Basic properties
| Modulus: | \(8280\) | |
| Conductor: | \(1035\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1035}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8280.hf
\(\chi_{8280}(113,\cdot)\) \(\chi_{8280}(497,\cdot)\) \(\chi_{8280}(617,\cdot)\) \(\chi_{8280}(833,\cdot)\) \(\chi_{8280}(977,\cdot)\) \(\chi_{8280}(1073,\cdot)\) \(\chi_{8280}(1193,\cdot)\) \(\chi_{8280}(1217,\cdot)\) \(\chi_{8280}(1433,\cdot)\) \(\chi_{8280}(1937,\cdot)\) \(\chi_{8280}(2057,\cdot)\) \(\chi_{8280}(2153,\cdot)\) \(\chi_{8280}(2273,\cdot)\) \(\chi_{8280}(2297,\cdot)\) \(\chi_{8280}(2633,\cdot)\) \(\chi_{8280}(2777,\cdot)\) \(\chi_{8280}(2873,\cdot)\) \(\chi_{8280}(3377,\cdot)\) \(\chi_{8280}(3593,\cdot)\) \(\chi_{8280}(3713,\cdot)\) \(\chi_{8280}(3737,\cdot)\) \(\chi_{8280}(3953,\cdot)\) \(\chi_{8280}(4433,\cdot)\) \(\chi_{8280}(4817,\cdot)\) \(\chi_{8280}(4937,\cdot)\) \(\chi_{8280}(5033,\cdot)\) \(\chi_{8280}(5297,\cdot)\) \(\chi_{8280}(5393,\cdot)\) \(\chi_{8280}(5537,\cdot)\) \(\chi_{8280}(6017,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((1,1,e\left(\frac{5}{6}\right),-i,e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(113, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{71}{132}\right)\) |