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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.gu
\(\chi_{7728}(179,\cdot)\) \(\chi_{7728}(347,\cdot)\) \(\chi_{7728}(443,\cdot)\) \(\chi_{7728}(515,\cdot)\) \(\chi_{7728}(611,\cdot)\) \(\chi_{7728}(683,\cdot)\) \(\chi_{7728}(947,\cdot)\) \(\chi_{7728}(1283,\cdot)\) \(\chi_{7728}(1451,\cdot)\) \(\chi_{7728}(1619,\cdot)\) \(\chi_{7728}(1691,\cdot)\) \(\chi_{7728}(1787,\cdot)\) \(\chi_{7728}(2027,\cdot)\) \(\chi_{7728}(2699,\cdot)\) \(\chi_{7728}(2795,\cdot)\) \(\chi_{7728}(3131,\cdot)\) \(\chi_{7728}(3203,\cdot)\) \(\chi_{7728}(3371,\cdot)\) \(\chi_{7728}(3707,\cdot)\) \(\chi_{7728}(3803,\cdot)\) \(\chi_{7728}(4043,\cdot)\) \(\chi_{7728}(4211,\cdot)\) \(\chi_{7728}(4307,\cdot)\) \(\chi_{7728}(4379,\cdot)\) \(\chi_{7728}(4475,\cdot)\) \(\chi_{7728}(4547,\cdot)\) \(\chi_{7728}(4811,\cdot)\) \(\chi_{7728}(5147,\cdot)\) \(\chi_{7728}(5315,\cdot)\) \(\chi_{7728}(5483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((-1,-i,-1,e\left(\frac{2}{3}\right),e\left(\frac{6}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{6}{11}\right)\) |