Basic properties
| Modulus: | \(8512\) | |
| Conductor: | \(8512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | 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 8512.ll
\(\chi_{8512}(51,\cdot)\) \(\chi_{8512}(219,\cdot)\) \(\chi_{8512}(459,\cdot)\) \(\chi_{8512}(515,\cdot)\) \(\chi_{8512}(907,\cdot)\) \(\chi_{8512}(1003,\cdot)\) \(\chi_{8512}(1115,\cdot)\) \(\chi_{8512}(1283,\cdot)\) \(\chi_{8512}(1523,\cdot)\) \(\chi_{8512}(1579,\cdot)\) \(\chi_{8512}(1971,\cdot)\) \(\chi_{8512}(2067,\cdot)\) \(\chi_{8512}(2179,\cdot)\) \(\chi_{8512}(2347,\cdot)\) \(\chi_{8512}(2587,\cdot)\) \(\chi_{8512}(2643,\cdot)\) \(\chi_{8512}(3035,\cdot)\) \(\chi_{8512}(3131,\cdot)\) \(\chi_{8512}(3243,\cdot)\) \(\chi_{8512}(3411,\cdot)\) \(\chi_{8512}(3651,\cdot)\) \(\chi_{8512}(3707,\cdot)\) \(\chi_{8512}(4099,\cdot)\) \(\chi_{8512}(4195,\cdot)\) \(\chi_{8512}(4307,\cdot)\) \(\chi_{8512}(4475,\cdot)\) \(\chi_{8512}(4715,\cdot)\) \(\chi_{8512}(4771,\cdot)\) \(\chi_{8512}(5163,\cdot)\) \(\chi_{8512}(5259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((5055,6917,7297,3137)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(3243, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{144}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{83}{144}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{31}{48}\right)\) |