Basic properties
| Modulus: | \(7728\) | |
| Conductor: | \(7728\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.hc
\(\chi_{7728}(11,\cdot)\) \(\chi_{7728}(107,\cdot)\) \(\chi_{7728}(779,\cdot)\) \(\chi_{7728}(1019,\cdot)\) \(\chi_{7728}(1115,\cdot)\) \(\chi_{7728}(1187,\cdot)\) \(\chi_{7728}(1355,\cdot)\) \(\chi_{7728}(1523,\cdot)\) \(\chi_{7728}(1859,\cdot)\) \(\chi_{7728}(2123,\cdot)\) \(\chi_{7728}(2195,\cdot)\) \(\chi_{7728}(2291,\cdot)\) \(\chi_{7728}(2363,\cdot)\) \(\chi_{7728}(2459,\cdot)\) \(\chi_{7728}(2627,\cdot)\) \(\chi_{7728}(2867,\cdot)\) \(\chi_{7728}(2963,\cdot)\) \(\chi_{7728}(3299,\cdot)\) \(\chi_{7728}(3467,\cdot)\) \(\chi_{7728}(3539,\cdot)\) \(\chi_{7728}(3875,\cdot)\) \(\chi_{7728}(3971,\cdot)\) \(\chi_{7728}(4643,\cdot)\) \(\chi_{7728}(4883,\cdot)\) \(\chi_{7728}(4979,\cdot)\) \(\chi_{7728}(5051,\cdot)\) \(\chi_{7728}(5219,\cdot)\) \(\chi_{7728}(5387,\cdot)\) \(\chi_{7728}(5723,\cdot)\) \(\chi_{7728}(5987,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((-1,i,-1,e\left(\frac{2}{3}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{10}{11}\right)\) |