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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8280.hc
\(\chi_{8280}(83,\cdot)\) \(\chi_{8280}(203,\cdot)\) \(\chi_{8280}(227,\cdot)\) \(\chi_{8280}(563,\cdot)\) \(\chi_{8280}(707,\cdot)\) \(\chi_{8280}(803,\cdot)\) \(\chi_{8280}(1307,\cdot)\) \(\chi_{8280}(1523,\cdot)\) \(\chi_{8280}(1643,\cdot)\) \(\chi_{8280}(1667,\cdot)\) \(\chi_{8280}(1883,\cdot)\) \(\chi_{8280}(2363,\cdot)\) \(\chi_{8280}(2747,\cdot)\) \(\chi_{8280}(2867,\cdot)\) \(\chi_{8280}(2963,\cdot)\) \(\chi_{8280}(3227,\cdot)\) \(\chi_{8280}(3323,\cdot)\) \(\chi_{8280}(3467,\cdot)\) \(\chi_{8280}(3947,\cdot)\) \(\chi_{8280}(4403,\cdot)\) \(\chi_{8280}(4523,\cdot)\) \(\chi_{8280}(4667,\cdot)\) \(\chi_{8280}(4883,\cdot)\) \(\chi_{8280}(5123,\cdot)\) \(\chi_{8280}(5387,\cdot)\) \(\chi_{8280}(5603,\cdot)\) \(\chi_{8280}(5627,\cdot)\) \(\chi_{8280}(5747,\cdot)\) \(\chi_{8280}(5987,\cdot)\) \(\chi_{8280}(6323,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((-1,-1,e\left(\frac{1}{6}\right),-i,e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) |