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.hd
\(\chi_{6025}(197,\cdot)\) \(\chi_{6025}(317,\cdot)\) \(\chi_{6025}(608,\cdot)\) \(\chi_{6025}(647,\cdot)\) \(\chi_{6025}(767,\cdot)\) \(\chi_{6025}(838,\cdot)\) \(\chi_{6025}(853,\cdot)\) \(\chi_{6025}(1402,\cdot)\) \(\chi_{6025}(1522,\cdot)\) \(\chi_{6025}(1798,\cdot)\) \(\chi_{6025}(1813,\cdot)\) \(\chi_{6025}(1852,\cdot)\) \(\chi_{6025}(1972,\cdot)\) \(\chi_{6025}(2058,\cdot)\) \(\chi_{6025}(2727,\cdot)\) \(\chi_{6025}(3003,\cdot)\) \(\chi_{6025}(3177,\cdot)\) \(\chi_{6025}(3248,\cdot)\) \(\chi_{6025}(3263,\cdot)\) \(\chi_{6025}(3812,\cdot)\) \(\chi_{6025}(4208,\cdot)\) \(\chi_{6025}(4223,\cdot)\) \(\chi_{6025}(4262,\cdot)\) \(\chi_{6025}(4453,\cdot)\) \(\chi_{6025}(5017,\cdot)\) \(\chi_{6025}(5137,\cdot)\) \(\chi_{6025}(5413,\cdot)\) \(\chi_{6025}(5428,\cdot)\) \(\chi_{6025}(5467,\cdot)\) \(\chi_{6025}(5587,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{3}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) |