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.ex
\(\chi_{3168}(29,\cdot)\) \(\chi_{3168}(101,\cdot)\) \(\chi_{3168}(149,\cdot)\) \(\chi_{3168}(173,\cdot)\) \(\chi_{3168}(293,\cdot)\) \(\chi_{3168}(365,\cdot)\) \(\chi_{3168}(437,\cdot)\) \(\chi_{3168}(677,\cdot)\) \(\chi_{3168}(821,\cdot)\) \(\chi_{3168}(893,\cdot)\) \(\chi_{3168}(941,\cdot)\) \(\chi_{3168}(965,\cdot)\) \(\chi_{3168}(1085,\cdot)\) \(\chi_{3168}(1157,\cdot)\) \(\chi_{3168}(1229,\cdot)\) \(\chi_{3168}(1469,\cdot)\) \(\chi_{3168}(1613,\cdot)\) \(\chi_{3168}(1685,\cdot)\) \(\chi_{3168}(1733,\cdot)\) \(\chi_{3168}(1757,\cdot)\) \(\chi_{3168}(1877,\cdot)\) \(\chi_{3168}(1949,\cdot)\) \(\chi_{3168}(2021,\cdot)\) \(\chi_{3168}(2261,\cdot)\) \(\chi_{3168}(2405,\cdot)\) \(\chi_{3168}(2477,\cdot)\) \(\chi_{3168}(2525,\cdot)\) \(\chi_{3168}(2549,\cdot)\) \(\chi_{3168}(2669,\cdot)\) \(\chi_{3168}(2741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((991,1189,353,1729)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3168 }(1613, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{33}{40}\right)\) |