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 \(\chi_{1280}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3840.do
\(\chi_{3840}(43,\cdot)\) \(\chi_{3840}(67,\cdot)\) \(\chi_{3840}(283,\cdot)\) \(\chi_{3840}(307,\cdot)\) \(\chi_{3840}(523,\cdot)\) \(\chi_{3840}(547,\cdot)\) \(\chi_{3840}(763,\cdot)\) \(\chi_{3840}(787,\cdot)\) \(\chi_{3840}(1003,\cdot)\) \(\chi_{3840}(1027,\cdot)\) \(\chi_{3840}(1243,\cdot)\) \(\chi_{3840}(1267,\cdot)\) \(\chi_{3840}(1483,\cdot)\) \(\chi_{3840}(1507,\cdot)\) \(\chi_{3840}(1723,\cdot)\) \(\chi_{3840}(1747,\cdot)\) \(\chi_{3840}(1963,\cdot)\) \(\chi_{3840}(1987,\cdot)\) \(\chi_{3840}(2203,\cdot)\) \(\chi_{3840}(2227,\cdot)\) \(\chi_{3840}(2443,\cdot)\) \(\chi_{3840}(2467,\cdot)\) \(\chi_{3840}(2683,\cdot)\) \(\chi_{3840}(2707,\cdot)\) \(\chi_{3840}(2923,\cdot)\) \(\chi_{3840}(2947,\cdot)\) \(\chi_{3840}(3163,\cdot)\) \(\chi_{3840}(3187,\cdot)\) \(\chi_{3840}(3403,\cdot)\) \(\chi_{3840}(3427,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((-1,e\left(\frac{61}{64}\right),1,-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3840 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) |