Basic properties
Modulus: | \(2003\) | |
Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | 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.l
\(\chi_{2003}(50,\cdot)\) \(\chi_{2003}(65,\cdot)\) \(\chi_{2003}(99,\cdot)\) \(\chi_{2003}(111,\cdot)\) \(\chi_{2003}(124,\cdot)\) \(\chi_{2003}(199,\cdot)\) \(\chi_{2003}(207,\cdot)\) \(\chi_{2003}(210,\cdot)\) \(\chi_{2003}(214,\cdot)\) \(\chi_{2003}(234,\cdot)\) \(\chi_{2003}(245,\cdot)\) \(\chi_{2003}(257,\cdot)\) \(\chi_{2003}(273,\cdot)\) \(\chi_{2003}(329,\cdot)\) \(\chi_{2003}(371,\cdot)\) \(\chi_{2003}(397,\cdot)\) \(\chi_{2003}(459,\cdot)\) \(\chi_{2003}(566,\cdot)\) \(\chi_{2003}(628,\cdot)\) \(\chi_{2003}(648,\cdot)\) \(\chi_{2003}(726,\cdot)\) \(\chi_{2003}(756,\cdot)\) \(\chi_{2003}(757,\cdot)\) \(\chi_{2003}(797,\cdot)\) \(\chi_{2003}(814,\cdot)\) \(\chi_{2003}(847,\cdot)\) \(\chi_{2003}(870,\cdot)\) \(\chi_{2003}(935,\cdot)\) \(\chi_{2003}(1015,\cdot)\) \(\chi_{2003}(1059,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{75}{154}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2003 }(111, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{19}{22}\right)\) |