Basic properties
Modulus: | \(3968\) | |
Conductor: | \(3968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3968.da
\(\chi_{3968}(99,\cdot)\) \(\chi_{3968}(243,\cdot)\) \(\chi_{3968}(347,\cdot)\) \(\chi_{3968}(491,\cdot)\) \(\chi_{3968}(595,\cdot)\) \(\chi_{3968}(739,\cdot)\) \(\chi_{3968}(843,\cdot)\) \(\chi_{3968}(987,\cdot)\) \(\chi_{3968}(1091,\cdot)\) \(\chi_{3968}(1235,\cdot)\) \(\chi_{3968}(1339,\cdot)\) \(\chi_{3968}(1483,\cdot)\) \(\chi_{3968}(1587,\cdot)\) \(\chi_{3968}(1731,\cdot)\) \(\chi_{3968}(1835,\cdot)\) \(\chi_{3968}(1979,\cdot)\) \(\chi_{3968}(2083,\cdot)\) \(\chi_{3968}(2227,\cdot)\) \(\chi_{3968}(2331,\cdot)\) \(\chi_{3968}(2475,\cdot)\) \(\chi_{3968}(2579,\cdot)\) \(\chi_{3968}(2723,\cdot)\) \(\chi_{3968}(2827,\cdot)\) \(\chi_{3968}(2971,\cdot)\) \(\chi_{3968}(3075,\cdot)\) \(\chi_{3968}(3219,\cdot)\) \(\chi_{3968}(3323,\cdot)\) \(\chi_{3968}(3467,\cdot)\) \(\chi_{3968}(3571,\cdot)\) \(\chi_{3968}(3715,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((2047,3845,2049)\) → \((-1,e\left(\frac{17}{32}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3968 }(1339, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{7}{96}\right)\) |