Basic properties
Modulus: | \(8024\) | |
Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(464\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8024.db
\(\chi_{8024}(5,\cdot)\) \(\chi_{8024}(29,\cdot)\) \(\chi_{8024}(45,\cdot)\) \(\chi_{8024}(125,\cdot)\) \(\chi_{8024}(133,\cdot)\) \(\chi_{8024}(181,\cdot)\) \(\chi_{8024}(197,\cdot)\) \(\chi_{8024}(245,\cdot)\) \(\chi_{8024}(261,\cdot)\) \(\chi_{8024}(277,\cdot)\) \(\chi_{8024}(317,\cdot)\) \(\chi_{8024}(381,\cdot)\) \(\chi_{8024}(405,\cdot)\) \(\chi_{8024}(517,\cdot)\) \(\chi_{8024}(605,\cdot)\) \(\chi_{8024}(653,\cdot)\) \(\chi_{8024}(669,\cdot)\) \(\chi_{8024}(677,\cdot)\) \(\chi_{8024}(685,\cdot)\) \(\chi_{8024}(717,\cdot)\) \(\chi_{8024}(725,\cdot)\) \(\chi_{8024}(789,\cdot)\) \(\chi_{8024}(813,\cdot)\) \(\chi_{8024}(845,\cdot)\) \(\chi_{8024}(853,\cdot)\) \(\chi_{8024}(861,\cdot)\) \(\chi_{8024}(877,\cdot)\) \(\chi_{8024}(949,\cdot)\) \(\chi_{8024}(989,\cdot)\) \(\chi_{8024}(997,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,-1,e\left(\frac{13}{16}\right),e\left(\frac{19}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 8024 }(845, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{464}\right)\) | \(e\left(\frac{229}{464}\right)\) | \(e\left(\frac{339}{464}\right)\) | \(e\left(\frac{33}{232}\right)\) | \(e\left(\frac{263}{464}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{179}{232}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{7}{464}\right)\) |