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.iz
\(\chi_{6048}(277,\cdot)\) \(\chi_{6048}(373,\cdot)\) \(\chi_{6048}(781,\cdot)\) \(\chi_{6048}(877,\cdot)\) \(\chi_{6048}(1285,\cdot)\) \(\chi_{6048}(1381,\cdot)\) \(\chi_{6048}(1789,\cdot)\) \(\chi_{6048}(1885,\cdot)\) \(\chi_{6048}(2293,\cdot)\) \(\chi_{6048}(2389,\cdot)\) \(\chi_{6048}(2797,\cdot)\) \(\chi_{6048}(2893,\cdot)\) \(\chi_{6048}(3301,\cdot)\) \(\chi_{6048}(3397,\cdot)\) \(\chi_{6048}(3805,\cdot)\) \(\chi_{6048}(3901,\cdot)\) \(\chi_{6048}(4309,\cdot)\) \(\chi_{6048}(4405,\cdot)\) \(\chi_{6048}(4813,\cdot)\) \(\chi_{6048}(4909,\cdot)\) \(\chi_{6048}(5317,\cdot)\) \(\chi_{6048}(5413,\cdot)\) \(\chi_{6048}(5821,\cdot)\) \(\chi_{6048}(5917,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{5}{9}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(2293, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{24}\right)\) |