Basic properties
Modulus: | \(8033\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{277}(102,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.bk
\(\chi_{8033}(59,\cdot)\) \(\chi_{8033}(146,\cdot)\) \(\chi_{8033}(1451,\cdot)\) \(\chi_{8033}(1683,\cdot)\) \(\chi_{8033}(1770,\cdot)\) \(\chi_{8033}(2147,\cdot)\) \(\chi_{8033}(2292,\cdot)\) \(\chi_{8033}(2466,\cdot)\) \(\chi_{8033}(2872,\cdot)\) \(\chi_{8033}(3017,\cdot)\) \(\chi_{8033}(3365,\cdot)\) \(\chi_{8033}(4380,\cdot)\) \(\chi_{8033}(4496,\cdot)\) \(\chi_{8033}(4554,\cdot)\) \(\chi_{8033}(4902,\cdot)\) \(\chi_{8033}(5337,\cdot)\) \(\chi_{8033}(5801,\cdot)\) \(\chi_{8033}(5830,\cdot)\) \(\chi_{8033}(6207,\cdot)\) \(\chi_{8033}(6352,\cdot)\) \(\chi_{8033}(7483,\cdot)\) \(\chi_{8033}(7599,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((5541,1944)\) → \((1,e\left(\frac{27}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(2872, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) |