Basic properties
Modulus: | \(8024\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(78,\cdot)\) | 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.cy
\(\chi_{8024}(41,\cdot)\) \(\chi_{8024}(57,\cdot)\) \(\chi_{8024}(105,\cdot)\) \(\chi_{8024}(193,\cdot)\) \(\chi_{8024}(241,\cdot)\) \(\chi_{8024}(265,\cdot)\) \(\chi_{8024}(369,\cdot)\) \(\chi_{8024}(449,\cdot)\) \(\chi_{8024}(481,\cdot)\) \(\chi_{8024}(513,\cdot)\) \(\chi_{8024}(521,\cdot)\) \(\chi_{8024}(609,\cdot)\) \(\chi_{8024}(617,\cdot)\) \(\chi_{8024}(641,\cdot)\) \(\chi_{8024}(737,\cdot)\) \(\chi_{8024}(753,\cdot)\) \(\chi_{8024}(793,\cdot)\) \(\chi_{8024}(889,\cdot)\) \(\chi_{8024}(913,\cdot)\) \(\chi_{8024}(921,\cdot)\) \(\chi_{8024}(993,\cdot)\) \(\chi_{8024}(1025,\cdot)\) \(\chi_{8024}(1049,\cdot)\) \(\chi_{8024}(1065,\cdot)\) \(\chi_{8024}(1081,\cdot)\) \(\chi_{8024}(1185,\cdot)\) \(\chi_{8024}(1201,\cdot)\) \(\chi_{8024}(1265,\cdot)\) \(\chi_{8024}(1425,\cdot)\) \(\chi_{8024}(1433,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,1,e\left(\frac{3}{16}\right),e\left(\frac{19}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 8024 }(1081, a) \) | \(-1\) | \(1\) | \(e\left(\frac{439}{464}\right)\) | \(e\left(\frac{403}{464}\right)\) | \(e\left(\frac{397}{464}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{321}{464}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{121}{232}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{297}{464}\right)\) |