Basic properties
| Modulus: | \(7728\) | |
| Conductor: | \(7728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7728.he
\(\chi_{7728}(101,\cdot)\) \(\chi_{7728}(173,\cdot)\) \(\chi_{7728}(269,\cdot)\) \(\chi_{7728}(509,\cdot)\) \(\chi_{7728}(1181,\cdot)\) \(\chi_{7728}(1277,\cdot)\) \(\chi_{7728}(1613,\cdot)\) \(\chi_{7728}(1685,\cdot)\) \(\chi_{7728}(1853,\cdot)\) \(\chi_{7728}(2189,\cdot)\) \(\chi_{7728}(2285,\cdot)\) \(\chi_{7728}(2525,\cdot)\) \(\chi_{7728}(2693,\cdot)\) \(\chi_{7728}(2789,\cdot)\) \(\chi_{7728}(2861,\cdot)\) \(\chi_{7728}(2957,\cdot)\) \(\chi_{7728}(3029,\cdot)\) \(\chi_{7728}(3293,\cdot)\) \(\chi_{7728}(3629,\cdot)\) \(\chi_{7728}(3797,\cdot)\) \(\chi_{7728}(3965,\cdot)\) \(\chi_{7728}(4037,\cdot)\) \(\chi_{7728}(4133,\cdot)\) \(\chi_{7728}(4373,\cdot)\) \(\chi_{7728}(5045,\cdot)\) \(\chi_{7728}(5141,\cdot)\) \(\chi_{7728}(5477,\cdot)\) \(\chi_{7728}(5549,\cdot)\) \(\chi_{7728}(5717,\cdot)\) \(\chi_{7728}(6053,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4831,5797,5153,6625,6721)\) → \((1,i,-1,e\left(\frac{1}{6}\right),e\left(\frac{5}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7728 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{21}{22}\right)\) |