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.lw
\(\chi_{8512}(93,\cdot)\) \(\chi_{8512}(149,\cdot)\) \(\chi_{8512}(389,\cdot)\) \(\chi_{8512}(557,\cdot)\) \(\chi_{8512}(669,\cdot)\) \(\chi_{8512}(765,\cdot)\) \(\chi_{8512}(1157,\cdot)\) \(\chi_{8512}(1213,\cdot)\) \(\chi_{8512}(1453,\cdot)\) \(\chi_{8512}(1621,\cdot)\) \(\chi_{8512}(1733,\cdot)\) \(\chi_{8512}(1829,\cdot)\) \(\chi_{8512}(2221,\cdot)\) \(\chi_{8512}(2277,\cdot)\) \(\chi_{8512}(2517,\cdot)\) \(\chi_{8512}(2685,\cdot)\) \(\chi_{8512}(2797,\cdot)\) \(\chi_{8512}(2893,\cdot)\) \(\chi_{8512}(3285,\cdot)\) \(\chi_{8512}(3341,\cdot)\) \(\chi_{8512}(3581,\cdot)\) \(\chi_{8512}(3749,\cdot)\) \(\chi_{8512}(3861,\cdot)\) \(\chi_{8512}(3957,\cdot)\) \(\chi_{8512}(4349,\cdot)\) \(\chi_{8512}(4405,\cdot)\) \(\chi_{8512}(4645,\cdot)\) \(\chi_{8512}(4813,\cdot)\) \(\chi_{8512}(4925,\cdot)\) \(\chi_{8512}(5021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((5055,6917,7297,3137)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{2}{3}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(557, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{144}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{13}{48}\right)\) |