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 \(\chi_{4256}(3163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8512.kr
\(\chi_{8512}(55,\cdot)\) \(\chi_{8512}(503,\cdot)\) \(\chi_{8512}(727,\cdot)\) \(\chi_{8512}(1175,\cdot)\) \(\chi_{8512}(1735,\cdot)\) \(\chi_{8512}(1847,\cdot)\) \(\chi_{8512}(2183,\cdot)\) \(\chi_{8512}(2631,\cdot)\) \(\chi_{8512}(2855,\cdot)\) \(\chi_{8512}(3303,\cdot)\) \(\chi_{8512}(3863,\cdot)\) \(\chi_{8512}(3975,\cdot)\) \(\chi_{8512}(4311,\cdot)\) \(\chi_{8512}(4759,\cdot)\) \(\chi_{8512}(4983,\cdot)\) \(\chi_{8512}(5431,\cdot)\) \(\chi_{8512}(5991,\cdot)\) \(\chi_{8512}(6103,\cdot)\) \(\chi_{8512}(6439,\cdot)\) \(\chi_{8512}(6887,\cdot)\) \(\chi_{8512}(7111,\cdot)\) \(\chi_{8512}(7559,\cdot)\) \(\chi_{8512}(8119,\cdot)\) \(\chi_{8512}(8231,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((5055,6917,7297,3137)\) → \((-1,e\left(\frac{1}{8}\right),-1,e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(6887, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{24}\right)\) |