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.hs
\(\chi_{6025}(33,\cdot)\) \(\chi_{6025}(198,\cdot)\) \(\chi_{6025}(208,\cdot)\) \(\chi_{6025}(267,\cdot)\) \(\chi_{6025}(503,\cdot)\) \(\chi_{6025}(587,\cdot)\) \(\chi_{6025}(1088,\cdot)\) \(\chi_{6025}(1102,\cdot)\) \(\chi_{6025}(1103,\cdot)\) \(\chi_{6025}(1188,\cdot)\) \(\chi_{6025}(1248,\cdot)\) \(\chi_{6025}(1463,\cdot)\) \(\chi_{6025}(1563,\cdot)\) \(\chi_{6025}(1602,\cdot)\) \(\chi_{6025}(2192,\cdot)\) \(\chi_{6025}(2708,\cdot)\) \(\chi_{6025}(2753,\cdot)\) \(\chi_{6025}(2787,\cdot)\) \(\chi_{6025}(2977,\cdot)\) \(\chi_{6025}(3273,\cdot)\) \(\chi_{6025}(3353,\cdot)\) \(\chi_{6025}(3447,\cdot)\) \(\chi_{6025}(3477,\cdot)\) \(\chi_{6025}(3522,\cdot)\) \(\chi_{6025}(3558,\cdot)\) \(\chi_{6025}(3587,\cdot)\) \(\chi_{6025}(3592,\cdot)\) \(\chi_{6025}(4198,\cdot)\) \(\chi_{6025}(4672,\cdot)\) \(\chi_{6025}(4747,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{57}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(1563, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) |