Basic properties
Modulus: | \(6048\) | |
Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{864}(661,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.jn
\(\chi_{6048}(85,\cdot)\) \(\chi_{6048}(421,\cdot)\) \(\chi_{6048}(589,\cdot)\) \(\chi_{6048}(925,\cdot)\) \(\chi_{6048}(1093,\cdot)\) \(\chi_{6048}(1429,\cdot)\) \(\chi_{6048}(1597,\cdot)\) \(\chi_{6048}(1933,\cdot)\) \(\chi_{6048}(2101,\cdot)\) \(\chi_{6048}(2437,\cdot)\) \(\chi_{6048}(2605,\cdot)\) \(\chi_{6048}(2941,\cdot)\) \(\chi_{6048}(3109,\cdot)\) \(\chi_{6048}(3445,\cdot)\) \(\chi_{6048}(3613,\cdot)\) \(\chi_{6048}(3949,\cdot)\) \(\chi_{6048}(4117,\cdot)\) \(\chi_{6048}(4453,\cdot)\) \(\chi_{6048}(4621,\cdot)\) \(\chi_{6048}(4957,\cdot)\) \(\chi_{6048}(5125,\cdot)\) \(\chi_{6048}(5461,\cdot)\) \(\chi_{6048}(5629,\cdot)\) \(\chi_{6048}(5965,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{4}{9}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(4117, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{24}\right)\) |