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 \(\chi_{2576}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.gy
\(\chi_{7728}(187,\cdot)\) \(\chi_{7728}(859,\cdot)\) \(\chi_{7728}(955,\cdot)\) \(\chi_{7728}(1291,\cdot)\) \(\chi_{7728}(1363,\cdot)\) \(\chi_{7728}(1531,\cdot)\) \(\chi_{7728}(1867,\cdot)\) \(\chi_{7728}(1963,\cdot)\) \(\chi_{7728}(2203,\cdot)\) \(\chi_{7728}(2371,\cdot)\) \(\chi_{7728}(2467,\cdot)\) \(\chi_{7728}(2539,\cdot)\) \(\chi_{7728}(2635,\cdot)\) \(\chi_{7728}(2707,\cdot)\) \(\chi_{7728}(2971,\cdot)\) \(\chi_{7728}(3307,\cdot)\) \(\chi_{7728}(3475,\cdot)\) \(\chi_{7728}(3643,\cdot)\) \(\chi_{7728}(3715,\cdot)\) \(\chi_{7728}(3811,\cdot)\) \(\chi_{7728}(4051,\cdot)\) \(\chi_{7728}(4723,\cdot)\) \(\chi_{7728}(4819,\cdot)\) \(\chi_{7728}(5155,\cdot)\) \(\chi_{7728}(5227,\cdot)\) \(\chi_{7728}(5395,\cdot)\) \(\chi_{7728}(5731,\cdot)\) \(\chi_{7728}(5827,\cdot)\) \(\chi_{7728}(6067,\cdot)\) \(\chi_{7728}(6235,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((-1,i,1,e\left(\frac{5}{6}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7728 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{8}{11}\right)\) |