Basic properties
Modulus: | \(6080\) | |
Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{608}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.hj
\(\chi_{6080}(71,\cdot)\) \(\chi_{6080}(231,\cdot)\) \(\chi_{6080}(471,\cdot)\) \(\chi_{6080}(1191,\cdot)\) \(\chi_{6080}(1351,\cdot)\) \(\chi_{6080}(1511,\cdot)\) \(\chi_{6080}(1591,\cdot)\) \(\chi_{6080}(1751,\cdot)\) \(\chi_{6080}(1991,\cdot)\) \(\chi_{6080}(2711,\cdot)\) \(\chi_{6080}(2871,\cdot)\) \(\chi_{6080}(3031,\cdot)\) \(\chi_{6080}(3111,\cdot)\) \(\chi_{6080}(3271,\cdot)\) \(\chi_{6080}(3511,\cdot)\) \(\chi_{6080}(4231,\cdot)\) \(\chi_{6080}(4391,\cdot)\) \(\chi_{6080}(4551,\cdot)\) \(\chi_{6080}(4631,\cdot)\) \(\chi_{6080}(4791,\cdot)\) \(\chi_{6080}(5031,\cdot)\) \(\chi_{6080}(5751,\cdot)\) \(\chi_{6080}(5911,\cdot)\) \(\chi_{6080}(6071,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{5}{8}\right),1,e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6080 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) |