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.hr
\(\chi_{6025}(28,\cdot)\) \(\chi_{6025}(73,\cdot)\) \(\chi_{6025}(102,\cdot)\) \(\chi_{6025}(148,\cdot)\) \(\chi_{6025}(342,\cdot)\) \(\chi_{6025}(702,\cdot)\) \(\chi_{6025}(808,\cdot)\) \(\chi_{6025}(828,\cdot)\) \(\chi_{6025}(847,\cdot)\) \(\chi_{6025}(938,\cdot)\) \(\chi_{6025}(947,\cdot)\) \(\chi_{6025}(1222,\cdot)\) \(\chi_{6025}(1262,\cdot)\) \(\chi_{6025}(1298,\cdot)\) \(\chi_{6025}(1308,\cdot)\) \(\chi_{6025}(1322,\cdot)\) \(\chi_{6025}(1373,\cdot)\) \(\chi_{6025}(1713,\cdot)\) \(\chi_{6025}(2112,\cdot)\) \(\chi_{6025}(2367,\cdot)\) \(\chi_{6025}(3028,\cdot)\) \(\chi_{6025}(3417,\cdot)\) \(\chi_{6025}(3638,\cdot)\) \(\chi_{6025}(3828,\cdot)\) \(\chi_{6025}(3877,\cdot)\) \(\chi_{6025}(4477,\cdot)\) \(\chi_{6025}(4612,\cdot)\) \(\chi_{6025}(4787,\cdot)\) \(\chi_{6025}(4958,\cdot)\) \(\chi_{6025}(5038,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{41}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(4477, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(i\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) |