Basic properties
| Modulus: | \(8040\) | |
| Conductor: | \(8040\) | 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 8040.hj
\(\chi_{8040}(77,\cdot)\) \(\chi_{8040}(173,\cdot)\) \(\chi_{8040}(317,\cdot)\) \(\chi_{8040}(437,\cdot)\) \(\chi_{8040}(557,\cdot)\) \(\chi_{8040}(773,\cdot)\) \(\chi_{8040}(797,\cdot)\) \(\chi_{8040}(1253,\cdot)\) \(\chi_{8040}(1277,\cdot)\) \(\chi_{8040}(1373,\cdot)\) \(\chi_{8040}(1493,\cdot)\) \(\chi_{8040}(1997,\cdot)\) \(\chi_{8040}(2093,\cdot)\) \(\chi_{8040}(2237,\cdot)\) \(\chi_{8040}(2333,\cdot)\) \(\chi_{8040}(2477,\cdot)\) \(\chi_{8040}(2837,\cdot)\) \(\chi_{8040}(3293,\cdot)\) \(\chi_{8040}(3533,\cdot)\) \(\chi_{8040}(3557,\cdot)\) \(\chi_{8040}(3653,\cdot)\) \(\chi_{8040}(3773,\cdot)\) \(\chi_{8040}(4013,\cdot)\) \(\chi_{8040}(4037,\cdot)\) \(\chi_{8040}(4277,\cdot)\) \(\chi_{8040}(4493,\cdot)\) \(\chi_{8040}(4997,\cdot)\) \(\chi_{8040}(5213,\cdot)\) \(\chi_{8040}(5453,\cdot)\) \(\chi_{8040}(5597,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6031,4021,2681,3217,5161)\) → \((1,-1,-1,i,e\left(\frac{8}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8040 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{66}\right)\) |