Basic properties
| Modulus: | \(8021\) | |
| Conductor: | \(8021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(264\) | 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.dj
\(\chi_{8021}(89,\cdot)\) \(\chi_{8021}(150,\cdot)\) \(\chi_{8021}(228,\cdot)\) \(\chi_{8021}(262,\cdot)\) \(\chi_{8021}(336,\cdot)\) \(\chi_{8021}(513,\cdot)\) \(\chi_{8021}(544,\cdot)\) \(\chi_{8021}(721,\cdot)\) \(\chi_{8021}(899,\cdot)\) \(\chi_{8021}(908,\cdot)\) \(\chi_{8021}(943,\cdot)\) \(\chi_{8021}(1016,\cdot)\) \(\chi_{8021}(1042,\cdot)\) \(\chi_{8021}(1133,\cdot)\) \(\chi_{8021}(1224,\cdot)\) \(\chi_{8021}(1263,\cdot)\) \(\chi_{8021}(1280,\cdot)\) \(\chi_{8021}(1307,\cdot)\) \(\chi_{8021}(1515,\cdot)\) \(\chi_{8021}(1623,\cdot)\) \(\chi_{8021}(1701,\cdot)\) \(\chi_{8021}(1762,\cdot)\) \(\chi_{8021}(1822,\cdot)\) \(\chi_{8021}(1861,\cdot)\) \(\chi_{8021}(1952,\cdot)\) \(\chi_{8021}(2043,\cdot)\) \(\chi_{8021}(2069,\cdot)\) \(\chi_{8021}(2182,\cdot)\) \(\chi_{8021}(2186,\cdot)\) \(\chi_{8021}(2234,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{264})$ |
| Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((6788,2471)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{39}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(899, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{205}{264}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{205}{264}\right)\) | \(e\left(\frac{7}{66}\right)\) |