Basic properties
| Modulus: | \(5185\) | |
| Conductor: | \(5185\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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.ki
\(\chi_{5185}(7,\cdot)\) \(\chi_{5185}(112,\cdot)\) \(\chi_{5185}(177,\cdot)\) \(\chi_{5185}(218,\cdot)\) \(\chi_{5185}(227,\cdot)\) \(\chi_{5185}(262,\cdot)\) \(\chi_{5185}(303,\cdot)\) \(\chi_{5185}(312,\cdot)\) \(\chi_{5185}(482,\cdot)\) \(\chi_{5185}(498,\cdot)\) \(\chi_{5185}(567,\cdot)\) \(\chi_{5185}(828,\cdot)\) \(\chi_{5185}(913,\cdot)\) \(\chi_{5185}(1027,\cdot)\) \(\chi_{5185}(1068,\cdot)\) \(\chi_{5185}(1108,\cdot)\) \(\chi_{5185}(1263,\cdot)\) \(\chi_{5185}(1332,\cdot)\) \(\chi_{5185}(1348,\cdot)\) \(\chi_{5185}(1518,\cdot)\) \(\chi_{5185}(1603,\cdot)\) \(\chi_{5185}(1677,\cdot)\) \(\chi_{5185}(1678,\cdot)\) \(\chi_{5185}(1873,\cdot)\) \(\chi_{5185}(1958,\cdot)\) \(\chi_{5185}(1982,\cdot)\) \(\chi_{5185}(2128,\cdot)\) \(\chi_{5185}(2213,\cdot)\) \(\chi_{5185}(2442,\cdot)\) \(\chi_{5185}(2527,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((3112,4576,2381)\) → \((i,e\left(\frac{11}{16}\right),e\left(\frac{49}{60}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{173}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |