Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | 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.bf
\(\chi_{8003}(603,\cdot)\) \(\chi_{8003}(754,\cdot)\) \(\chi_{8003}(1207,\cdot)\) \(\chi_{8003}(1358,\cdot)\) \(\chi_{8003}(2566,\cdot)\) \(\chi_{8003}(2717,\cdot)\) \(\chi_{8003}(3019,\cdot)\) \(\chi_{8003}(3321,\cdot)\) \(\chi_{8003}(3472,\cdot)\) \(\chi_{8003}(3623,\cdot)\) \(\chi_{8003}(3925,\cdot)\) \(\chi_{8003}(4076,\cdot)\) \(\chi_{8003}(4378,\cdot)\) \(\chi_{8003}(4831,\cdot)\) \(\chi_{8003}(5133,\cdot)\) \(\chi_{8003}(5586,\cdot)\) \(\chi_{8003}(5888,\cdot)\) \(\chi_{8003}(6039,\cdot)\) \(\chi_{8003}(6341,\cdot)\) \(\chi_{8003}(6492,\cdot)\) \(\chi_{8003}(6643,\cdot)\) \(\chi_{8003}(6945,\cdot)\) \(\chi_{8003}(7247,\cdot)\) \(\chi_{8003}(7398,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4984,7103)\) → \((e\left(\frac{49}{52}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(603, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) |