Basic properties
Modulus: | \(3920\) | |
Conductor: | \(3920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.gb
\(\chi_{3920}(173,\cdot)\) \(\chi_{3920}(437,\cdot)\) \(\chi_{3920}(493,\cdot)\) \(\chi_{3920}(677,\cdot)\) \(\chi_{3920}(733,\cdot)\) \(\chi_{3920}(997,\cdot)\) \(\chi_{3920}(1053,\cdot)\) \(\chi_{3920}(1237,\cdot)\) \(\chi_{3920}(1557,\cdot)\) \(\chi_{3920}(1613,\cdot)\) \(\chi_{3920}(1797,\cdot)\) \(\chi_{3920}(1853,\cdot)\) \(\chi_{3920}(2117,\cdot)\) \(\chi_{3920}(2173,\cdot)\) \(\chi_{3920}(2357,\cdot)\) \(\chi_{3920}(2413,\cdot)\) \(\chi_{3920}(2733,\cdot)\) \(\chi_{3920}(2917,\cdot)\) \(\chi_{3920}(2973,\cdot)\) \(\chi_{3920}(3237,\cdot)\) \(\chi_{3920}(3293,\cdot)\) \(\chi_{3920}(3477,\cdot)\) \(\chi_{3920}(3533,\cdot)\) \(\chi_{3920}(3797,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,-i,e\left(\frac{17}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |