Basic properties
| Modulus: | \(5185\) | |
| Conductor: | \(5185\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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.ju
\(\chi_{5185}(42,\cdot)\) \(\chi_{5185}(77,\cdot)\) \(\chi_{5185}(83,\cdot)\) \(\chi_{5185}(138,\cdot)\) \(\chi_{5185}(382,\cdot)\) \(\chi_{5185}(423,\cdot)\) \(\chi_{5185}(757,\cdot)\) \(\chi_{5185}(818,\cdot)\) \(\chi_{5185}(927,\cdot)\) \(\chi_{5185}(988,\cdot)\) \(\chi_{5185}(1018,\cdot)\) \(\chi_{5185}(1062,\cdot)\) \(\chi_{5185}(1232,\cdot)\) \(\chi_{5185}(1358,\cdot)\) \(\chi_{5185}(1947,\cdot)\) \(\chi_{5185}(2008,\cdot)\) \(\chi_{5185}(2038,\cdot)\) \(\chi_{5185}(2208,\cdot)\) \(\chi_{5185}(2252,\cdot)\) \(\chi_{5185}(2882,\cdot)\) \(\chi_{5185}(2943,\cdot)\) \(\chi_{5185}(3187,\cdot)\) \(\chi_{5185}(3228,\cdot)\) \(\chi_{5185}(3987,\cdot)\) \(\chi_{5185}(4048,\cdot)\) \(\chi_{5185}(4163,\cdot)\) \(\chi_{5185}(4292,\cdot)\) \(\chi_{5185}(4327,\cdot)\) \(\chi_{5185}(4388,\cdot)\) \(\chi_{5185}(4632,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((3112,4576,2381)\) → \((i,e\left(\frac{5}{8}\right),e\left(\frac{14}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(42, a) \) | \(-1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) |