Basic properties
Modulus: | \(6048\) | |
Conductor: | \(6048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.ji
\(\chi_{6048}(139,\cdot)\) \(\chi_{6048}(475,\cdot)\) \(\chi_{6048}(643,\cdot)\) \(\chi_{6048}(979,\cdot)\) \(\chi_{6048}(1147,\cdot)\) \(\chi_{6048}(1483,\cdot)\) \(\chi_{6048}(1651,\cdot)\) \(\chi_{6048}(1987,\cdot)\) \(\chi_{6048}(2155,\cdot)\) \(\chi_{6048}(2491,\cdot)\) \(\chi_{6048}(2659,\cdot)\) \(\chi_{6048}(2995,\cdot)\) \(\chi_{6048}(3163,\cdot)\) \(\chi_{6048}(3499,\cdot)\) \(\chi_{6048}(3667,\cdot)\) \(\chi_{6048}(4003,\cdot)\) \(\chi_{6048}(4171,\cdot)\) \(\chi_{6048}(4507,\cdot)\) \(\chi_{6048}(4675,\cdot)\) \(\chi_{6048}(5011,\cdot)\) \(\chi_{6048}(5179,\cdot)\) \(\chi_{6048}(5515,\cdot)\) \(\chi_{6048}(5683,\cdot)\) \(\chi_{6048}(6019,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{2}{9}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(3499, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{23}{24}\right)\) |