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.gw
\(\chi_{7728}(5,\cdot)\) \(\chi_{7728}(341,\cdot)\) \(\chi_{7728}(605,\cdot)\) \(\chi_{7728}(677,\cdot)\) \(\chi_{7728}(773,\cdot)\) \(\chi_{7728}(845,\cdot)\) \(\chi_{7728}(941,\cdot)\) \(\chi_{7728}(1109,\cdot)\) \(\chi_{7728}(1349,\cdot)\) \(\chi_{7728}(1445,\cdot)\) \(\chi_{7728}(1781,\cdot)\) \(\chi_{7728}(1949,\cdot)\) \(\chi_{7728}(2021,\cdot)\) \(\chi_{7728}(2357,\cdot)\) \(\chi_{7728}(2453,\cdot)\) \(\chi_{7728}(3125,\cdot)\) \(\chi_{7728}(3365,\cdot)\) \(\chi_{7728}(3461,\cdot)\) \(\chi_{7728}(3533,\cdot)\) \(\chi_{7728}(3701,\cdot)\) \(\chi_{7728}(3869,\cdot)\) \(\chi_{7728}(4205,\cdot)\) \(\chi_{7728}(4469,\cdot)\) \(\chi_{7728}(4541,\cdot)\) \(\chi_{7728}(4637,\cdot)\) \(\chi_{7728}(4709,\cdot)\) \(\chi_{7728}(4805,\cdot)\) \(\chi_{7728}(4973,\cdot)\) \(\chi_{7728}(5213,\cdot)\) \(\chi_{7728}(5309,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((1,i,-1,e\left(\frac{5}{6}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(2021, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{5}{22}\right)\) |