Basic properties
| Modulus: | \(4508\) | |
| Conductor: | \(4508\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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 4508.cb
\(\chi_{4508}(27,\cdot)\) \(\chi_{4508}(55,\cdot)\) \(\chi_{4508}(167,\cdot)\) \(\chi_{4508}(223,\cdot)\) \(\chi_{4508}(279,\cdot)\) \(\chi_{4508}(307,\cdot)\) \(\chi_{4508}(335,\cdot)\) \(\chi_{4508}(363,\cdot)\) \(\chi_{4508}(531,\cdot)\) \(\chi_{4508}(671,\cdot)\) \(\chi_{4508}(699,\cdot)\) \(\chi_{4508}(811,\cdot)\) \(\chi_{4508}(867,\cdot)\) \(\chi_{4508}(923,\cdot)\) \(\chi_{4508}(951,\cdot)\) \(\chi_{4508}(1007,\cdot)\) \(\chi_{4508}(1231,\cdot)\) \(\chi_{4508}(1315,\cdot)\) \(\chi_{4508}(1343,\cdot)\) \(\chi_{4508}(1455,\cdot)\) \(\chi_{4508}(1511,\cdot)\) \(\chi_{4508}(1595,\cdot)\) \(\chi_{4508}(1623,\cdot)\) \(\chi_{4508}(1651,\cdot)\) \(\chi_{4508}(1819,\cdot)\) \(\chi_{4508}(1875,\cdot)\) \(\chi_{4508}(1987,\cdot)\) \(\chi_{4508}(2099,\cdot)\) \(\chi_{4508}(2211,\cdot)\) \(\chi_{4508}(2239,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,1473,1569)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
| \( \chi_{ 4508 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{34}{77}\right)\) |