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.jm
\(\chi_{6048}(293,\cdot)\) \(\chi_{6048}(461,\cdot)\) \(\chi_{6048}(797,\cdot)\) \(\chi_{6048}(965,\cdot)\) \(\chi_{6048}(1301,\cdot)\) \(\chi_{6048}(1469,\cdot)\) \(\chi_{6048}(1805,\cdot)\) \(\chi_{6048}(1973,\cdot)\) \(\chi_{6048}(2309,\cdot)\) \(\chi_{6048}(2477,\cdot)\) \(\chi_{6048}(2813,\cdot)\) \(\chi_{6048}(2981,\cdot)\) \(\chi_{6048}(3317,\cdot)\) \(\chi_{6048}(3485,\cdot)\) \(\chi_{6048}(3821,\cdot)\) \(\chi_{6048}(3989,\cdot)\) \(\chi_{6048}(4325,\cdot)\) \(\chi_{6048}(4493,\cdot)\) \(\chi_{6048}(4829,\cdot)\) \(\chi_{6048}(4997,\cdot)\) \(\chi_{6048}(5333,\cdot)\) \(\chi_{6048}(5501,\cdot)\) \(\chi_{6048}(5837,\cdot)\) \(\chi_{6048}(6005,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{18}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(5837, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{24}\right)\) |