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.ju
\(\chi_{6048}(115,\cdot)\) \(\chi_{6048}(355,\cdot)\) \(\chi_{6048}(619,\cdot)\) \(\chi_{6048}(859,\cdot)\) \(\chi_{6048}(1123,\cdot)\) \(\chi_{6048}(1363,\cdot)\) \(\chi_{6048}(1627,\cdot)\) \(\chi_{6048}(1867,\cdot)\) \(\chi_{6048}(2131,\cdot)\) \(\chi_{6048}(2371,\cdot)\) \(\chi_{6048}(2635,\cdot)\) \(\chi_{6048}(2875,\cdot)\) \(\chi_{6048}(3139,\cdot)\) \(\chi_{6048}(3379,\cdot)\) \(\chi_{6048}(3643,\cdot)\) \(\chi_{6048}(3883,\cdot)\) \(\chi_{6048}(4147,\cdot)\) \(\chi_{6048}(4387,\cdot)\) \(\chi_{6048}(4651,\cdot)\) \(\chi_{6048}(4891,\cdot)\) \(\chi_{6048}(5155,\cdot)\) \(\chi_{6048}(5395,\cdot)\) \(\chi_{6048}(5659,\cdot)\) \(\chi_{6048}(5899,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{4}{9}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(1363, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{24}\right)\) |