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.bl
\(\chi_{8033}(434,\cdot)\) \(\chi_{8033}(550,\cdot)\) \(\chi_{8033}(1681,\cdot)\) \(\chi_{8033}(1826,\cdot)\) \(\chi_{8033}(2203,\cdot)\) \(\chi_{8033}(2232,\cdot)\) \(\chi_{8033}(2696,\cdot)\) \(\chi_{8033}(3131,\cdot)\) \(\chi_{8033}(3479,\cdot)\) \(\chi_{8033}(3537,\cdot)\) \(\chi_{8033}(3653,\cdot)\) \(\chi_{8033}(4668,\cdot)\) \(\chi_{8033}(5016,\cdot)\) \(\chi_{8033}(5161,\cdot)\) \(\chi_{8033}(5567,\cdot)\) \(\chi_{8033}(5741,\cdot)\) \(\chi_{8033}(5886,\cdot)\) \(\chi_{8033}(6263,\cdot)\) \(\chi_{8033}(6350,\cdot)\) \(\chi_{8033}(6582,\cdot)\) \(\chi_{8033}(7887,\cdot)\) \(\chi_{8033}(7974,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((5541,1944)\) → \((-1,e\left(\frac{8}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(2696, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) |