Basic properties
| Modulus: | \(8512\) | |
| Conductor: | \(4256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4256}(325,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8512.lh
\(\chi_{8512}(89,\cdot)\) \(\chi_{8512}(185,\cdot)\) \(\chi_{8512}(857,\cdot)\) \(\chi_{8512}(1321,\cdot)\) \(\chi_{8512}(1865,\cdot)\) \(\chi_{8512}(2105,\cdot)\) \(\chi_{8512}(2217,\cdot)\) \(\chi_{8512}(2313,\cdot)\) \(\chi_{8512}(2985,\cdot)\) \(\chi_{8512}(3449,\cdot)\) \(\chi_{8512}(3993,\cdot)\) \(\chi_{8512}(4233,\cdot)\) \(\chi_{8512}(4345,\cdot)\) \(\chi_{8512}(4441,\cdot)\) \(\chi_{8512}(5113,\cdot)\) \(\chi_{8512}(5577,\cdot)\) \(\chi_{8512}(6121,\cdot)\) \(\chi_{8512}(6361,\cdot)\) \(\chi_{8512}(6473,\cdot)\) \(\chi_{8512}(6569,\cdot)\) \(\chi_{8512}(7241,\cdot)\) \(\chi_{8512}(7705,\cdot)\) \(\chi_{8512}(8249,\cdot)\) \(\chi_{8512}(8489,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((5055,6917,7297,3137)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(857, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{19}{24}\right)\) |