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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5185.is
\(\chi_{5185}(3,\cdot)\) \(\chi_{5185}(27,\cdot)\) \(\chi_{5185}(88,\cdot)\) \(\chi_{5185}(857,\cdot)\) \(\chi_{5185}(942,\cdot)\) \(\chi_{5185}(1162,\cdot)\) \(\chi_{5185}(1247,\cdot)\) \(\chi_{5185}(1688,\cdot)\) \(\chi_{5185}(1833,\cdot)\) \(\chi_{5185}(1918,\cdot)\) \(\chi_{5185}(1932,\cdot)\) \(\chi_{5185}(1943,\cdot)\) \(\chi_{5185}(2187,\cdot)\) \(\chi_{5185}(2237,\cdot)\) \(\chi_{5185}(2298,\cdot)\) \(\chi_{5185}(2443,\cdot)\) \(\chi_{5185}(2492,\cdot)\) \(\chi_{5185}(2528,\cdot)\) \(\chi_{5185}(2553,\cdot)\) \(\chi_{5185}(3152,\cdot)\) \(\chi_{5185}(3407,\cdot)\) \(\chi_{5185}(3457,\cdot)\) \(\chi_{5185}(3712,\cdot)\) \(\chi_{5185}(4128,\cdot)\) \(\chi_{5185}(4383,\cdot)\) \(\chi_{5185}(4578,\cdot)\) \(\chi_{5185}(4663,\cdot)\) \(\chi_{5185}(4738,\cdot)\) \(\chi_{5185}(4822,\cdot)\) \(\chi_{5185}(4907,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((3112,4576,2381)\) → \((-i,e\left(\frac{1}{16}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(-1\) |