Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(46\) | 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.bj
\(\chi_{8033}(318,\cdot)\) \(\chi_{8033}(1333,\cdot)\) \(\chi_{8033}(1449,\cdot)\) \(\chi_{8033}(1507,\cdot)\) \(\chi_{8033}(1855,\cdot)\) \(\chi_{8033}(2290,\cdot)\) \(\chi_{8033}(2754,\cdot)\) \(\chi_{8033}(2783,\cdot)\) \(\chi_{8033}(3160,\cdot)\) \(\chi_{8033}(3305,\cdot)\) \(\chi_{8033}(4436,\cdot)\) \(\chi_{8033}(4552,\cdot)\) \(\chi_{8033}(5045,\cdot)\) \(\chi_{8033}(5132,\cdot)\) \(\chi_{8033}(6437,\cdot)\) \(\chi_{8033}(6669,\cdot)\) \(\chi_{8033}(6756,\cdot)\) \(\chi_{8033}(7133,\cdot)\) \(\chi_{8033}(7278,\cdot)\) \(\chi_{8033}(7452,\cdot)\) \(\chi_{8033}(7858,\cdot)\) \(\chi_{8033}(8003,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((5541,1944)\) → \((-1,e\left(\frac{21}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(318, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) |