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.lf
\(\chi_{5733}(137,\cdot)\) \(\chi_{5733}(401,\cdot)\) \(\chi_{5733}(578,\cdot)\) \(\chi_{5733}(956,\cdot)\) \(\chi_{5733}(1094,\cdot)\) \(\chi_{5733}(1220,\cdot)\) \(\chi_{5733}(1397,\cdot)\) \(\chi_{5733}(1775,\cdot)\) \(\chi_{5733}(1913,\cdot)\) \(\chi_{5733}(2216,\cdot)\) \(\chi_{5733}(2594,\cdot)\) \(\chi_{5733}(2732,\cdot)\) \(\chi_{5733}(2858,\cdot)\) \(\chi_{5733}(3035,\cdot)\) \(\chi_{5733}(3413,\cdot)\) \(\chi_{5733}(3551,\cdot)\) \(\chi_{5733}(3677,\cdot)\) \(\chi_{5733}(3854,\cdot)\) \(\chi_{5733}(4370,\cdot)\) \(\chi_{5733}(4496,\cdot)\) \(\chi_{5733}(5051,\cdot)\) \(\chi_{5733}(5189,\cdot)\) \(\chi_{5733}(5315,\cdot)\) \(\chi_{5733}(5492,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{21}\right),e\left(\frac{11}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{28}\right)\) |