Basic properties
| Modulus: | \(5185\) | |
| Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1037}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5185.jq
\(\chi_{5185}(36,\cdot)\) \(\chi_{5185}(66,\cdot)\) \(\chi_{5185}(161,\cdot)\) \(\chi_{5185}(716,\cdot)\) \(\chi_{5185}(961,\cdot)\) \(\chi_{5185}(1056,\cdot)\) \(\chi_{5185}(1086,\cdot)\) \(\chi_{5185}(1256,\cdot)\) \(\chi_{5185}(1266,\cdot)\) \(\chi_{5185}(1651,\cdot)\) \(\chi_{5185}(1896,\cdot)\) \(\chi_{5185}(1936,\cdot)\) \(\chi_{5185}(1991,\cdot)\) \(\chi_{5185}(2201,\cdot)\) \(\chi_{5185}(2276,\cdot)\) \(\chi_{5185}(2871,\cdot)\) \(\chi_{5185}(2916,\cdot)\) \(\chi_{5185}(3086,\cdot)\) \(\chi_{5185}(3096,\cdot)\) \(\chi_{5185}(3211,\cdot)\) \(\chi_{5185}(3221,\cdot)\) \(\chi_{5185}(3391,\cdot)\) \(\chi_{5185}(3766,\cdot)\) \(\chi_{5185}(4031,\cdot)\) \(\chi_{5185}(4071,\cdot)\) \(\chi_{5185}(4106,\cdot)\) \(\chi_{5185}(4316,\cdot)\) \(\chi_{5185}(4411,\cdot)\) \(\chi_{5185}(4701,\cdot)\) \(\chi_{5185}(5006,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((3112,4576,2381)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{7}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5185 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{5}{6}\right)\) |