Basic properties
| Modulus: | \(6400\) | |
| 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 \(\chi_{1280}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.cy
\(\chi_{6400}(149,\cdot)\) \(\chi_{6400}(349,\cdot)\) \(\chi_{6400}(549,\cdot)\) \(\chi_{6400}(749,\cdot)\) \(\chi_{6400}(949,\cdot)\) \(\chi_{6400}(1149,\cdot)\) \(\chi_{6400}(1349,\cdot)\) \(\chi_{6400}(1549,\cdot)\) \(\chi_{6400}(1749,\cdot)\) \(\chi_{6400}(1949,\cdot)\) \(\chi_{6400}(2149,\cdot)\) \(\chi_{6400}(2349,\cdot)\) \(\chi_{6400}(2549,\cdot)\) \(\chi_{6400}(2749,\cdot)\) \(\chi_{6400}(2949,\cdot)\) \(\chi_{6400}(3149,\cdot)\) \(\chi_{6400}(3349,\cdot)\) \(\chi_{6400}(3549,\cdot)\) \(\chi_{6400}(3749,\cdot)\) \(\chi_{6400}(3949,\cdot)\) \(\chi_{6400}(4149,\cdot)\) \(\chi_{6400}(4349,\cdot)\) \(\chi_{6400}(4549,\cdot)\) \(\chi_{6400}(4749,\cdot)\) \(\chi_{6400}(4949,\cdot)\) \(\chi_{6400}(5149,\cdot)\) \(\chi_{6400}(5349,\cdot)\) \(\chi_{6400}(5549,\cdot)\) \(\chi_{6400}(5749,\cdot)\) \(\chi_{6400}(5949,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{13}{64}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) |