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.gw
\(\chi_{8280}(43,\cdot)\) \(\chi_{8280}(67,\cdot)\) \(\chi_{8280}(283,\cdot)\) \(\chi_{8280}(787,\cdot)\) \(\chi_{8280}(907,\cdot)\) \(\chi_{8280}(1003,\cdot)\) \(\chi_{8280}(1123,\cdot)\) \(\chi_{8280}(1147,\cdot)\) \(\chi_{8280}(1483,\cdot)\) \(\chi_{8280}(1627,\cdot)\) \(\chi_{8280}(1723,\cdot)\) \(\chi_{8280}(2227,\cdot)\) \(\chi_{8280}(2443,\cdot)\) \(\chi_{8280}(2563,\cdot)\) \(\chi_{8280}(2587,\cdot)\) \(\chi_{8280}(2803,\cdot)\) \(\chi_{8280}(3283,\cdot)\) \(\chi_{8280}(3667,\cdot)\) \(\chi_{8280}(3787,\cdot)\) \(\chi_{8280}(3883,\cdot)\) \(\chi_{8280}(4147,\cdot)\) \(\chi_{8280}(4243,\cdot)\) \(\chi_{8280}(4387,\cdot)\) \(\chi_{8280}(4867,\cdot)\) \(\chi_{8280}(5323,\cdot)\) \(\chi_{8280}(5443,\cdot)\) \(\chi_{8280}(5587,\cdot)\) \(\chi_{8280}(5803,\cdot)\) \(\chi_{8280}(6043,\cdot)\) \(\chi_{8280}(6307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((-1,-1,e\left(\frac{2}{3}\right),-i,e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{7}{132}\right)\) |