Basic properties
| Modulus: | \(2415\) | |
| Conductor: | \(2415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 2415.do
\(\chi_{2415}(17,\cdot)\) \(\chi_{2415}(38,\cdot)\) \(\chi_{2415}(122,\cdot)\) \(\chi_{2415}(143,\cdot)\) \(\chi_{2415}(152,\cdot)\) \(\chi_{2415}(227,\cdot)\) \(\chi_{2415}(332,\cdot)\) \(\chi_{2415}(362,\cdot)\) \(\chi_{2415}(383,\cdot)\) \(\chi_{2415}(458,\cdot)\) \(\chi_{2415}(467,\cdot)\) \(\chi_{2415}(488,\cdot)\) \(\chi_{2415}(563,\cdot)\) \(\chi_{2415}(572,\cdot)\) \(\chi_{2415}(677,\cdot)\) \(\chi_{2415}(773,\cdot)\) \(\chi_{2415}(803,\cdot)\) \(\chi_{2415}(908,\cdot)\) \(\chi_{2415}(962,\cdot)\) \(\chi_{2415}(983,\cdot)\) \(\chi_{2415}(1088,\cdot)\) \(\chi_{2415}(1118,\cdot)\) \(\chi_{2415}(1193,\cdot)\) \(\chi_{2415}(1298,\cdot)\) \(\chi_{2415}(1307,\cdot)\) \(\chi_{2415}(1328,\cdot)\) \(\chi_{2415}(1433,\cdot)\) \(\chi_{2415}(1487,\cdot)\) \(\chi_{2415}(1538,\cdot)\) \(\chi_{2415}(1592,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((-1,-i,e\left(\frac{5}{6}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(488, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(i\) | \(e\left(\frac{13}{33}\right)\) |