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.ce
\(\chi_{4225}(116,\cdot)\) \(\chi_{4225}(181,\cdot)\) \(\chi_{4225}(246,\cdot)\) \(\chi_{4225}(311,\cdot)\) \(\chi_{4225}(441,\cdot)\) \(\chi_{4225}(571,\cdot)\) \(\chi_{4225}(636,\cdot)\) \(\chi_{4225}(766,\cdot)\) \(\chi_{4225}(831,\cdot)\) \(\chi_{4225}(896,\cdot)\) \(\chi_{4225}(961,\cdot)\) \(\chi_{4225}(1091,\cdot)\) \(\chi_{4225}(1156,\cdot)\) \(\chi_{4225}(1221,\cdot)\) \(\chi_{4225}(1286,\cdot)\) \(\chi_{4225}(1416,\cdot)\) \(\chi_{4225}(1481,\cdot)\) \(\chi_{4225}(1546,\cdot)\) \(\chi_{4225}(1611,\cdot)\) \(\chi_{4225}(1741,\cdot)\) \(\chi_{4225}(1806,\cdot)\) \(\chi_{4225}(1871,\cdot)\) \(\chi_{4225}(1936,\cdot)\) \(\chi_{4225}(2066,\cdot)\) \(\chi_{4225}(2131,\cdot)\) \(\chi_{4225}(2261,\cdot)\) \(\chi_{4225}(2391,\cdot)\) \(\chi_{4225}(2456,\cdot)\) \(\chi_{4225}(2521,\cdot)\) \(\chi_{4225}(2586,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{7}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(116, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) |