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.hj
\(\chi_{7728}(59,\cdot)\) \(\chi_{7728}(131,\cdot)\) \(\chi_{7728}(395,\cdot)\) \(\chi_{7728}(731,\cdot)\) \(\chi_{7728}(899,\cdot)\) \(\chi_{7728}(1067,\cdot)\) \(\chi_{7728}(1139,\cdot)\) \(\chi_{7728}(1235,\cdot)\) \(\chi_{7728}(1475,\cdot)\) \(\chi_{7728}(2147,\cdot)\) \(\chi_{7728}(2243,\cdot)\) \(\chi_{7728}(2579,\cdot)\) \(\chi_{7728}(2651,\cdot)\) \(\chi_{7728}(2819,\cdot)\) \(\chi_{7728}(3155,\cdot)\) \(\chi_{7728}(3251,\cdot)\) \(\chi_{7728}(3491,\cdot)\) \(\chi_{7728}(3659,\cdot)\) \(\chi_{7728}(3755,\cdot)\) \(\chi_{7728}(3827,\cdot)\) \(\chi_{7728}(3923,\cdot)\) \(\chi_{7728}(3995,\cdot)\) \(\chi_{7728}(4259,\cdot)\) \(\chi_{7728}(4595,\cdot)\) \(\chi_{7728}(4763,\cdot)\) \(\chi_{7728}(4931,\cdot)\) \(\chi_{7728}(5003,\cdot)\) \(\chi_{7728}(5099,\cdot)\) \(\chi_{7728}(5339,\cdot)\) \(\chi_{7728}(6011,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((-1,i,-1,e\left(\frac{1}{6}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{3}{22}\right)\) |