Basic properties
| Modulus: | \(8280\) | |
| Conductor: | \(4140\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4140}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8280.hg
\(\chi_{8280}(7,\cdot)\) \(\chi_{8280}(103,\cdot)\) \(\chi_{8280}(247,\cdot)\) \(\chi_{8280}(727,\cdot)\) \(\chi_{8280}(1183,\cdot)\) \(\chi_{8280}(1303,\cdot)\) \(\chi_{8280}(1447,\cdot)\) \(\chi_{8280}(1663,\cdot)\) \(\chi_{8280}(1903,\cdot)\) \(\chi_{8280}(2167,\cdot)\) \(\chi_{8280}(2383,\cdot)\) \(\chi_{8280}(2407,\cdot)\) \(\chi_{8280}(2527,\cdot)\) \(\chi_{8280}(2767,\cdot)\) \(\chi_{8280}(3103,\cdot)\) \(\chi_{8280}(3487,\cdot)\) \(\chi_{8280}(3607,\cdot)\) \(\chi_{8280}(3823,\cdot)\) \(\chi_{8280}(3967,\cdot)\) \(\chi_{8280}(4063,\cdot)\) \(\chi_{8280}(4183,\cdot)\) \(\chi_{8280}(4207,\cdot)\) \(\chi_{8280}(4423,\cdot)\) \(\chi_{8280}(4927,\cdot)\) \(\chi_{8280}(5047,\cdot)\) \(\chi_{8280}(5143,\cdot)\) \(\chi_{8280}(5263,\cdot)\) \(\chi_{8280}(5287,\cdot)\) \(\chi_{8280}(5623,\cdot)\) \(\chi_{8280}(5767,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((-1,1,e\left(\frac{2}{3}\right),i,e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{31}{132}\right)\) |