Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8003.br
\(\chi_{8003}(59,\cdot)\) \(\chi_{8003}(64,\cdot)\) \(\chi_{8003}(170,\cdot)\) \(\chi_{8003}(361,\cdot)\) \(\chi_{8003}(461,\cdot)\) \(\chi_{8003}(517,\cdot)\) \(\chi_{8003}(612,\cdot)\) \(\chi_{8003}(623,\cdot)\) \(\chi_{8003}(965,\cdot)\) \(\chi_{8003}(1418,\cdot)\) \(\chi_{8003}(1574,\cdot)\) \(\chi_{8003}(1680,\cdot)\) \(\chi_{8003}(1725,\cdot)\) \(\chi_{8003}(1831,\cdot)\) \(\chi_{8003}(2475,\cdot)\) \(\chi_{8003}(2626,\cdot)\) \(\chi_{8003}(3028,\cdot)\) \(\chi_{8003}(4085,\cdot)\) \(\chi_{8003}(4141,\cdot)\) \(\chi_{8003}(4247,\cdot)\) \(\chi_{8003}(4689,\cdot)\) \(\chi_{8003}(4840,\cdot)\) \(\chi_{8003}(4991,\cdot)\) \(\chi_{8003}(5042,\cdot)\) \(\chi_{8003}(5198,\cdot)\) \(\chi_{8003}(5304,\cdot)\) \(\chi_{8003}(5444,\cdot)\) \(\chi_{8003}(5802,\cdot)\) \(\chi_{8003}(5908,\cdot)\) \(\chi_{8003}(5953,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{9}{26}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) |