Basic properties
| Modulus: | \(8021\) | |
| Conductor: | \(8021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(616\) | 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 8021.dw
\(\chi_{8021}(5,\cdot)\) \(\chi_{8021}(34,\cdot)\) \(\chi_{8021}(96,\cdot)\) \(\chi_{8021}(109,\cdot)\) \(\chi_{8021}(122,\cdot)\) \(\chi_{8021}(125,\cdot)\) \(\chi_{8021}(177,\cdot)\) \(\chi_{8021}(187,\cdot)\) \(\chi_{8021}(190,\cdot)\) \(\chi_{8021}(203,\cdot)\) \(\chi_{8021}(213,\cdot)\) \(\chi_{8021}(239,\cdot)\) \(\chi_{8021}(278,\cdot)\) \(\chi_{8021}(346,\cdot)\) \(\chi_{8021}(411,\cdot)\) \(\chi_{8021}(437,\cdot)\) \(\chi_{8021}(486,\cdot)\) \(\chi_{8021}(525,\cdot)\) \(\chi_{8021}(564,\cdot)\) \(\chi_{8021}(577,\cdot)\) \(\chi_{8021}(629,\cdot)\) \(\chi_{8021}(671,\cdot)\) \(\chi_{8021}(733,\cdot)\) \(\chi_{8021}(746,\cdot)\) \(\chi_{8021}(749,\cdot)\) \(\chi_{8021}(772,\cdot)\) \(\chi_{8021}(798,\cdot)\) \(\chi_{8021}(850,\cdot)\) \(\chi_{8021}(928,\cdot)\) \(\chi_{8021}(970,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{616})$ |
| Fixed field: | Number field defined by a degree 616 polynomial (not computed) |
Values on generators
\((6788,2471)\) → \((-i,e\left(\frac{321}{616}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{321}{616}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{15}{616}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{107}{308}\right)\) | \(e\left(\frac{13}{308}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{101}{154}\right)\) |