Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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.ec
\(\chi_{8041}(98,\cdot)\) \(\chi_{8041}(846,\cdot)\) \(\chi_{8041}(1517,\cdot)\) \(\chi_{8041}(1594,\cdot)\) \(\chi_{8041}(1781,\cdot)\) \(\chi_{8041}(1968,\cdot)\) \(\chi_{8041}(2155,\cdot)\) \(\chi_{8041}(2265,\cdot)\) \(\chi_{8041}(2342,\cdot)\) \(\chi_{8041}(3013,\cdot)\) \(\chi_{8041}(3200,\cdot)\) \(\chi_{8041}(3387,\cdot)\) \(\chi_{8041}(3574,\cdot)\) \(\chi_{8041}(3761,\cdot)\) \(\chi_{8041}(4025,\cdot)\) \(\chi_{8041}(4586,\cdot)\) \(\chi_{8041}(5147,\cdot)\) \(\chi_{8041}(5444,\cdot)\) \(\chi_{8041}(6005,\cdot)\) \(\chi_{8041}(6082,\cdot)\) \(\chi_{8041}(6269,\cdot)\) \(\chi_{8041}(6566,\cdot)\) \(\chi_{8041}(7501,\cdot)\) \(\chi_{8041}(7688,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6580,2366,562)\) → \((-1,i,e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(5147, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) |