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 \(\chi_{864}(443,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.jj
\(\chi_{6048}(155,\cdot)\) \(\chi_{6048}(491,\cdot)\) \(\chi_{6048}(659,\cdot)\) \(\chi_{6048}(995,\cdot)\) \(\chi_{6048}(1163,\cdot)\) \(\chi_{6048}(1499,\cdot)\) \(\chi_{6048}(1667,\cdot)\) \(\chi_{6048}(2003,\cdot)\) \(\chi_{6048}(2171,\cdot)\) \(\chi_{6048}(2507,\cdot)\) \(\chi_{6048}(2675,\cdot)\) \(\chi_{6048}(3011,\cdot)\) \(\chi_{6048}(3179,\cdot)\) \(\chi_{6048}(3515,\cdot)\) \(\chi_{6048}(3683,\cdot)\) \(\chi_{6048}(4019,\cdot)\) \(\chi_{6048}(4187,\cdot)\) \(\chi_{6048}(4523,\cdot)\) \(\chi_{6048}(4691,\cdot)\) \(\chi_{6048}(5027,\cdot)\) \(\chi_{6048}(5195,\cdot)\) \(\chi_{6048}(5531,\cdot)\) \(\chi_{6048}(5699,\cdot)\) \(\chi_{6048}(6035,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{13}{18}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 6048 }(2171, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{24}\right)\) |