Basic properties
| Modulus: | \(8280\) | |
| Conductor: | \(8280\) | 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 8280.gx
\(\chi_{8280}(13,\cdot)\) \(\chi_{8280}(133,\cdot)\) \(\chi_{8280}(637,\cdot)\) \(\chi_{8280}(853,\cdot)\) \(\chi_{8280}(877,\cdot)\) \(\chi_{8280}(997,\cdot)\) \(\chi_{8280}(1093,\cdot)\) \(\chi_{8280}(1237,\cdot)\) \(\chi_{8280}(1453,\cdot)\) \(\chi_{8280}(1573,\cdot)\) \(\chi_{8280}(1957,\cdot)\) \(\chi_{8280}(2293,\cdot)\) \(\chi_{8280}(2533,\cdot)\) \(\chi_{8280}(2653,\cdot)\) \(\chi_{8280}(2677,\cdot)\) \(\chi_{8280}(2893,\cdot)\) \(\chi_{8280}(3157,\cdot)\) \(\chi_{8280}(3397,\cdot)\) \(\chi_{8280}(3613,\cdot)\) \(\chi_{8280}(3757,\cdot)\) \(\chi_{8280}(3877,\cdot)\) \(\chi_{8280}(4333,\cdot)\) \(\chi_{8280}(4813,\cdot)\) \(\chi_{8280}(4957,\cdot)\) \(\chi_{8280}(5053,\cdot)\) \(\chi_{8280}(5317,\cdot)\) \(\chi_{8280}(5413,\cdot)\) \(\chi_{8280}(5533,\cdot)\) \(\chi_{8280}(5917,\cdot)\) \(\chi_{8280}(6397,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((1,-1,e\left(\frac{1}{3}\right),-i,e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(1453, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{131}{132}\right)\) |