Basic properties
| Modulus: | \(3840\) | |
| Conductor: | \(1280\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1280}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3840.ds
\(\chi_{3840}(163,\cdot)\) \(\chi_{3840}(187,\cdot)\) \(\chi_{3840}(403,\cdot)\) \(\chi_{3840}(427,\cdot)\) \(\chi_{3840}(643,\cdot)\) \(\chi_{3840}(667,\cdot)\) \(\chi_{3840}(883,\cdot)\) \(\chi_{3840}(907,\cdot)\) \(\chi_{3840}(1123,\cdot)\) \(\chi_{3840}(1147,\cdot)\) \(\chi_{3840}(1363,\cdot)\) \(\chi_{3840}(1387,\cdot)\) \(\chi_{3840}(1603,\cdot)\) \(\chi_{3840}(1627,\cdot)\) \(\chi_{3840}(1843,\cdot)\) \(\chi_{3840}(1867,\cdot)\) \(\chi_{3840}(2083,\cdot)\) \(\chi_{3840}(2107,\cdot)\) \(\chi_{3840}(2323,\cdot)\) \(\chi_{3840}(2347,\cdot)\) \(\chi_{3840}(2563,\cdot)\) \(\chi_{3840}(2587,\cdot)\) \(\chi_{3840}(2803,\cdot)\) \(\chi_{3840}(2827,\cdot)\) \(\chi_{3840}(3043,\cdot)\) \(\chi_{3840}(3067,\cdot)\) \(\chi_{3840}(3283,\cdot)\) \(\chi_{3840}(3307,\cdot)\) \(\chi_{3840}(3523,\cdot)\) \(\chi_{3840}(3547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((-1,e\left(\frac{43}{64}\right),1,-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3840 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) |