Basic properties
| Modulus: | \(4508\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1127}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4508.ci
\(\chi_{4508}(5,\cdot)\) \(\chi_{4508}(17,\cdot)\) \(\chi_{4508}(33,\cdot)\) \(\chi_{4508}(61,\cdot)\) \(\chi_{4508}(89,\cdot)\) \(\chi_{4508}(145,\cdot)\) \(\chi_{4508}(157,\cdot)\) \(\chi_{4508}(201,\cdot)\) \(\chi_{4508}(241,\cdot)\) \(\chi_{4508}(297,\cdot)\) \(\chi_{4508}(341,\cdot)\) \(\chi_{4508}(425,\cdot)\) \(\chi_{4508}(465,\cdot)\) \(\chi_{4508}(481,\cdot)\) \(\chi_{4508}(493,\cdot)\) \(\chi_{4508}(549,\cdot)\) \(\chi_{4508}(605,\cdot)\) \(\chi_{4508}(649,\cdot)\) \(\chi_{4508}(661,\cdot)\) \(\chi_{4508}(677,\cdot)\) \(\chi_{4508}(733,\cdot)\) \(\chi_{4508}(773,\cdot)\) \(\chi_{4508}(789,\cdot)\) \(\chi_{4508}(801,\cdot)\) \(\chi_{4508}(845,\cdot)\) \(\chi_{4508}(885,\cdot)\) \(\chi_{4508}(941,\cdot)\) \(\chi_{4508}(957,\cdot)\) \(\chi_{4508}(985,\cdot)\) \(\chi_{4508}(1069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,1473,1569)\) → \((1,e\left(\frac{29}{42}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
| \( \chi_{ 4508 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{462}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{39}{154}\right)\) |