Basic properties
Modulus: | \(3920\) | |
Conductor: | \(3920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fg
\(\chi_{3920}(3,\cdot)\) \(\chi_{3920}(187,\cdot)\) \(\chi_{3920}(243,\cdot)\) \(\chi_{3920}(507,\cdot)\) \(\chi_{3920}(563,\cdot)\) \(\chi_{3920}(747,\cdot)\) \(\chi_{3920}(1067,\cdot)\) \(\chi_{3920}(1123,\cdot)\) \(\chi_{3920}(1307,\cdot)\) \(\chi_{3920}(1363,\cdot)\) \(\chi_{3920}(1627,\cdot)\) \(\chi_{3920}(1683,\cdot)\) \(\chi_{3920}(1867,\cdot)\) \(\chi_{3920}(1923,\cdot)\) \(\chi_{3920}(2243,\cdot)\) \(\chi_{3920}(2427,\cdot)\) \(\chi_{3920}(2483,\cdot)\) \(\chi_{3920}(2747,\cdot)\) \(\chi_{3920}(2803,\cdot)\) \(\chi_{3920}(2987,\cdot)\) \(\chi_{3920}(3043,\cdot)\) \(\chi_{3920}(3307,\cdot)\) \(\chi_{3920}(3603,\cdot)\) \(\chi_{3920}(3867,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,i,i,e\left(\frac{19}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(1067, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |