Basic properties
| Modulus: | \(2576\) | |
| Conductor: | \(2576\) | 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 2576.dl
\(\chi_{2576}(11,\cdot)\) \(\chi_{2576}(51,\cdot)\) \(\chi_{2576}(67,\cdot)\) \(\chi_{2576}(107,\cdot)\) \(\chi_{2576}(235,\cdot)\) \(\chi_{2576}(291,\cdot)\) \(\chi_{2576}(387,\cdot)\) \(\chi_{2576}(571,\cdot)\) \(\chi_{2576}(723,\cdot)\) \(\chi_{2576}(779,\cdot)\) \(\chi_{2576}(835,\cdot)\) \(\chi_{2576}(891,\cdot)\) \(\chi_{2576}(907,\cdot)\) \(\chi_{2576}(963,\cdot)\) \(\chi_{2576}(1003,\cdot)\) \(\chi_{2576}(1019,\cdot)\) \(\chi_{2576}(1075,\cdot)\) \(\chi_{2576}(1115,\cdot)\) \(\chi_{2576}(1171,\cdot)\) \(\chi_{2576}(1187,\cdot)\) \(\chi_{2576}(1299,\cdot)\) \(\chi_{2576}(1339,\cdot)\) \(\chi_{2576}(1355,\cdot)\) \(\chi_{2576}(1395,\cdot)\) \(\chi_{2576}(1523,\cdot)\) \(\chi_{2576}(1579,\cdot)\) \(\chi_{2576}(1675,\cdot)\) \(\chi_{2576}(1859,\cdot)\) \(\chi_{2576}(2011,\cdot)\) \(\chi_{2576}(2067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2255,645,1473,1569)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
| \( \chi_{ 2576 }(907, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{13}{44}\right)\) |