Basic properties
Modulus: | \(4012\) | |
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 \(\chi_{1003}(105,\cdot)\) | 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)
|
Galois orbit 4012.bm
\(\chi_{4012}(5,\cdot)\) \(\chi_{4012}(29,\cdot)\) \(\chi_{4012}(41,\cdot)\) \(\chi_{4012}(45,\cdot)\) \(\chi_{4012}(57,\cdot)\) \(\chi_{4012}(105,\cdot)\) \(\chi_{4012}(125,\cdot)\) \(\chi_{4012}(133,\cdot)\) \(\chi_{4012}(181,\cdot)\) \(\chi_{4012}(193,\cdot)\) \(\chi_{4012}(197,\cdot)\) \(\chi_{4012}(241,\cdot)\) \(\chi_{4012}(245,\cdot)\) \(\chi_{4012}(261,\cdot)\) \(\chi_{4012}(265,\cdot)\) \(\chi_{4012}(277,\cdot)\) \(\chi_{4012}(317,\cdot)\) \(\chi_{4012}(369,\cdot)\) \(\chi_{4012}(381,\cdot)\) \(\chi_{4012}(405,\cdot)\) \(\chi_{4012}(449,\cdot)\) \(\chi_{4012}(481,\cdot)\) \(\chi_{4012}(513,\cdot)\) \(\chi_{4012}(517,\cdot)\) \(\chi_{4012}(521,\cdot)\) \(\chi_{4012}(605,\cdot)\) \(\chi_{4012}(609,\cdot)\) \(\chi_{4012}(617,\cdot)\) \(\chi_{4012}(641,\cdot)\) \(\chi_{4012}(653,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{8}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(105, a) \) | \(-1\) | \(1\) | \(e\left(\frac{397}{464}\right)\) | \(e\left(\frac{449}{464}\right)\) | \(e\left(\frac{303}{464}\right)\) | \(e\left(\frac{165}{232}\right)\) | \(e\left(\frac{155}{464}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{191}{232}\right)\) | \(e\left(\frac{83}{232}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{35}{464}\right)\) |