Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(195\) | 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.by
\(\chi_{8003}(16,\cdot)\) \(\chi_{8003}(153,\cdot)\) \(\chi_{8003}(155,\cdot)\) \(\chi_{8003}(227,\cdot)\) \(\chi_{8003}(236,\cdot)\) \(\chi_{8003}(256,\cdot)\) \(\chi_{8003}(387,\cdot)\) \(\chi_{8003}(407,\cdot)\) \(\chi_{8003}(558,\cdot)\) \(\chi_{8003}(680,\cdot)\) \(\chi_{8003}(757,\cdot)\) \(\chi_{8003}(831,\cdot)\) \(\chi_{8003}(982,\cdot)\) \(\chi_{8003}(1073,\cdot)\) \(\chi_{8003}(1162,\cdot)\) \(\chi_{8003}(1210,\cdot)\) \(\chi_{8003}(1212,\cdot)\) \(\chi_{8003}(1361,\cdot)\) \(\chi_{8003}(1444,\cdot)\) \(\chi_{8003}(1512,\cdot)\) \(\chi_{8003}(1526,\cdot)\) \(\chi_{8003}(1586,\cdot)\) \(\chi_{8003}(1897,\cdot)\) \(\chi_{8003}(2091,\cdot)\) \(\chi_{8003}(2116,\cdot)\) \(\chi_{8003}(2130,\cdot)\) \(\chi_{8003}(2219,\cdot)\) \(\chi_{8003}(2242,\cdot)\) \(\chi_{8003}(2303,\cdot)\) \(\chi_{8003}(2432,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{1}{13}\right),e\left(\frac{13}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{133}{195}\right)\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{28}{195}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{181}{195}\right)\) |