Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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.ck
\(\chi_{8003}(75,\cdot)\) \(\chi_{8003}(147,\cdot)\) \(\chi_{8003}(217,\cdot)\) \(\chi_{8003}(226,\cdot)\) \(\chi_{8003}(286,\cdot)\) \(\chi_{8003}(298,\cdot)\) \(\chi_{8003}(300,\cdot)\) \(\chi_{8003}(368,\cdot)\) \(\chi_{8003}(451,\cdot)\) \(\chi_{8003}(499,\cdot)\) \(\chi_{8003}(528,\cdot)\) \(\chi_{8003}(588,\cdot)\) \(\chi_{8003}(602,\cdot)\) \(\chi_{8003}(650,\cdot)\) \(\chi_{8003}(670,\cdot)\) \(\chi_{8003}(739,\cdot)\) \(\chi_{8003}(821,\cdot)\) \(\chi_{8003}(830,\cdot)\) \(\chi_{8003}(868,\cdot)\) \(\chi_{8003}(904,\cdot)\) \(\chi_{8003}(952,\cdot)\) \(\chi_{8003}(972,\cdot)\) \(\chi_{8003}(981,\cdot)\) \(\chi_{8003}(1019,\cdot)\) \(\chi_{8003}(1041,\cdot)\) \(\chi_{8003}(1055,\cdot)\) \(\chi_{8003}(1080,\cdot)\) \(\chi_{8003}(1132,\cdot)\) \(\chi_{8003}(1192,\cdot)\) \(\chi_{8003}(1231,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{7}{52}\right),e\left(\frac{1}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{47}{780}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{103}{195}\right)\) | \(e\left(\frac{367}{390}\right)\) |