Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(150\) | 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.bt
\(\chi_{8003}(423,\cdot)\) \(\chi_{8003}(635,\cdot)\) \(\chi_{8003}(741,\cdot)\) \(\chi_{8003}(794,\cdot)\) \(\chi_{8003}(900,\cdot)\) \(\chi_{8003}(953,\cdot)\) \(\chi_{8003}(1006,\cdot)\) \(\chi_{8003}(1112,\cdot)\) \(\chi_{8003}(1218,\cdot)\) \(\chi_{8003}(1324,\cdot)\) \(\chi_{8003}(1377,\cdot)\) \(\chi_{8003}(1695,\cdot)\) \(\chi_{8003}(1854,\cdot)\) \(\chi_{8003}(1907,\cdot)\) \(\chi_{8003}(2066,\cdot)\) \(\chi_{8003}(2119,\cdot)\) \(\chi_{8003}(2172,\cdot)\) \(\chi_{8003}(2437,\cdot)\) \(\chi_{8003}(2490,\cdot)\) \(\chi_{8003}(2755,\cdot)\) \(\chi_{8003}(2808,\cdot)\) \(\chi_{8003}(2914,\cdot)\) \(\chi_{8003}(3391,\cdot)\) \(\chi_{8003}(3762,\cdot)\) \(\chi_{8003}(3815,\cdot)\) \(\chi_{8003}(4239,\cdot)\) \(\chi_{8003}(4610,\cdot)\) \(\chi_{8003}(4769,\cdot)\) \(\chi_{8003}(4875,\cdot)\) \(\chi_{8003}(5458,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((-1,e\left(\frac{28}{75}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(1112, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{47}{150}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{7}{75}\right)\) |