Basic properties
Modulus: | \(4006\) | |
Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2002\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2003}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4006.p
\(\chi_{4006}(5,\cdot)\) \(\chi_{4006}(7,\cdot)\) \(\chi_{4006}(15,\cdot)\) \(\chi_{4006}(29,\cdot)\) \(\chi_{4006}(31,\cdot)\) \(\chi_{4006}(33,\cdot)\) \(\chi_{4006}(37,\cdot)\) \(\chi_{4006}(41,\cdot)\) \(\chi_{4006}(43,\cdot)\) \(\chi_{4006}(51,\cdot)\) \(\chi_{4006}(61,\cdot)\) \(\chi_{4006}(63,\cdot)\) \(\chi_{4006}(83,\cdot)\) \(\chi_{4006}(93,\cdot)\) \(\chi_{4006}(97,\cdot)\) \(\chi_{4006}(103,\cdot)\) \(\chi_{4006}(109,\cdot)\) \(\chi_{4006}(123,\cdot)\) \(\chi_{4006}(125,\cdot)\) \(\chi_{4006}(127,\cdot)\) \(\chi_{4006}(129,\cdot)\) \(\chi_{4006}(131,\cdot)\) \(\chi_{4006}(133,\cdot)\) \(\chi_{4006}(135,\cdot)\) \(\chi_{4006}(137,\cdot)\) \(\chi_{4006}(139,\cdot)\) \(\chi_{4006}(143,\cdot)\) \(\chi_{4006}(151,\cdot)\) \(\chi_{4006}(153,\cdot)\) \(\chi_{4006}(157,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1001})$ |
Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{621}{2002}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4006 }(51, a) \) | \(-1\) | \(1\) | \(e\left(\frac{326}{1001}\right)\) | \(e\left(\frac{621}{2002}\right)\) | \(e\left(\frac{307}{2002}\right)\) | \(e\left(\frac{652}{1001}\right)\) | \(e\left(\frac{57}{286}\right)\) | \(e\left(\frac{424}{1001}\right)\) | \(e\left(\frac{1273}{2002}\right)\) | \(e\left(\frac{55}{182}\right)\) | \(e\left(\frac{883}{1001}\right)\) | \(e\left(\frac{137}{286}\right)\) |