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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3840.dt
\(\chi_{3840}(83,\cdot)\) \(\chi_{3840}(107,\cdot)\) \(\chi_{3840}(323,\cdot)\) \(\chi_{3840}(347,\cdot)\) \(\chi_{3840}(563,\cdot)\) \(\chi_{3840}(587,\cdot)\) \(\chi_{3840}(803,\cdot)\) \(\chi_{3840}(827,\cdot)\) \(\chi_{3840}(1043,\cdot)\) \(\chi_{3840}(1067,\cdot)\) \(\chi_{3840}(1283,\cdot)\) \(\chi_{3840}(1307,\cdot)\) \(\chi_{3840}(1523,\cdot)\) \(\chi_{3840}(1547,\cdot)\) \(\chi_{3840}(1763,\cdot)\) \(\chi_{3840}(1787,\cdot)\) \(\chi_{3840}(2003,\cdot)\) \(\chi_{3840}(2027,\cdot)\) \(\chi_{3840}(2243,\cdot)\) \(\chi_{3840}(2267,\cdot)\) \(\chi_{3840}(2483,\cdot)\) \(\chi_{3840}(2507,\cdot)\) \(\chi_{3840}(2723,\cdot)\) \(\chi_{3840}(2747,\cdot)\) \(\chi_{3840}(2963,\cdot)\) \(\chi_{3840}(2987,\cdot)\) \(\chi_{3840}(3203,\cdot)\) \(\chi_{3840}(3227,\cdot)\) \(\chi_{3840}(3443,\cdot)\) \(\chi_{3840}(3467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((-1,e\left(\frac{19}{64}\right),-1,-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3840 }(2243, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) |