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.md
\(\chi_{8512}(67,\cdot)\) \(\chi_{8512}(611,\cdot)\) \(\chi_{8512}(667,\cdot)\) \(\chi_{8512}(851,\cdot)\) \(\chi_{8512}(963,\cdot)\) \(\chi_{8512}(1059,\cdot)\) \(\chi_{8512}(1131,\cdot)\) \(\chi_{8512}(1675,\cdot)\) \(\chi_{8512}(1731,\cdot)\) \(\chi_{8512}(1915,\cdot)\) \(\chi_{8512}(2027,\cdot)\) \(\chi_{8512}(2123,\cdot)\) \(\chi_{8512}(2195,\cdot)\) \(\chi_{8512}(2739,\cdot)\) \(\chi_{8512}(2795,\cdot)\) \(\chi_{8512}(2979,\cdot)\) \(\chi_{8512}(3091,\cdot)\) \(\chi_{8512}(3187,\cdot)\) \(\chi_{8512}(3259,\cdot)\) \(\chi_{8512}(3803,\cdot)\) \(\chi_{8512}(3859,\cdot)\) \(\chi_{8512}(4043,\cdot)\) \(\chi_{8512}(4155,\cdot)\) \(\chi_{8512}(4251,\cdot)\) \(\chi_{8512}(4323,\cdot)\) \(\chi_{8512}(4867,\cdot)\) \(\chi_{8512}(4923,\cdot)\) \(\chi_{8512}(5107,\cdot)\) \(\chi_{8512}(5219,\cdot)\) \(\chi_{8512}(5315,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((5055,6917,7297,3137)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(4251, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{144}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{35}{48}\right)\) |