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.mj
\(\chi_{5733}(124,\cdot)\) \(\chi_{5733}(535,\cdot)\) \(\chi_{5733}(565,\cdot)\) \(\chi_{5733}(661,\cdot)\) \(\chi_{5733}(943,\cdot)\) \(\chi_{5733}(1384,\cdot)\) \(\chi_{5733}(1480,\cdot)\) \(\chi_{5733}(1762,\cdot)\) \(\chi_{5733}(2173,\cdot)\) \(\chi_{5733}(2203,\cdot)\) \(\chi_{5733}(2299,\cdot)\) \(\chi_{5733}(2581,\cdot)\) \(\chi_{5733}(2992,\cdot)\) \(\chi_{5733}(3022,\cdot)\) \(\chi_{5733}(3811,\cdot)\) \(\chi_{5733}(3937,\cdot)\) \(\chi_{5733}(4219,\cdot)\) \(\chi_{5733}(4630,\cdot)\) \(\chi_{5733}(4660,\cdot)\) \(\chi_{5733}(4756,\cdot)\) \(\chi_{5733}(5038,\cdot)\) \(\chi_{5733}(5449,\cdot)\) \(\chi_{5733}(5479,\cdot)\) \(\chi_{5733}(5575,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{17}{42}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(124, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(-i\) | \(e\left(\frac{15}{28}\right)\) |