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 \(\chi_{4256}(1677,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8512.lj
\(\chi_{8512}(9,\cdot)\) \(\chi_{8512}(473,\cdot)\) \(\chi_{8512}(1145,\cdot)\) \(\chi_{8512}(1241,\cdot)\) \(\chi_{8512}(1353,\cdot)\) \(\chi_{8512}(1593,\cdot)\) \(\chi_{8512}(2137,\cdot)\) \(\chi_{8512}(2601,\cdot)\) \(\chi_{8512}(3273,\cdot)\) \(\chi_{8512}(3369,\cdot)\) \(\chi_{8512}(3481,\cdot)\) \(\chi_{8512}(3721,\cdot)\) \(\chi_{8512}(4265,\cdot)\) \(\chi_{8512}(4729,\cdot)\) \(\chi_{8512}(5401,\cdot)\) \(\chi_{8512}(5497,\cdot)\) \(\chi_{8512}(5609,\cdot)\) \(\chi_{8512}(5849,\cdot)\) \(\chi_{8512}(6393,\cdot)\) \(\chi_{8512}(6857,\cdot)\) \(\chi_{8512}(7529,\cdot)\) \(\chi_{8512}(7625,\cdot)\) \(\chi_{8512}(7737,\cdot)\) \(\chi_{8512}(7977,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((5055,6917,7297,3137)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{2}{3}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(7529, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{13}{24}\right)\) |