Basic properties
| Modulus: | \(8512\) | |
| Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{608}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8512.kv
\(\chi_{8512}(71,\cdot)\) \(\chi_{8512}(295,\cdot)\) \(\chi_{8512}(743,\cdot)\) \(\chi_{8512}(1079,\cdot)\) \(\chi_{8512}(1191,\cdot)\) \(\chi_{8512}(1751,\cdot)\) \(\chi_{8512}(2199,\cdot)\) \(\chi_{8512}(2423,\cdot)\) \(\chi_{8512}(2871,\cdot)\) \(\chi_{8512}(3207,\cdot)\) \(\chi_{8512}(3319,\cdot)\) \(\chi_{8512}(3879,\cdot)\) \(\chi_{8512}(4327,\cdot)\) \(\chi_{8512}(4551,\cdot)\) \(\chi_{8512}(4999,\cdot)\) \(\chi_{8512}(5335,\cdot)\) \(\chi_{8512}(5447,\cdot)\) \(\chi_{8512}(6007,\cdot)\) \(\chi_{8512}(6455,\cdot)\) \(\chi_{8512}(6679,\cdot)\) \(\chi_{8512}(7127,\cdot)\) \(\chi_{8512}(7463,\cdot)\) \(\chi_{8512}(7575,\cdot)\) \(\chi_{8512}(8135,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((5055,6917,7297,3137)\) → \((-1,e\left(\frac{5}{8}\right),1,e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) |