Basic properties
| Modulus: | \(4508\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1127}(125,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4508.bz
\(\chi_{4508}(125,\cdot)\) \(\chi_{4508}(153,\cdot)\) \(\chi_{4508}(181,\cdot)\) \(\chi_{4508}(237,\cdot)\) \(\chi_{4508}(405,\cdot)\) \(\chi_{4508}(433,\cdot)\) \(\chi_{4508}(517,\cdot)\) \(\chi_{4508}(573,\cdot)\) \(\chi_{4508}(741,\cdot)\) \(\chi_{4508}(769,\cdot)\) \(\chi_{4508}(797,\cdot)\) \(\chi_{4508}(825,\cdot)\) \(\chi_{4508}(937,\cdot)\) \(\chi_{4508}(1049,\cdot)\) \(\chi_{4508}(1161,\cdot)\) \(\chi_{4508}(1217,\cdot)\) \(\chi_{4508}(1385,\cdot)\) \(\chi_{4508}(1413,\cdot)\) \(\chi_{4508}(1441,\cdot)\) \(\chi_{4508}(1525,\cdot)\) \(\chi_{4508}(1581,\cdot)\) \(\chi_{4508}(1693,\cdot)\) \(\chi_{4508}(1721,\cdot)\) \(\chi_{4508}(1805,\cdot)\) \(\chi_{4508}(2029,\cdot)\) \(\chi_{4508}(2085,\cdot)\) \(\chi_{4508}(2113,\cdot)\) \(\chi_{4508}(2169,\cdot)\) \(\chi_{4508}(2225,\cdot)\) \(\chi_{4508}(2337,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,1473,1569)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
| \( \chi_{ 4508 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{117}{154}\right)\) |