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.dy
\(\chi_{3840}(29,\cdot)\) \(\chi_{3840}(149,\cdot)\) \(\chi_{3840}(269,\cdot)\) \(\chi_{3840}(389,\cdot)\) \(\chi_{3840}(509,\cdot)\) \(\chi_{3840}(629,\cdot)\) \(\chi_{3840}(749,\cdot)\) \(\chi_{3840}(869,\cdot)\) \(\chi_{3840}(989,\cdot)\) \(\chi_{3840}(1109,\cdot)\) \(\chi_{3840}(1229,\cdot)\) \(\chi_{3840}(1349,\cdot)\) \(\chi_{3840}(1469,\cdot)\) \(\chi_{3840}(1589,\cdot)\) \(\chi_{3840}(1709,\cdot)\) \(\chi_{3840}(1829,\cdot)\) \(\chi_{3840}(1949,\cdot)\) \(\chi_{3840}(2069,\cdot)\) \(\chi_{3840}(2189,\cdot)\) \(\chi_{3840}(2309,\cdot)\) \(\chi_{3840}(2429,\cdot)\) \(\chi_{3840}(2549,\cdot)\) \(\chi_{3840}(2669,\cdot)\) \(\chi_{3840}(2789,\cdot)\) \(\chi_{3840}(2909,\cdot)\) \(\chi_{3840}(3029,\cdot)\) \(\chi_{3840}(3149,\cdot)\) \(\chi_{3840}(3269,\cdot)\) \(\chi_{3840}(3389,\cdot)\) \(\chi_{3840}(3509,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((1,e\left(\frac{9}{64}\right),-1,-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3840 }(869, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) |