Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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.cu
\(\chi_{4225}(36,\cdot)\) \(\chi_{4225}(56,\cdot)\) \(\chi_{4225}(121,\cdot)\) \(\chi_{4225}(166,\cdot)\) \(\chi_{4225}(186,\cdot)\) \(\chi_{4225}(231,\cdot)\) \(\chi_{4225}(296,\cdot)\) \(\chi_{4225}(381,\cdot)\) \(\chi_{4225}(446,\cdot)\) \(\chi_{4225}(491,\cdot)\) \(\chi_{4225}(511,\cdot)\) \(\chi_{4225}(556,\cdot)\) \(\chi_{4225}(621,\cdot)\) \(\chi_{4225}(641,\cdot)\) \(\chi_{4225}(686,\cdot)\) \(\chi_{4225}(706,\cdot)\) \(\chi_{4225}(771,\cdot)\) \(\chi_{4225}(816,\cdot)\) \(\chi_{4225}(836,\cdot)\) \(\chi_{4225}(881,\cdot)\) \(\chi_{4225}(946,\cdot)\) \(\chi_{4225}(966,\cdot)\) \(\chi_{4225}(1011,\cdot)\) \(\chi_{4225}(1031,\cdot)\) \(\chi_{4225}(1096,\cdot)\) \(\chi_{4225}(1141,\cdot)\) \(\chi_{4225}(1271,\cdot)\) \(\chi_{4225}(1291,\cdot)\) \(\chi_{4225}(1336,\cdot)\) \(\chi_{4225}(1356,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{47}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{62}{195}\right)\) | \(e\left(\frac{157}{195}\right)\) | \(e\left(\frac{281}{390}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{337}{390}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) |