Basic properties
| Modulus: | \(5733\) | |
| Conductor: | \(5733\) | 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 5733.mf
\(\chi_{5733}(11,\cdot)\) \(\chi_{5733}(149,\cdot)\) \(\chi_{5733}(527,\cdot)\) \(\chi_{5733}(830,\cdot)\) \(\chi_{5733}(968,\cdot)\) \(\chi_{5733}(1346,\cdot)\) \(\chi_{5733}(1523,\cdot)\) \(\chi_{5733}(1649,\cdot)\) \(\chi_{5733}(1787,\cdot)\) \(\chi_{5733}(2165,\cdot)\) \(\chi_{5733}(2342,\cdot)\) \(\chi_{5733}(2606,\cdot)\) \(\chi_{5733}(2984,\cdot)\) \(\chi_{5733}(3161,\cdot)\) \(\chi_{5733}(3287,\cdot)\) \(\chi_{5733}(3425,\cdot)\) \(\chi_{5733}(3980,\cdot)\) \(\chi_{5733}(4106,\cdot)\) \(\chi_{5733}(4622,\cdot)\) \(\chi_{5733}(4799,\cdot)\) \(\chi_{5733}(4925,\cdot)\) \(\chi_{5733}(5063,\cdot)\) \(\chi_{5733}(5441,\cdot)\) \(\chi_{5733}(5618,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{16}{21}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(527, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(i\) | \(e\left(\frac{53}{84}\right)\) |