Basic properties
Modulus: | \(2003\) | |
Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(286\) | 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.n
\(\chi_{2003}(2,\cdot)\) \(\chi_{2003}(8,\cdot)\) \(\chi_{2003}(11,\cdot)\) \(\chi_{2003}(21,\cdot)\) \(\chi_{2003}(23,\cdot)\) \(\chi_{2003}(32,\cdot)\) \(\chi_{2003}(44,\cdot)\) \(\chi_{2003}(67,\cdot)\) \(\chi_{2003}(71,\cdot)\) \(\chi_{2003}(84,\cdot)\) \(\chi_{2003}(92,\cdot)\) \(\chi_{2003}(128,\cdot)\) \(\chi_{2003}(149,\cdot)\) \(\chi_{2003}(176,\cdot)\) \(\chi_{2003}(178,\cdot)\) \(\chi_{2003}(195,\cdot)\) \(\chi_{2003}(226,\cdot)\) \(\chi_{2003}(239,\cdot)\) \(\chi_{2003}(242,\cdot)\) \(\chi_{2003}(249,\cdot)\) \(\chi_{2003}(268,\cdot)\) \(\chi_{2003}(284,\cdot)\) \(\chi_{2003}(310,\cdot)\) \(\chi_{2003}(313,\cdot)\) \(\chi_{2003}(336,\cdot)\) \(\chi_{2003}(348,\cdot)\) \(\chi_{2003}(364,\cdot)\) \(\chi_{2003}(368,\cdot)\) \(\chi_{2003}(370,\cdot)\) \(\chi_{2003}(377,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{143})$ |
Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{87}{286}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2003 }(239, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{286}\right)\) | \(e\left(\frac{36}{143}\right)\) | \(e\left(\frac{60}{143}\right)\) | \(e\left(\frac{87}{286}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{119}{286}\right)\) | \(e\left(\frac{37}{286}\right)\) | \(e\left(\frac{72}{143}\right)\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{259}{286}\right)\) |