Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | 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 8041.dh
\(\chi_{8041}(32,\cdot)\) \(\chi_{8041}(604,\cdot)\) \(\chi_{8041}(978,\cdot)\) \(\chi_{8041}(1011,\cdot)\) \(\chi_{8041}(1341,\cdot)\) \(\chi_{8041}(1759,\cdot)\) \(\chi_{8041}(1957,\cdot)\) \(\chi_{8041}(2287,\cdot)\) \(\chi_{8041}(2650,\cdot)\) \(\chi_{8041}(2705,\cdot)\) \(\chi_{8041}(3442,\cdot)\) \(\chi_{8041}(3596,\cdot)\) \(\chi_{8041}(3816,\cdot)\) \(\chi_{8041}(4388,\cdot)\) \(\chi_{8041}(4762,\cdot)\) \(\chi_{8041}(5125,\cdot)\) \(\chi_{8041}(5268,\cdot)\) \(\chi_{8041}(6016,\cdot)\) \(\chi_{8041}(6071,\cdot)\) \(\chi_{8041}(6214,\cdot)\) \(\chi_{8041}(6434,\cdot)\) \(\chi_{8041}(6962,\cdot)\) \(\chi_{8041}(7380,\cdot)\) \(\chi_{8041}(7699,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6580,2366,562)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{13}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2287, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) |