Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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.hj
\(\chi_{6025}(21,\cdot)\) \(\chi_{6025}(456,\cdot)\) \(\chi_{6025}(621,\cdot)\) \(\chi_{6025}(756,\cdot)\) \(\chi_{6025}(796,\cdot)\) \(\chi_{6025}(861,\cdot)\) \(\chi_{6025}(871,\cdot)\) \(\chi_{6025}(931,\cdot)\) \(\chi_{6025}(1231,\cdot)\) \(\chi_{6025}(1341,\cdot)\) \(\chi_{6025}(1361,\cdot)\) \(\chi_{6025}(1586,\cdot)\) \(\chi_{6025}(2021,\cdot)\) \(\chi_{6025}(2096,\cdot)\) \(\chi_{6025}(2141,\cdot)\) \(\chi_{6025}(2271,\cdot)\) \(\chi_{6025}(2511,\cdot)\) \(\chi_{6025}(2736,\cdot)\) \(\chi_{6025}(2871,\cdot)\) \(\chi_{6025}(3016,\cdot)\) \(\chi_{6025}(3116,\cdot)\) \(\chi_{6025}(3156,\cdot)\) \(\chi_{6025}(3236,\cdot)\) \(\chi_{6025}(3391,\cdot)\) \(\chi_{6025}(3431,\cdot)\) \(\chi_{6025}(3491,\cdot)\) \(\chi_{6025}(4281,\cdot)\) \(\chi_{6025}(4366,\cdot)\) \(\chi_{6025}(4536,\cdot)\) \(\chi_{6025}(4556,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{61}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) |