Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.bm
\(\chi_{8003}(269,\cdot)\) \(\chi_{8003}(873,\cdot)\) \(\chi_{8003}(938,\cdot)\) \(\chi_{8003}(1024,\cdot)\) \(\chi_{8003}(1089,\cdot)\) \(\chi_{8003}(1175,\cdot)\) \(\chi_{8003}(1628,\cdot)\) \(\chi_{8003}(2232,\cdot)\) \(\chi_{8003}(2534,\cdot)\) \(\chi_{8003}(3138,\cdot)\) \(\chi_{8003}(3505,\cdot)\) \(\chi_{8003}(3591,\cdot)\) \(\chi_{8003}(4562,\cdot)\) \(\chi_{8003}(4648,\cdot)\) \(\chi_{8003}(4799,\cdot)\) \(\chi_{8003}(5166,\cdot)\) \(\chi_{8003}(5317,\cdot)\) \(\chi_{8003}(5468,\cdot)\) \(\chi_{8003}(5921,\cdot)\) \(\chi_{8003}(6525,\cdot)\) \(\chi_{8003}(6827,\cdot)\) \(\chi_{8003}(7215,\cdot)\) \(\chi_{8003}(7431,\cdot)\) \(\chi_{8003}(7884,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4984,7103)\) → \((e\left(\frac{1}{26}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(269, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) |