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.hn
\(\chi_{6025}(17,\cdot)\) \(\chi_{6025}(23,\cdot)\) \(\chi_{6025}(103,\cdot)\) \(\chi_{6025}(117,\cdot)\) \(\chi_{6025}(262,\cdot)\) \(\chi_{6025}(622,\cdot)\) \(\chi_{6025}(862,\cdot)\) \(\chi_{6025}(1233,\cdot)\) \(\chi_{6025}(1423,\cdot)\) \(\chi_{6025}(1547,\cdot)\) \(\chi_{6025}(2033,\cdot)\) \(\chi_{6025}(2202,\cdot)\) \(\chi_{6025}(2377,\cdot)\) \(\chi_{6025}(2512,\cdot)\) \(\chi_{6025}(3112,\cdot)\) \(\chi_{6025}(3348,\cdot)\) \(\chi_{6025}(3572,\cdot)\) \(\chi_{6025}(3688,\cdot)\) \(\chi_{6025}(3753,\cdot)\) \(\chi_{6025}(3763,\cdot)\) \(\chi_{6025}(4123,\cdot)\) \(\chi_{6025}(4233,\cdot)\) \(\chi_{6025}(4253,\cdot)\) \(\chi_{6025}(4622,\cdot)\) \(\chi_{6025}(4877,\cdot)\) \(\chi_{6025}(4913,\cdot)\) \(\chi_{6025}(4988,\cdot)\) \(\chi_{6025}(5033,\cdot)\) \(\chi_{6025}(5628,\cdot)\) \(\chi_{6025}(5667,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{11}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(4988, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-i\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) |