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.di
\(\chi_{8021}(46,\cdot)\) \(\chi_{8021}(310,\cdot)\) \(\chi_{8021}(331,\cdot)\) \(\chi_{8021}(383,\cdot)\) \(\chi_{8021}(851,\cdot)\) \(\chi_{8021}(903,\cdot)\) \(\chi_{8021}(1029,\cdot)\) \(\chi_{8021}(1384,\cdot)\) \(\chi_{8021}(1419,\cdot)\) \(\chi_{8021}(1462,\cdot)\) \(\chi_{8021}(1541,\cdot)\) \(\chi_{8021}(1666,\cdot)\) \(\chi_{8021}(1805,\cdot)\) \(\chi_{8021}(2056,\cdot)\) \(\chi_{8021}(2113,\cdot)\) \(\chi_{8021}(2177,\cdot)\) \(\chi_{8021}(2364,\cdot)\) \(\chi_{8021}(2541,\cdot)\) \(\chi_{8021}(2572,\cdot)\) \(\chi_{8021}(2749,\cdot)\) \(\chi_{8021}(2750,\cdot)\) \(\chi_{8021}(2867,\cdot)\) \(\chi_{8021}(2893,\cdot)\) \(\chi_{8021}(2984,\cdot)\) \(\chi_{8021}(2996,\cdot)\) \(\chi_{8021}(3075,\cdot)\) \(\chi_{8021}(3114,\cdot)\) \(\chi_{8021}(3131,\cdot)\) \(\chi_{8021}(3174,\cdot)\) \(\chi_{8021}(3421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{264})$ |
| Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((6788,2471)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{7}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{197}{264}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{197}{264}\right)\) | \(e\left(\frac{16}{33}\right)\) |