Basic properties
Modulus: | \(3840\) | |
Conductor: | \(3840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | 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 3840.dn
\(\chi_{3840}(59,\cdot)\) \(\chi_{3840}(179,\cdot)\) \(\chi_{3840}(299,\cdot)\) \(\chi_{3840}(419,\cdot)\) \(\chi_{3840}(539,\cdot)\) \(\chi_{3840}(659,\cdot)\) \(\chi_{3840}(779,\cdot)\) \(\chi_{3840}(899,\cdot)\) \(\chi_{3840}(1019,\cdot)\) \(\chi_{3840}(1139,\cdot)\) \(\chi_{3840}(1259,\cdot)\) \(\chi_{3840}(1379,\cdot)\) \(\chi_{3840}(1499,\cdot)\) \(\chi_{3840}(1619,\cdot)\) \(\chi_{3840}(1739,\cdot)\) \(\chi_{3840}(1859,\cdot)\) \(\chi_{3840}(1979,\cdot)\) \(\chi_{3840}(2099,\cdot)\) \(\chi_{3840}(2219,\cdot)\) \(\chi_{3840}(2339,\cdot)\) \(\chi_{3840}(2459,\cdot)\) \(\chi_{3840}(2579,\cdot)\) \(\chi_{3840}(2699,\cdot)\) \(\chi_{3840}(2819,\cdot)\) \(\chi_{3840}(2939,\cdot)\) \(\chi_{3840}(3059,\cdot)\) \(\chi_{3840}(3179,\cdot)\) \(\chi_{3840}(3299,\cdot)\) \(\chi_{3840}(3419,\cdot)\) \(\chi_{3840}(3539,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((-1,e\left(\frac{57}{64}\right),-1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3840 }(3419, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) |