Basic properties
Modulus: | \(8047\) | |
Conductor: | \(8047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1236\) | 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 8047.cd
\(\chi_{8047}(2,\cdot)\) \(\chi_{8047}(11,\cdot)\) \(\chi_{8047}(15,\cdot)\) \(\chi_{8047}(19,\cdot)\) \(\chi_{8047}(32,\cdot)\) \(\chi_{8047}(46,\cdot)\) \(\chi_{8047}(67,\cdot)\) \(\chi_{8047}(76,\cdot)\) \(\chi_{8047}(98,\cdot)\) \(\chi_{8047}(102,\cdot)\) \(\chi_{8047}(111,\cdot)\) \(\chi_{8047}(128,\cdot)\) \(\chi_{8047}(145,\cdot)\) \(\chi_{8047}(149,\cdot)\) \(\chi_{8047}(158,\cdot)\) \(\chi_{8047}(176,\cdot)\) \(\chi_{8047}(184,\cdot)\) \(\chi_{8047}(188,\cdot)\) \(\chi_{8047}(189,\cdot)\) \(\chi_{8047}(193,\cdot)\) \(\chi_{8047}(240,\cdot)\) \(\chi_{8047}(258,\cdot)\) \(\chi_{8047}(345,\cdot)\) \(\chi_{8047}(392,\cdot)\) \(\chi_{8047}(418,\cdot)\) \(\chi_{8047}(444,\cdot)\) \(\chi_{8047}(449,\cdot)\) \(\chi_{8047}(501,\cdot)\) \(\chi_{8047}(531,\cdot)\) \(\chi_{8047}(539,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1236})$ |
Fixed field: | Number field defined by a degree 1236 polynomial (not computed) |
Values on generators
\((3096,4954)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{1}{618}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8047 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{412}\right)\) | \(e\left(\frac{281}{618}\right)\) | \(e\left(\frac{35}{206}\right)\) | \(e\left(\frac{347}{1236}\right)\) | \(e\left(\frac{667}{1236}\right)\) | \(e\left(\frac{139}{412}\right)\) | \(e\left(\frac{105}{412}\right)\) | \(e\left(\frac{281}{309}\right)\) | \(e\left(\frac{113}{309}\right)\) | \(e\left(\frac{321}{412}\right)\) |