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 \(\chi_{2576}(37,\cdot)\) | 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
\((4831,5797,5153,6625,6721)\) → \((1,i,1,e\left(\frac{1}{3}\right),e\left(\frac{21}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7728 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{21}{22}\right)\) |