Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | 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.cf
\(\chi_{4225}(64,\cdot)\) \(\chi_{4225}(129,\cdot)\) \(\chi_{4225}(194,\cdot)\) \(\chi_{4225}(259,\cdot)\) \(\chi_{4225}(389,\cdot)\) \(\chi_{4225}(454,\cdot)\) \(\chi_{4225}(519,\cdot)\) \(\chi_{4225}(584,\cdot)\) \(\chi_{4225}(714,\cdot)\) \(\chi_{4225}(779,\cdot)\) \(\chi_{4225}(909,\cdot)\) \(\chi_{4225}(1039,\cdot)\) \(\chi_{4225}(1104,\cdot)\) \(\chi_{4225}(1169,\cdot)\) \(\chi_{4225}(1234,\cdot)\) \(\chi_{4225}(1364,\cdot)\) \(\chi_{4225}(1429,\cdot)\) \(\chi_{4225}(1494,\cdot)\) \(\chi_{4225}(1559,\cdot)\) \(\chi_{4225}(1754,\cdot)\) \(\chi_{4225}(1819,\cdot)\) \(\chi_{4225}(1884,\cdot)\) \(\chi_{4225}(2014,\cdot)\) \(\chi_{4225}(2079,\cdot)\) \(\chi_{4225}(2144,\cdot)\) \(\chi_{4225}(2209,\cdot)\) \(\chi_{4225}(2339,\cdot)\) \(\chi_{4225}(2404,\cdot)\) \(\chi_{4225}(2469,\cdot)\) \(\chi_{4225}(2664,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{62}{65}\right)\) |