdot)\) \(\chi_{6080}(1913,\cdot)\) \(\chi_{6080}(2073,\cdot)\) \(\chi_{6080}(2217,\cdot)\) \(\chi_{6080}(2233,\cdot)\) \(\chi_{6080}(2377,\cdot)\) \(\chi_{6080}(2537,\cdot)\) \(\chi_{6080}(2713,\cdot)\) \(\chi_{6080}(3017,\cdot)\) \(\chi_{6080}(3833,\cdot)\) \(\chi_{6080}(3993,\cdot)\) \(\chi_{6080}(4137,\cdot)\) \(\chi_{6080}(4297,\cdot)\) \(\chi_{6080}(4953,\cdot)\) \(\chi_{6080}(5113,\cdot)\) \(\chi_{6080}(5257,\cdot)\) \(\chi_{6080}(5273,\cdot)\) \(\chi_{6080}(5417,\cdot)\) \(\chi_{6080}(5577,\cdot)\) \(\chi_{6080}(5753,\cdot)\) \(\chi_{6080}(6057,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,5701,1217,1921)\) → \((1,e\left(\frac{1}{8}\right),-i,e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(793, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) |