Basic properties
| Modulus: | \(3822\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.ec
\(\chi_{3822}(109,\cdot)\) \(\chi_{3822}(151,\cdot)\) \(\chi_{3822}(499,\cdot)\) \(\chi_{3822}(541,\cdot)\) \(\chi_{3822}(697,\cdot)\) \(\chi_{3822}(1045,\cdot)\) \(\chi_{3822}(1087,\cdot)\) \(\chi_{3822}(1201,\cdot)\) \(\chi_{3822}(1591,\cdot)\) \(\chi_{3822}(1633,\cdot)\) \(\chi_{3822}(1747,\cdot)\) \(\chi_{3822}(1789,\cdot)\) \(\chi_{3822}(2179,\cdot)\) \(\chi_{3822}(2293,\cdot)\) \(\chi_{3822}(2335,\cdot)\) \(\chi_{3822}(2683,\cdot)\) \(\chi_{3822}(2839,\cdot)\) \(\chi_{3822}(2881,\cdot)\) \(\chi_{3822}(3229,\cdot)\) \(\chi_{3822}(3271,\cdot)\) \(\chi_{3822}(3385,\cdot)\) \(\chi_{3822}(3427,\cdot)\) \(\chi_{3822}(3775,\cdot)\) \(\chi_{3822}(3817,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((1,e\left(\frac{20}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) |