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.hd
\(\chi_{8280}(77,\cdot)\) \(\chi_{8280}(173,\cdot)\) \(\chi_{8280}(317,\cdot)\) \(\chi_{8280}(533,\cdot)\) \(\chi_{8280}(653,\cdot)\) \(\chi_{8280}(1037,\cdot)\) \(\chi_{8280}(1373,\cdot)\) \(\chi_{8280}(1613,\cdot)\) \(\chi_{8280}(1733,\cdot)\) \(\chi_{8280}(1757,\cdot)\) \(\chi_{8280}(1973,\cdot)\) \(\chi_{8280}(2237,\cdot)\) \(\chi_{8280}(2477,\cdot)\) \(\chi_{8280}(2693,\cdot)\) \(\chi_{8280}(2837,\cdot)\) \(\chi_{8280}(2957,\cdot)\) \(\chi_{8280}(3413,\cdot)\) \(\chi_{8280}(3893,\cdot)\) \(\chi_{8280}(4037,\cdot)\) \(\chi_{8280}(4133,\cdot)\) \(\chi_{8280}(4397,\cdot)\) \(\chi_{8280}(4493,\cdot)\) \(\chi_{8280}(4613,\cdot)\) \(\chi_{8280}(4997,\cdot)\) \(\chi_{8280}(5477,\cdot)\) \(\chi_{8280}(5693,\cdot)\) \(\chi_{8280}(5717,\cdot)\) \(\chi_{8280}(5837,\cdot)\) \(\chi_{8280}(6053,\cdot)\) \(\chi_{8280}(6557,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((1,-1,e\left(\frac{5}{6}\right),-i,e\left(\frac{5}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(653, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{47}{132}\right)\) |