Basic properties
| Modulus: | \(3822\) | |
| Conductor: | \(1911\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1911}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.eg
\(\chi_{3822}(5,\cdot)\) \(\chi_{3822}(47,\cdot)\) \(\chi_{3822}(395,\cdot)\) \(\chi_{3822}(437,\cdot)\) \(\chi_{3822}(551,\cdot)\) \(\chi_{3822}(593,\cdot)\) \(\chi_{3822}(941,\cdot)\) \(\chi_{3822}(983,\cdot)\) \(\chi_{3822}(1139,\cdot)\) \(\chi_{3822}(1487,\cdot)\) \(\chi_{3822}(1529,\cdot)\) \(\chi_{3822}(1643,\cdot)\) \(\chi_{3822}(2033,\cdot)\) \(\chi_{3822}(2075,\cdot)\) \(\chi_{3822}(2189,\cdot)\) \(\chi_{3822}(2231,\cdot)\) \(\chi_{3822}(2621,\cdot)\) \(\chi_{3822}(2735,\cdot)\) \(\chi_{3822}(2777,\cdot)\) \(\chi_{3822}(3125,\cdot)\) \(\chi_{3822}(3281,\cdot)\) \(\chi_{3822}(3323,\cdot)\) \(\chi_{3822}(3671,\cdot)\) \(\chi_{3822}(3713,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((-1,e\left(\frac{29}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) |