Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | 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.cs
\(\chi_{4225}(8,\cdot)\) \(\chi_{4225}(73,\cdot)\) \(\chi_{4225}(122,\cdot)\) \(\chi_{4225}(138,\cdot)\) \(\chi_{4225}(187,\cdot)\) \(\chi_{4225}(203,\cdot)\) \(\chi_{4225}(252,\cdot)\) \(\chi_{4225}(317,\cdot)\) \(\chi_{4225}(333,\cdot)\) \(\chi_{4225}(398,\cdot)\) \(\chi_{4225}(447,\cdot)\) \(\chi_{4225}(463,\cdot)\) \(\chi_{4225}(512,\cdot)\) \(\chi_{4225}(528,\cdot)\) \(\chi_{4225}(642,\cdot)\) \(\chi_{4225}(658,\cdot)\) \(\chi_{4225}(723,\cdot)\) \(\chi_{4225}(772,\cdot)\) \(\chi_{4225}(788,\cdot)\) \(\chi_{4225}(837,\cdot)\) \(\chi_{4225}(853,\cdot)\) \(\chi_{4225}(902,\cdot)\) \(\chi_{4225}(967,\cdot)\) \(\chi_{4225}(983,\cdot)\) \(\chi_{4225}(1048,\cdot)\) \(\chi_{4225}(1097,\cdot)\) \(\chi_{4225}(1162,\cdot)\) \(\chi_{4225}(1178,\cdot)\) \(\chi_{4225}(1227,\cdot)\) \(\chi_{4225}(1292,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{260})$ |
| Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{23}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(3177, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{47}{260}\right)\) | \(e\left(\frac{9}{130}\right)\) |