Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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.by
\(\chi_{8033}(331,\cdot)\) \(\chi_{8033}(481,\cdot)\) \(\chi_{8033}(592,\cdot)\) \(\chi_{8033}(679,\cdot)\) \(\chi_{8033}(829,\cdot)\) \(\chi_{8033}(882,\cdot)\) \(\chi_{8033}(969,\cdot)\) \(\chi_{8033}(1467,\cdot)\) \(\chi_{8033}(1636,\cdot)\) \(\chi_{8033}(1670,\cdot)\) \(\chi_{8033}(1694,\cdot)\) \(\chi_{8033}(1723,\cdot)\) \(\chi_{8033}(1897,\cdot)\) \(\chi_{8033}(1902,\cdot)\) \(\chi_{8033}(2361,\cdot)\) \(\chi_{8033}(2622,\cdot)\) \(\chi_{8033}(2888,\cdot)\) \(\chi_{8033}(3062,\cdot)\) \(\chi_{8033}(3492,\cdot)\) \(\chi_{8033}(3497,\cdot)\) \(\chi_{8033}(3729,\cdot)\) \(\chi_{8033}(3845,\cdot)\) \(\chi_{8033}(4188,\cdot)\) \(\chi_{8033}(4304,\cdot)\) \(\chi_{8033}(4536,\cdot)\) \(\chi_{8033}(4541,\cdot)\) \(\chi_{8033}(4971,\cdot)\) \(\chi_{8033}(5145,\cdot)\) \(\chi_{8033}(5411,\cdot)\) \(\chi_{8033}(5672,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((5541,1944)\) → \((i,e\left(\frac{13}{92}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1723, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{59}{92}\right)\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{11}{46}\right)\) |