Basic properties
| Modulus: | \(6400\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1600}(547,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.di
\(\chi_{6400}(47,\cdot)\) \(\chi_{6400}(367,\cdot)\) \(\chi_{6400}(463,\cdot)\) \(\chi_{6400}(687,\cdot)\) \(\chi_{6400}(783,\cdot)\) \(\chi_{6400}(1103,\cdot)\) \(\chi_{6400}(1327,\cdot)\) \(\chi_{6400}(1423,\cdot)\) \(\chi_{6400}(1647,\cdot)\) \(\chi_{6400}(1967,\cdot)\) \(\chi_{6400}(2063,\cdot)\) \(\chi_{6400}(2287,\cdot)\) \(\chi_{6400}(2383,\cdot)\) \(\chi_{6400}(2703,\cdot)\) \(\chi_{6400}(2927,\cdot)\) \(\chi_{6400}(3023,\cdot)\) \(\chi_{6400}(3247,\cdot)\) \(\chi_{6400}(3567,\cdot)\) \(\chi_{6400}(3663,\cdot)\) \(\chi_{6400}(3887,\cdot)\) \(\chi_{6400}(3983,\cdot)\) \(\chi_{6400}(4303,\cdot)\) \(\chi_{6400}(4527,\cdot)\) \(\chi_{6400}(4623,\cdot)\) \(\chi_{6400}(4847,\cdot)\) \(\chi_{6400}(5167,\cdot)\) \(\chi_{6400}(5263,\cdot)\) \(\chi_{6400}(5487,\cdot)\) \(\chi_{6400}(5583,\cdot)\) \(\chi_{6400}(5903,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,4101,5377)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) |