Basic properties
| Modulus: | \(5185\) | |
| Conductor: | \(5185\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5185.jc
\(\chi_{5185}(23,\cdot)\) \(\chi_{5185}(37,\cdot)\) \(\chi_{5185}(252,\cdot)\) \(\chi_{5185}(862,\cdot)\) \(\chi_{5185}(878,\cdot)\) \(\chi_{5185}(1183,\cdot)\) \(\chi_{5185}(1187,\cdot)\) \(\chi_{5185}(1558,\cdot)\) \(\chi_{5185}(1797,\cdot)\) \(\chi_{5185}(1807,\cdot)\) \(\chi_{5185}(1863,\cdot)\) \(\chi_{5185}(1867,\cdot)\) \(\chi_{5185}(2098,\cdot)\) \(\chi_{5185}(2403,\cdot)\) \(\chi_{5185}(2417,\cdot)\) \(\chi_{5185}(2477,\cdot)\) \(\chi_{5185}(2493,\cdot)\) \(\chi_{5185}(2778,\cdot)\) \(\chi_{5185}(2798,\cdot)\) \(\chi_{5185}(2997,\cdot)\) \(\chi_{5185}(3083,\cdot)\) \(\chi_{5185}(3607,\cdot)\) \(\chi_{5185}(3683,\cdot)\) \(\chi_{5185}(3713,\cdot)\) \(\chi_{5185}(3932,\cdot)\) \(\chi_{5185}(3988,\cdot)\) \(\chi_{5185}(4018,\cdot)\) \(\chi_{5185}(4247,\cdot)\) \(\chi_{5185}(4542,\cdot)\) \(\chi_{5185}(4612,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((3112,4576,2381)\) → \((i,e\left(\frac{1}{16}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(1\) |