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 \(\chi_{637}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.ei
\(\chi_{3822}(73,\cdot)\) \(\chi_{3822}(187,\cdot)\) \(\chi_{3822}(229,\cdot)\) \(\chi_{3822}(577,\cdot)\) \(\chi_{3822}(733,\cdot)\) \(\chi_{3822}(775,\cdot)\) \(\chi_{3822}(1123,\cdot)\) \(\chi_{3822}(1165,\cdot)\) \(\chi_{3822}(1279,\cdot)\) \(\chi_{3822}(1321,\cdot)\) \(\chi_{3822}(1669,\cdot)\) \(\chi_{3822}(1711,\cdot)\) \(\chi_{3822}(1825,\cdot)\) \(\chi_{3822}(1867,\cdot)\) \(\chi_{3822}(2215,\cdot)\) \(\chi_{3822}(2257,\cdot)\) \(\chi_{3822}(2413,\cdot)\) \(\chi_{3822}(2761,\cdot)\) \(\chi_{3822}(2803,\cdot)\) \(\chi_{3822}(2917,\cdot)\) \(\chi_{3822}(3307,\cdot)\) \(\chi_{3822}(3349,\cdot)\) \(\chi_{3822}(3463,\cdot)\) \(\chi_{3822}(3505,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((1,e\left(\frac{23}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3822 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) |