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
\((5541,1944)\) → \((e\left(\frac{11}{28}\right),e\left(\frac{1}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(2251, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) |