Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(975\) | 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.cm
\(\chi_{8003}(10,\cdot)\) \(\chi_{8003}(36,\cdot)\) \(\chi_{8003}(42,\cdot)\) \(\chi_{8003}(47,\cdot)\) \(\chi_{8003}(49,\cdot)\) \(\chi_{8003}(69,\cdot)\) \(\chi_{8003}(95,\cdot)\) \(\chi_{8003}(97,\cdot)\) \(\chi_{8003}(99,\cdot)\) \(\chi_{8003}(100,\cdot)\) \(\chi_{8003}(116,\cdot)\) \(\chi_{8003}(121,\cdot)\) \(\chi_{8003}(169,\cdot)\) \(\chi_{8003}(172,\cdot)\) \(\chi_{8003}(187,\cdot)\) \(\chi_{8003}(206,\cdot)\) \(\chi_{8003}(225,\cdot)\) \(\chi_{8003}(248,\cdot)\) \(\chi_{8003}(254,\cdot)\) \(\chi_{8003}(289,\cdot)\) \(\chi_{8003}(307,\cdot)\) \(\chi_{8003}(312,\cdot)\) \(\chi_{8003}(333,\cdot)\) \(\chi_{8003}(342,\cdot)\) \(\chi_{8003}(360,\cdot)\) \(\chi_{8003}(364,\cdot)\) \(\chi_{8003}(399,\cdot)\) \(\chi_{8003}(418,\cdot)\) \(\chi_{8003}(439,\cdot)\) \(\chi_{8003}(440,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{975})$ |
Fixed field: | Number field defined by a degree 975 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{12}{13}\right),e\left(\frac{16}{75}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{316}{325}\right)\) | \(e\left(\frac{139}{195}\right)\) | \(e\left(\frac{271}{975}\right)\) | \(e\left(\frac{808}{975}\right)\) | \(e\left(\frac{211}{975}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{307}{325}\right)\) | \(e\left(\frac{131}{975}\right)\) | \(e\left(\frac{577}{975}\right)\) |