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 \(\chi_{2576}(907,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.gx
\(\chi_{7728}(67,\cdot)\) \(\chi_{7728}(235,\cdot)\) \(\chi_{7728}(571,\cdot)\) \(\chi_{7728}(835,\cdot)\) \(\chi_{7728}(907,\cdot)\) \(\chi_{7728}(1003,\cdot)\) \(\chi_{7728}(1075,\cdot)\) \(\chi_{7728}(1171,\cdot)\) \(\chi_{7728}(1339,\cdot)\) \(\chi_{7728}(1579,\cdot)\) \(\chi_{7728}(1675,\cdot)\) \(\chi_{7728}(2011,\cdot)\) \(\chi_{7728}(2179,\cdot)\) \(\chi_{7728}(2251,\cdot)\) \(\chi_{7728}(2587,\cdot)\) \(\chi_{7728}(2683,\cdot)\) \(\chi_{7728}(3355,\cdot)\) \(\chi_{7728}(3595,\cdot)\) \(\chi_{7728}(3691,\cdot)\) \(\chi_{7728}(3763,\cdot)\) \(\chi_{7728}(3931,\cdot)\) \(\chi_{7728}(4099,\cdot)\) \(\chi_{7728}(4435,\cdot)\) \(\chi_{7728}(4699,\cdot)\) \(\chi_{7728}(4771,\cdot)\) \(\chi_{7728}(4867,\cdot)\) \(\chi_{7728}(4939,\cdot)\) \(\chi_{7728}(5035,\cdot)\) \(\chi_{7728}(5203,\cdot)\) \(\chi_{7728}(5443,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((-1,i,1,e\left(\frac{2}{3}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(907, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{3}{22}\right)\) |