Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(276\) | 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 8033.cd
\(\chi_{8033}(17,\cdot)\) \(\chi_{8033}(46,\cdot)\) \(\chi_{8033}(162,\cdot)\) \(\chi_{8033}(510,\cdot)\) \(\chi_{8033}(534,\cdot)\) \(\chi_{8033}(597,\cdot)\) \(\chi_{8033}(766,\cdot)\) \(\chi_{8033}(887,\cdot)\) \(\chi_{8033}(911,\cdot)\) \(\chi_{8033}(945,\cdot)\) \(\chi_{8033}(998,\cdot)\) \(\chi_{8033}(1119,\cdot)\) \(\chi_{8033}(1206,\cdot)\) \(\chi_{8033}(1235,\cdot)\) \(\chi_{8033}(1380,\cdot)\) \(\chi_{8033}(1438,\cdot)\) \(\chi_{8033}(1462,\cdot)\) \(\chi_{8033}(1496,\cdot)\) \(\chi_{8033}(1520,\cdot)\) \(\chi_{8033}(1612,\cdot)\) \(\chi_{8033}(1781,\cdot)\) \(\chi_{8033}(1815,\cdot)\) \(\chi_{8033}(1984,\cdot)\) \(\chi_{8033}(2076,\cdot)\) \(\chi_{8033}(2192,\cdot)\) \(\chi_{8033}(2274,\cdot)\) \(\chi_{8033}(2390,\cdot)\) \(\chi_{8033}(2511,\cdot)\) \(\chi_{8033}(2598,\cdot)\) \(\chi_{8033}(2627,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{276})$ |
Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((-i,e\left(\frac{187}{276}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(887, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{35}{276}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{49}{276}\right)\) | \(e\left(\frac{131}{276}\right)\) | \(e\left(\frac{125}{138}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{35}{138}\right)\) | \(e\left(\frac{145}{276}\right)\) | \(e\left(\frac{34}{69}\right)\) |