Basic properties
Modulus: | \(8014\) | |
Conductor: | \(4007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4006\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4007}(17,\cdot)\) | 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 8014.d
\(\chi_{8014}(5,\cdot)\) \(\chi_{8014}(11,\cdot)\) \(\chi_{8014}(15,\cdot)\) \(\chi_{8014}(17,\cdot)\) \(\chi_{8014}(19,\cdot)\) \(\chi_{8014}(31,\cdot)\) \(\chi_{8014}(33,\cdot)\) \(\chi_{8014}(35,\cdot)\) \(\chi_{8014}(41,\cdot)\) \(\chi_{8014}(45,\cdot)\) \(\chi_{8014}(47,\cdot)\) \(\chi_{8014}(51,\cdot)\) \(\chi_{8014}(53,\cdot)\) \(\chi_{8014}(57,\cdot)\) \(\chi_{8014}(65,\cdot)\) \(\chi_{8014}(67,\cdot)\) \(\chi_{8014}(77,\cdot)\) \(\chi_{8014}(83,\cdot)\) \(\chi_{8014}(93,\cdot)\) \(\chi_{8014}(97,\cdot)\) \(\chi_{8014}(99,\cdot)\) \(\chi_{8014}(103,\cdot)\) \(\chi_{8014}(105,\cdot)\) \(\chi_{8014}(107,\cdot)\) \(\chi_{8014}(115,\cdot)\) \(\chi_{8014}(119,\cdot)\) \(\chi_{8014}(123,\cdot)\) \(\chi_{8014}(125,\cdot)\) \(\chi_{8014}(127,\cdot)\) \(\chi_{8014}(131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2003})$ |
Fixed field: | Number field defined by a degree 4006 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{581}{4006}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8014 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1372}{2003}\right)\) | \(e\left(\frac{581}{4006}\right)\) | \(e\left(\frac{1131}{2003}\right)\) | \(e\left(\frac{741}{2003}\right)\) | \(e\left(\frac{141}{4006}\right)\) | \(e\left(\frac{267}{2003}\right)\) | \(e\left(\frac{3325}{4006}\right)\) | \(e\left(\frac{1057}{4006}\right)\) | \(e\left(\frac{2577}{4006}\right)\) | \(e\left(\frac{500}{2003}\right)\) |