Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | 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 4225.bz
\(\chi_{4225}(66,\cdot)\) \(\chi_{4225}(131,\cdot)\) \(\chi_{4225}(196,\cdot)\) \(\chi_{4225}(261,\cdot)\) \(\chi_{4225}(391,\cdot)\) \(\chi_{4225}(456,\cdot)\) \(\chi_{4225}(521,\cdot)\) \(\chi_{4225}(586,\cdot)\) \(\chi_{4225}(716,\cdot)\) \(\chi_{4225}(781,\cdot)\) \(\chi_{4225}(911,\cdot)\) \(\chi_{4225}(1041,\cdot)\) \(\chi_{4225}(1106,\cdot)\) \(\chi_{4225}(1171,\cdot)\) \(\chi_{4225}(1236,\cdot)\) \(\chi_{4225}(1366,\cdot)\) \(\chi_{4225}(1431,\cdot)\) \(\chi_{4225}(1496,\cdot)\) \(\chi_{4225}(1561,\cdot)\) \(\chi_{4225}(1756,\cdot)\) \(\chi_{4225}(1821,\cdot)\) \(\chi_{4225}(1886,\cdot)\) \(\chi_{4225}(2016,\cdot)\) \(\chi_{4225}(2081,\cdot)\) \(\chi_{4225}(2146,\cdot)\) \(\chi_{4225}(2211,\cdot)\) \(\chi_{4225}(2341,\cdot)\) \(\chi_{4225}(2406,\cdot)\) \(\chi_{4225}(2471,\cdot)\) \(\chi_{4225}(2666,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(66, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) |