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 \(\chi_{2576}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.ha
\(\chi_{7728}(37,\cdot)\) \(\chi_{7728}(109,\cdot)\) \(\chi_{7728}(205,\cdot)\) \(\chi_{7728}(373,\cdot)\) \(\chi_{7728}(613,\cdot)\) \(\chi_{7728}(709,\cdot)\) \(\chi_{7728}(1045,\cdot)\) \(\chi_{7728}(1213,\cdot)\) \(\chi_{7728}(1285,\cdot)\) \(\chi_{7728}(1621,\cdot)\) \(\chi_{7728}(1717,\cdot)\) \(\chi_{7728}(2389,\cdot)\) \(\chi_{7728}(2629,\cdot)\) \(\chi_{7728}(2725,\cdot)\) \(\chi_{7728}(2797,\cdot)\) \(\chi_{7728}(2965,\cdot)\) \(\chi_{7728}(3133,\cdot)\) \(\chi_{7728}(3469,\cdot)\) \(\chi_{7728}(3733,\cdot)\) \(\chi_{7728}(3805,\cdot)\) \(\chi_{7728}(3901,\cdot)\) \(\chi_{7728}(3973,\cdot)\) \(\chi_{7728}(4069,\cdot)\) \(\chi_{7728}(4237,\cdot)\) \(\chi_{7728}(4477,\cdot)\) \(\chi_{7728}(4573,\cdot)\) \(\chi_{7728}(4909,\cdot)\) \(\chi_{7728}(5077,\cdot)\) \(\chi_{7728}(5149,\cdot)\) \(\chi_{7728}(5485,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((1,-i,1,e\left(\frac{2}{3}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{37}{132}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{7}{22}\right)\) |