Basic properties
Modulus: | \(8033\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{277}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.z
\(\chi_{8033}(30,\cdot)\) \(\chi_{8033}(175,\cdot)\) \(\chi_{8033}(581,\cdot)\) \(\chi_{8033}(755,\cdot)\) \(\chi_{8033}(900,\cdot)\) \(\chi_{8033}(1277,\cdot)\) \(\chi_{8033}(1364,\cdot)\) \(\chi_{8033}(1596,\cdot)\) \(\chi_{8033}(2901,\cdot)\) \(\chi_{8033}(2988,\cdot)\) \(\chi_{8033}(3481,\cdot)\) \(\chi_{8033}(3597,\cdot)\) \(\chi_{8033}(4728,\cdot)\) \(\chi_{8033}(4873,\cdot)\) \(\chi_{8033}(5250,\cdot)\) \(\chi_{8033}(5279,\cdot)\) \(\chi_{8033}(5743,\cdot)\) \(\chi_{8033}(6178,\cdot)\) \(\chi_{8033}(6526,\cdot)\) \(\chi_{8033}(6584,\cdot)\) \(\chi_{8033}(6700,\cdot)\) \(\chi_{8033}(7715,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 23 polynomial |
Values on generators
\((5541,1944)\) → \((1,e\left(\frac{19}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(6178, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) |