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.lz
\(\chi_{5733}(187,\cdot)\) \(\chi_{5733}(346,\cdot)\) \(\chi_{5733}(502,\cdot)\) \(\chi_{5733}(850,\cdot)\) \(\chi_{5733}(1006,\cdot)\) \(\chi_{5733}(1165,\cdot)\) \(\chi_{5733}(1321,\cdot)\) \(\chi_{5733}(1669,\cdot)\) \(\chi_{5733}(1825,\cdot)\) \(\chi_{5733}(1984,\cdot)\) \(\chi_{5733}(2140,\cdot)\) \(\chi_{5733}(2488,\cdot)\) \(\chi_{5733}(2644,\cdot)\) \(\chi_{5733}(2803,\cdot)\) \(\chi_{5733}(3307,\cdot)\) \(\chi_{5733}(3463,\cdot)\) \(\chi_{5733}(3622,\cdot)\) \(\chi_{5733}(3778,\cdot)\) \(\chi_{5733}(4126,\cdot)\) \(\chi_{5733}(4597,\cdot)\) \(\chi_{5733}(4945,\cdot)\) \(\chi_{5733}(5101,\cdot)\) \(\chi_{5733}(5260,\cdot)\) \(\chi_{5733}(5416,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{23}{42}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{84}\right)\) |