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 \(\chi_{637}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.ep
\(\chi_{3822}(37,\cdot)\) \(\chi_{3822}(319,\cdot)\) \(\chi_{3822}(457,\cdot)\) \(\chi_{3822}(487,\cdot)\) \(\chi_{3822}(583,\cdot)\) \(\chi_{3822}(865,\cdot)\) \(\chi_{3822}(1003,\cdot)\) \(\chi_{3822}(1033,\cdot)\) \(\chi_{3822}(1129,\cdot)\) \(\chi_{3822}(1411,\cdot)\) \(\chi_{3822}(1579,\cdot)\) \(\chi_{3822}(1675,\cdot)\) \(\chi_{3822}(1957,\cdot)\) \(\chi_{3822}(2095,\cdot)\) \(\chi_{3822}(2221,\cdot)\) \(\chi_{3822}(2503,\cdot)\) \(\chi_{3822}(2641,\cdot)\) \(\chi_{3822}(2671,\cdot)\) \(\chi_{3822}(2767,\cdot)\) \(\chi_{3822}(3049,\cdot)\) \(\chi_{3822}(3187,\cdot)\) \(\chi_{3822}(3217,\cdot)\) \(\chi_{3822}(3733,\cdot)\) \(\chi_{3822}(3763,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((1,e\left(\frac{16}{21}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{1}{84}\right)\) |