Basic properties
| Modulus: | \(3168\) | |
| Conductor: | \(3168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 3168.eq
\(\chi_{3168}(59,\cdot)\) \(\chi_{3168}(203,\cdot)\) \(\chi_{3168}(443,\cdot)\) \(\chi_{3168}(515,\cdot)\) \(\chi_{3168}(587,\cdot)\) \(\chi_{3168}(707,\cdot)\) \(\chi_{3168}(731,\cdot)\) \(\chi_{3168}(779,\cdot)\) \(\chi_{3168}(851,\cdot)\) \(\chi_{3168}(995,\cdot)\) \(\chi_{3168}(1235,\cdot)\) \(\chi_{3168}(1307,\cdot)\) \(\chi_{3168}(1379,\cdot)\) \(\chi_{3168}(1499,\cdot)\) \(\chi_{3168}(1523,\cdot)\) \(\chi_{3168}(1571,\cdot)\) \(\chi_{3168}(1643,\cdot)\) \(\chi_{3168}(1787,\cdot)\) \(\chi_{3168}(2027,\cdot)\) \(\chi_{3168}(2099,\cdot)\) \(\chi_{3168}(2171,\cdot)\) \(\chi_{3168}(2291,\cdot)\) \(\chi_{3168}(2315,\cdot)\) \(\chi_{3168}(2363,\cdot)\) \(\chi_{3168}(2435,\cdot)\) \(\chi_{3168}(2579,\cdot)\) \(\chi_{3168}(2819,\cdot)\) \(\chi_{3168}(2891,\cdot)\) \(\chi_{3168}(2963,\cdot)\) \(\chi_{3168}(3083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((991,1189,353,1729)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3168 }(1643, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{40}\right)\) |