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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2415.dq
\(\chi_{2415}(53,\cdot)\) \(\chi_{2415}(107,\cdot)\) \(\chi_{2415}(158,\cdot)\) \(\chi_{2415}(212,\cdot)\) \(\chi_{2415}(263,\cdot)\) \(\chi_{2415}(452,\cdot)\) \(\chi_{2415}(527,\cdot)\) \(\chi_{2415}(548,\cdot)\) \(\chi_{2415}(557,\cdot)\) \(\chi_{2415}(632,\cdot)\) \(\chi_{2415}(842,\cdot)\) \(\chi_{2415}(872,\cdot)\) \(\chi_{2415}(893,\cdot)\) \(\chi_{2415}(977,\cdot)\) \(\chi_{2415}(1052,\cdot)\) \(\chi_{2415}(1073,\cdot)\) \(\chi_{2415}(1157,\cdot)\) \(\chi_{2415}(1178,\cdot)\) \(\chi_{2415}(1187,\cdot)\) \(\chi_{2415}(1262,\cdot)\) \(\chi_{2415}(1367,\cdot)\) \(\chi_{2415}(1397,\cdot)\) \(\chi_{2415}(1418,\cdot)\) \(\chi_{2415}(1493,\cdot)\) \(\chi_{2415}(1502,\cdot)\) \(\chi_{2415}(1523,\cdot)\) \(\chi_{2415}(1598,\cdot)\) \(\chi_{2415}(1607,\cdot)\) \(\chi_{2415}(1712,\cdot)\) \(\chi_{2415}(1808,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(212, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(-i\) | \(e\left(\frac{59}{66}\right)\) |