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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.hm
\(\chi_{6025}(258,\cdot)\) \(\chi_{6025}(298,\cdot)\) \(\chi_{6025}(358,\cdot)\) \(\chi_{6025}(397,\cdot)\) \(\chi_{6025}(992,\cdot)\) \(\chi_{6025}(1037,\cdot)\) \(\chi_{6025}(1112,\cdot)\) \(\chi_{6025}(1148,\cdot)\) \(\chi_{6025}(1403,\cdot)\) \(\chi_{6025}(1772,\cdot)\) \(\chi_{6025}(1792,\cdot)\) \(\chi_{6025}(1902,\cdot)\) \(\chi_{6025}(2262,\cdot)\) \(\chi_{6025}(2272,\cdot)\) \(\chi_{6025}(2337,\cdot)\) \(\chi_{6025}(2453,\cdot)\) \(\chi_{6025}(2677,\cdot)\) \(\chi_{6025}(2913,\cdot)\) \(\chi_{6025}(3513,\cdot)\) \(\chi_{6025}(3648,\cdot)\) \(\chi_{6025}(3823,\cdot)\) \(\chi_{6025}(3992,\cdot)\) \(\chi_{6025}(4478,\cdot)\) \(\chi_{6025}(4602,\cdot)\) \(\chi_{6025}(4792,\cdot)\) \(\chi_{6025}(5163,\cdot)\) \(\chi_{6025}(5403,\cdot)\) \(\chi_{6025}(5763,\cdot)\) \(\chi_{6025}(5908,\cdot)\) \(\chi_{6025}(5922,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{31}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(2262, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-i\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) |