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 \(\chi_{1280}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3840.dx
\(\chi_{3840}(109,\cdot)\) \(\chi_{3840}(229,\cdot)\) \(\chi_{3840}(349,\cdot)\) \(\chi_{3840}(469,\cdot)\) \(\chi_{3840}(589,\cdot)\) \(\chi_{3840}(709,\cdot)\) \(\chi_{3840}(829,\cdot)\) \(\chi_{3840}(949,\cdot)\) \(\chi_{3840}(1069,\cdot)\) \(\chi_{3840}(1189,\cdot)\) \(\chi_{3840}(1309,\cdot)\) \(\chi_{3840}(1429,\cdot)\) \(\chi_{3840}(1549,\cdot)\) \(\chi_{3840}(1669,\cdot)\) \(\chi_{3840}(1789,\cdot)\) \(\chi_{3840}(1909,\cdot)\) \(\chi_{3840}(2029,\cdot)\) \(\chi_{3840}(2149,\cdot)\) \(\chi_{3840}(2269,\cdot)\) \(\chi_{3840}(2389,\cdot)\) \(\chi_{3840}(2509,\cdot)\) \(\chi_{3840}(2629,\cdot)\) \(\chi_{3840}(2749,\cdot)\) \(\chi_{3840}(2869,\cdot)\) \(\chi_{3840}(2989,\cdot)\) \(\chi_{3840}(3109,\cdot)\) \(\chi_{3840}(3229,\cdot)\) \(\chi_{3840}(3349,\cdot)\) \(\chi_{3840}(3469,\cdot)\) \(\chi_{3840}(3589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,2821,2561,1537)\) → \((1,e\left(\frac{55}{64}\right),1,-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3840 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) |