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.jf
\(\chi_{5185}(28,\cdot)\) \(\chi_{5185}(207,\cdot)\) \(\chi_{5185}(267,\cdot)\) \(\chi_{5185}(277,\cdot)\) \(\chi_{5185}(313,\cdot)\) \(\chi_{5185}(333,\cdot)\) \(\chi_{5185}(618,\cdot)\) \(\chi_{5185}(708,\cdot)\) \(\chi_{5185}(887,\cdot)\) \(\chi_{5185}(1013,\cdot)\) \(\chi_{5185}(1212,\cdot)\) \(\chi_{5185}(1248,\cdot)\) \(\chi_{5185}(1553,\cdot)\) \(\chi_{5185}(1822,\cdot)\) \(\chi_{5185}(1928,\cdot)\) \(\chi_{5185}(2037,\cdot)\) \(\chi_{5185}(2233,\cdot)\) \(\chi_{5185}(2402,\cdot)\) \(\chi_{5185}(2647,\cdot)\) \(\chi_{5185}(2717,\cdot)\) \(\chi_{5185}(3012,\cdot)\) \(\chi_{5185}(3088,\cdot)\) \(\chi_{5185}(3327,\cdot)\) \(\chi_{5185}(3393,\cdot)\) \(\chi_{5185}(3652,\cdot)\) \(\chi_{5185}(4262,\cdot)\) \(\chi_{5185}(4278,\cdot)\) \(\chi_{5185}(4308,\cdot)\) \(\chi_{5185}(4583,\cdot)\) \(\chi_{5185}(4613,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((3112,4576,2381)\) → \((-i,e\left(\frac{7}{16}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(28, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(1\) |