Basic properties
| Modulus: | \(7728\) | |
| Conductor: | \(2576\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2576}(445,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.hi
\(\chi_{7728}(445,\cdot)\) \(\chi_{7728}(541,\cdot)\) \(\chi_{7728}(877,\cdot)\) \(\chi_{7728}(949,\cdot)\) \(\chi_{7728}(1117,\cdot)\) \(\chi_{7728}(1453,\cdot)\) \(\chi_{7728}(1549,\cdot)\) \(\chi_{7728}(1789,\cdot)\) \(\chi_{7728}(1957,\cdot)\) \(\chi_{7728}(2053,\cdot)\) \(\chi_{7728}(2125,\cdot)\) \(\chi_{7728}(2221,\cdot)\) \(\chi_{7728}(2293,\cdot)\) \(\chi_{7728}(2557,\cdot)\) \(\chi_{7728}(2893,\cdot)\) \(\chi_{7728}(3061,\cdot)\) \(\chi_{7728}(3229,\cdot)\) \(\chi_{7728}(3301,\cdot)\) \(\chi_{7728}(3397,\cdot)\) \(\chi_{7728}(3637,\cdot)\) \(\chi_{7728}(4309,\cdot)\) \(\chi_{7728}(4405,\cdot)\) \(\chi_{7728}(4741,\cdot)\) \(\chi_{7728}(4813,\cdot)\) \(\chi_{7728}(4981,\cdot)\) \(\chi_{7728}(5317,\cdot)\) \(\chi_{7728}(5413,\cdot)\) \(\chi_{7728}(5653,\cdot)\) \(\chi_{7728}(5821,\cdot)\) \(\chi_{7728}(5917,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((1,-i,1,e\left(\frac{2}{3}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(445, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{17}{22}\right)\) |