Basic properties
Modulus: | \(2003\) | |
Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2002\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2003.p
\(\chi_{2003}(5,\cdot)\) \(\chi_{2003}(7,\cdot)\) \(\chi_{2003}(15,\cdot)\) \(\chi_{2003}(18,\cdot)\) \(\chi_{2003}(20,\cdot)\) \(\chi_{2003}(24,\cdot)\) \(\chi_{2003}(26,\cdot)\) \(\chi_{2003}(28,\cdot)\) \(\chi_{2003}(29,\cdot)\) \(\chi_{2003}(31,\cdot)\) \(\chi_{2003}(33,\cdot)\) \(\chi_{2003}(37,\cdot)\) \(\chi_{2003}(38,\cdot)\) \(\chi_{2003}(41,\cdot)\) \(\chi_{2003}(43,\cdot)\) \(\chi_{2003}(51,\cdot)\) \(\chi_{2003}(54,\cdot)\) \(\chi_{2003}(60,\cdot)\) \(\chi_{2003}(61,\cdot)\) \(\chi_{2003}(63,\cdot)\) \(\chi_{2003}(68,\cdot)\) \(\chi_{2003}(70,\cdot)\) \(\chi_{2003}(72,\cdot)\) \(\chi_{2003}(78,\cdot)\) \(\chi_{2003}(80,\cdot)\) \(\chi_{2003}(83,\cdot)\) \(\chi_{2003}(93,\cdot)\) \(\chi_{2003}(94,\cdot)\) \(\chi_{2003}(96,\cdot)\) \(\chi_{2003}(97,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1001})$ |
Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1255}{2002}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2003 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{286}\right)\) | \(e\left(\frac{899}{1001}\right)\) | \(e\left(\frac{37}{143}\right)\) | \(e\left(\frac{1255}{2002}\right)\) | \(e\left(\frac{5}{182}\right)\) | \(e\left(\frac{211}{2002}\right)\) | \(e\left(\frac{111}{286}\right)\) | \(e\left(\frac{797}{1001}\right)\) | \(e\left(\frac{757}{1001}\right)\) | \(e\left(\frac{205}{286}\right)\) |