Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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.bs
\(\chi_{8033}(182,\cdot)\) \(\chi_{8033}(649,\cdot)\) \(\chi_{8033}(1013,\cdot)\) \(\chi_{8033}(1203,\cdot)\) \(\chi_{8033}(1627,\cdot)\) \(\chi_{8033}(1697,\cdot)\) \(\chi_{8033}(1904,\cdot)\) \(\chi_{8033}(2251,\cdot)\) \(\chi_{8033}(3082,\cdot)\) \(\chi_{8033}(3229,\cdot)\) \(\chi_{8033}(3506,\cdot)\) \(\chi_{8033}(3913,\cdot)\) \(\chi_{8033}(4120,\cdot)\) \(\chi_{8033}(4527,\cdot)\) \(\chi_{8033}(4804,\cdot)\) \(\chi_{8033}(4951,\cdot)\) \(\chi_{8033}(5782,\cdot)\) \(\chi_{8033}(6129,\cdot)\) \(\chi_{8033}(6336,\cdot)\) \(\chi_{8033}(6406,\cdot)\) \(\chi_{8033}(6830,\cdot)\) \(\chi_{8033}(7020,\cdot)\) \(\chi_{8033}(7384,\cdot)\) \(\chi_{8033}(7851,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5541,1944)\) → \((e\left(\frac{11}{28}\right),e\left(\frac{5}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(7384, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) |