Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(6025\) | 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 6025.iu
\(\chi_{6025}(11,\cdot)\) \(\chi_{6025}(306,\cdot)\) \(\chi_{6025}(471,\cdot)\) \(\chi_{6025}(571,\cdot)\) \(\chi_{6025}(761,\cdot)\) \(\chi_{6025}(786,\cdot)\) \(\chi_{6025}(811,\cdot)\) \(\chi_{6025}(986,\cdot)\) \(\chi_{6025}(1116,\cdot)\) \(\chi_{6025}(1186,\cdot)\) \(\chi_{6025}(1216,\cdot)\) \(\chi_{6025}(1381,\cdot)\) \(\chi_{6025}(1511,\cdot)\) \(\chi_{6025}(1706,\cdot)\) \(\chi_{6025}(1906,\cdot)\) \(\chi_{6025}(1966,\cdot)\) \(\chi_{6025}(1991,\cdot)\) \(\chi_{6025}(2016,\cdot)\) \(\chi_{6025}(2081,\cdot)\) \(\chi_{6025}(2106,\cdot)\) \(\chi_{6025}(2131,\cdot)\) \(\chi_{6025}(2191,\cdot)\) \(\chi_{6025}(2321,\cdot)\) \(\chi_{6025}(2391,\cdot)\) \(\chi_{6025}(2421,\cdot)\) \(\chi_{6025}(2586,\cdot)\) \(\chi_{6025}(2716,\cdot)\) \(\chi_{6025}(2881,\cdot)\) \(\chi_{6025}(2911,\cdot)\) \(\chi_{6025}(2981,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{5}{48}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{23}{240}\right)\) |