Basic properties
Modulus: | \(6048\) | |
Conductor: | \(6048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.jh
\(\chi_{6048}(187,\cdot)\) \(\chi_{6048}(283,\cdot)\) \(\chi_{6048}(691,\cdot)\) \(\chi_{6048}(787,\cdot)\) \(\chi_{6048}(1195,\cdot)\) \(\chi_{6048}(1291,\cdot)\) \(\chi_{6048}(1699,\cdot)\) \(\chi_{6048}(1795,\cdot)\) \(\chi_{6048}(2203,\cdot)\) \(\chi_{6048}(2299,\cdot)\) \(\chi_{6048}(2707,\cdot)\) \(\chi_{6048}(2803,\cdot)\) \(\chi_{6048}(3211,\cdot)\) \(\chi_{6048}(3307,\cdot)\) \(\chi_{6048}(3715,\cdot)\) \(\chi_{6048}(3811,\cdot)\) \(\chi_{6048}(4219,\cdot)\) \(\chi_{6048}(4315,\cdot)\) \(\chi_{6048}(4723,\cdot)\) \(\chi_{6048}(4819,\cdot)\) \(\chi_{6048}(5227,\cdot)\) \(\chi_{6048}(5323,\cdot)\) \(\chi_{6048}(5731,\cdot)\) \(\chi_{6048}(5827,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{4}{9}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(4819, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{8}\right)\) |