Basic properties
Modulus: | \(8038\) | |
Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2009\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4019}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8038.k
\(\chi_{8038}(5,\cdot)\) \(\chi_{8038}(15,\cdot)\) \(\chi_{8038}(19,\cdot)\) \(\chi_{8038}(23,\cdot)\) \(\chi_{8038}(25,\cdot)\) \(\chi_{8038}(43,\cdot)\) \(\chi_{8038}(45,\cdot)\) \(\chi_{8038}(49,\cdot)\) \(\chi_{8038}(53,\cdot)\) \(\chi_{8038}(57,\cdot)\) \(\chi_{8038}(67,\cdot)\) \(\chi_{8038}(69,\cdot)\) \(\chi_{8038}(73,\cdot)\) \(\chi_{8038}(75,\cdot)\) \(\chi_{8038}(77,\cdot)\) \(\chi_{8038}(79,\cdot)\) \(\chi_{8038}(83,\cdot)\) \(\chi_{8038}(95,\cdot)\) \(\chi_{8038}(101,\cdot)\) \(\chi_{8038}(107,\cdot)\) \(\chi_{8038}(113,\cdot)\) \(\chi_{8038}(115,\cdot)\) \(\chi_{8038}(119,\cdot)\) \(\chi_{8038}(121,\cdot)\) \(\chi_{8038}(123,\cdot)\) \(\chi_{8038}(125,\cdot)\) \(\chi_{8038}(129,\cdot)\) \(\chi_{8038}(143,\cdot)\) \(\chi_{8038}(147,\cdot)\) \(\chi_{8038}(151,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2009})$ |
Fixed field: | Number field defined by a degree 2009 polynomial (not computed) |
Values on generators
\(4021\) → \(e\left(\frac{1058}{2009}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8038 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{49}\right)\) | \(e\left(\frac{397}{2009}\right)\) | \(e\left(\frac{1746}{2009}\right)\) | \(e\left(\frac{29}{49}\right)\) | \(e\left(\frac{905}{2009}\right)\) | \(e\left(\frac{1247}{2009}\right)\) | \(e\left(\frac{1996}{2009}\right)\) | \(e\left(\frac{2001}{2009}\right)\) | \(e\left(\frac{454}{2009}\right)\) | \(e\left(\frac{1336}{2009}\right)\) |