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.ci
\(\chi_{8033}(99,\cdot)\) \(\chi_{8033}(447,\cdot)\) \(\chi_{8033}(476,\cdot)\) \(\chi_{8033}(568,\cdot)\) \(\chi_{8033}(626,\cdot)\) \(\chi_{8033}(650,\cdot)\) \(\chi_{8033}(655,\cdot)\) \(\chi_{8033}(737,\cdot)\) \(\chi_{8033}(800,\cdot)\) \(\chi_{8033}(974,\cdot)\) \(\chi_{8033}(1003,\cdot)\) \(\chi_{8033}(1090,\cdot)\) \(\chi_{8033}(1114,\cdot)\) \(\chi_{8033}(1201,\cdot)\) \(\chi_{8033}(1259,\cdot)\) \(\chi_{8033}(1288,\cdot)\) \(\chi_{8033}(1317,\cdot)\) \(\chi_{8033}(1409,\cdot)\) \(\chi_{8033}(1525,\cdot)\) \(\chi_{8033}(1786,\cdot)\) \(\chi_{8033}(1989,\cdot)\) \(\chi_{8033}(2042,\cdot)\) \(\chi_{8033}(2105,\cdot)\) \(\chi_{8033}(2158,\cdot)\) \(\chi_{8033}(2163,\cdot)\) \(\chi_{8033}(2221,\cdot)\) \(\chi_{8033}(2366,\cdot)\) \(\chi_{8033}(2395,\cdot)\) \(\chi_{8033}(2448,\cdot)\) \(\chi_{8033}(2482,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{276})$ |
Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((-i,e\left(\frac{73}{276}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1003, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{131}{276}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{211}{276}\right)\) | \(e\left(\frac{29}{276}\right)\) | \(e\left(\frac{113}{138}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{109}{276}\right)\) | \(e\left(\frac{83}{138}\right)\) |