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.hp
\(\chi_{6025}(138,\cdot)\) \(\chi_{6025}(638,\cdot)\) \(\chi_{6025}(997,\cdot)\) \(\chi_{6025}(1162,\cdot)\) \(\chi_{6025}(1172,\cdot)\) \(\chi_{6025}(1228,\cdot)\) \(\chi_{6025}(1467,\cdot)\) \(\chi_{6025}(1823,\cdot)\) \(\chi_{6025}(2013,\cdot)\) \(\chi_{6025}(2052,\cdot)\) \(\chi_{6025}(2067,\cdot)\) \(\chi_{6025}(2152,\cdot)\) \(\chi_{6025}(2212,\cdot)\) \(\chi_{6025}(2427,\cdot)\) \(\chi_{6025}(2483,\cdot)\) \(\chi_{6025}(2513,\cdot)\) \(\chi_{6025}(2527,\cdot)\) \(\chi_{6025}(2558,\cdot)\) \(\chi_{6025}(2623,\cdot)\) \(\chi_{6025}(2628,\cdot)\) \(\chi_{6025}(3672,\cdot)\) \(\chi_{6025}(3708,\cdot)\) \(\chi_{6025}(3717,\cdot)\) \(\chi_{6025}(3783,\cdot)\) \(\chi_{6025}(4237,\cdot)\) \(\chi_{6025}(4317,\cdot)\) \(\chi_{6025}(4522,\cdot)\) \(\chi_{6025}(4553,\cdot)\) \(\chi_{6025}(4848,\cdot)\) \(\chi_{6025}(5162,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{69}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(997, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) |