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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5185.jl
\(\chi_{5185}(19,\cdot)\) \(\chi_{5185}(49,\cdot)\) \(\chi_{5185}(219,\cdot)\) \(\chi_{5185}(229,\cdot)\) \(\chi_{5185}(614,\cdot)\) \(\chi_{5185}(859,\cdot)\) \(\chi_{5185}(899,\cdot)\) \(\chi_{5185}(954,\cdot)\) \(\chi_{5185}(1164,\cdot)\) \(\chi_{5185}(1239,\cdot)\) \(\chi_{5185}(1834,\cdot)\) \(\chi_{5185}(1879,\cdot)\) \(\chi_{5185}(2049,\cdot)\) \(\chi_{5185}(2059,\cdot)\) \(\chi_{5185}(2174,\cdot)\) \(\chi_{5185}(2184,\cdot)\) \(\chi_{5185}(2354,\cdot)\) \(\chi_{5185}(2729,\cdot)\) \(\chi_{5185}(2994,\cdot)\) \(\chi_{5185}(3034,\cdot)\) \(\chi_{5185}(3069,\cdot)\) \(\chi_{5185}(3279,\cdot)\) \(\chi_{5185}(3374,\cdot)\) \(\chi_{5185}(3664,\cdot)\) \(\chi_{5185}(3969,\cdot)\) \(\chi_{5185}(4004,\cdot)\) \(\chi_{5185}(4014,\cdot)\) \(\chi_{5185}(4184,\cdot)\) \(\chi_{5185}(4214,\cdot)\) \(\chi_{5185}(4309,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((3112,4576,2381)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(1239, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{1}{3}\right)\) |