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 \(\chi_{637}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3822.eb
\(\chi_{3822}(145,\cdot)\) \(\chi_{3822}(241,\cdot)\) \(\chi_{3822}(271,\cdot)\) \(\chi_{3822}(409,\cdot)\) \(\chi_{3822}(691,\cdot)\) \(\chi_{3822}(787,\cdot)\) \(\chi_{3822}(817,\cdot)\) \(\chi_{3822}(955,\cdot)\) \(\chi_{3822}(1237,\cdot)\) \(\chi_{3822}(1333,\cdot)\) \(\chi_{3822}(1363,\cdot)\) \(\chi_{3822}(1879,\cdot)\) \(\chi_{3822}(1909,\cdot)\) \(\chi_{3822}(2047,\cdot)\) \(\chi_{3822}(2329,\cdot)\) \(\chi_{3822}(2425,\cdot)\) \(\chi_{3822}(2455,\cdot)\) \(\chi_{3822}(2593,\cdot)\) \(\chi_{3822}(2875,\cdot)\) \(\chi_{3822}(3001,\cdot)\) \(\chi_{3822}(3139,\cdot)\) \(\chi_{3822}(3421,\cdot)\) \(\chi_{3822}(3517,\cdot)\) \(\chi_{3822}(3685,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,3433,1471)\) → \((1,e\left(\frac{5}{42}\right),e\left(\frac{1}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3822 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{73}{84}\right)\) |