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 \(\chi_{1911}(1112,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.eh
\(\chi_{3822}(41,\cdot)\) \(\chi_{3822}(167,\cdot)\) \(\chi_{3822}(461,\cdot)\) \(\chi_{3822}(713,\cdot)\) \(\chi_{3822}(839,\cdot)\) \(\chi_{3822}(1007,\cdot)\) \(\chi_{3822}(1133,\cdot)\) \(\chi_{3822}(1259,\cdot)\) \(\chi_{3822}(1385,\cdot)\) \(\chi_{3822}(1553,\cdot)\) \(\chi_{3822}(1679,\cdot)\) \(\chi_{3822}(1805,\cdot)\) \(\chi_{3822}(1931,\cdot)\) \(\chi_{3822}(2099,\cdot)\) \(\chi_{3822}(2225,\cdot)\) \(\chi_{3822}(2477,\cdot)\) \(\chi_{3822}(2771,\cdot)\) \(\chi_{3822}(2897,\cdot)\) \(\chi_{3822}(3023,\cdot)\) \(\chi_{3822}(3191,\cdot)\) \(\chi_{3822}(3317,\cdot)\) \(\chi_{3822}(3443,\cdot)\) \(\chi_{3822}(3569,\cdot)\) \(\chi_{3822}(3737,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((-1,e\left(\frac{3}{14}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(3023, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(-i\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) |