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 \(\chi_{2576}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.hd
\(\chi_{7728}(61,\cdot)\) \(\chi_{7728}(157,\cdot)\) \(\chi_{7728}(493,\cdot)\) \(\chi_{7728}(661,\cdot)\) \(\chi_{7728}(733,\cdot)\) \(\chi_{7728}(1069,\cdot)\) \(\chi_{7728}(1165,\cdot)\) \(\chi_{7728}(1837,\cdot)\) \(\chi_{7728}(2077,\cdot)\) \(\chi_{7728}(2173,\cdot)\) \(\chi_{7728}(2245,\cdot)\) \(\chi_{7728}(2413,\cdot)\) \(\chi_{7728}(2581,\cdot)\) \(\chi_{7728}(2917,\cdot)\) \(\chi_{7728}(3181,\cdot)\) \(\chi_{7728}(3253,\cdot)\) \(\chi_{7728}(3349,\cdot)\) \(\chi_{7728}(3421,\cdot)\) \(\chi_{7728}(3517,\cdot)\) \(\chi_{7728}(3685,\cdot)\) \(\chi_{7728}(3925,\cdot)\) \(\chi_{7728}(4021,\cdot)\) \(\chi_{7728}(4357,\cdot)\) \(\chi_{7728}(4525,\cdot)\) \(\chi_{7728}(4597,\cdot)\) \(\chi_{7728}(4933,\cdot)\) \(\chi_{7728}(5029,\cdot)\) \(\chi_{7728}(5701,\cdot)\) \(\chi_{7728}(5941,\cdot)\) \(\chi_{7728}(6037,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((1,-i,1,e\left(\frac{5}{6}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{3}{11}\right)\) |