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 \(\chi_{637}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.ej
\(\chi_{3822}(115,\cdot)\) \(\chi_{3822}(397,\cdot)\) \(\chi_{3822}(535,\cdot)\) \(\chi_{3822}(565,\cdot)\) \(\chi_{3822}(661,\cdot)\) \(\chi_{3822}(943,\cdot)\) \(\chi_{3822}(1081,\cdot)\) \(\chi_{3822}(1111,\cdot)\) \(\chi_{3822}(1627,\cdot)\) \(\chi_{3822}(1657,\cdot)\) \(\chi_{3822}(1753,\cdot)\) \(\chi_{3822}(2035,\cdot)\) \(\chi_{3822}(2173,\cdot)\) \(\chi_{3822}(2203,\cdot)\) \(\chi_{3822}(2299,\cdot)\) \(\chi_{3822}(2581,\cdot)\) \(\chi_{3822}(2719,\cdot)\) \(\chi_{3822}(2749,\cdot)\) \(\chi_{3822}(2845,\cdot)\) \(\chi_{3822}(3127,\cdot)\) \(\chi_{3822}(3295,\cdot)\) \(\chi_{3822}(3391,\cdot)\) \(\chi_{3822}(3673,\cdot)\) \(\chi_{3822}(3811,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((1,e\left(\frac{25}{42}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(-i\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{43}{84}\right)\) |