Basic properties
Modulus: | \(7728\) | |
Conductor: | \(2576\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2576}(1019,\cdot)\) | 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
\((4831,5797,5153,6625,6721)\) → \((-1,i,1,e\left(\frac{2}{3}\right),e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7728 }(3595, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{19}{22}\right)\) |