Basic properties
| Modulus: | \(4224\) | |
| Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{704}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4224.df
\(\chi_{4224}(103,\cdot)\) \(\chi_{4224}(247,\cdot)\) \(\chi_{4224}(295,\cdot)\) \(\chi_{4224}(487,\cdot)\) \(\chi_{4224}(631,\cdot)\) \(\chi_{4224}(775,\cdot)\) \(\chi_{4224}(823,\cdot)\) \(\chi_{4224}(1015,\cdot)\) \(\chi_{4224}(1159,\cdot)\) \(\chi_{4224}(1303,\cdot)\) \(\chi_{4224}(1351,\cdot)\) \(\chi_{4224}(1543,\cdot)\) \(\chi_{4224}(1687,\cdot)\) \(\chi_{4224}(1831,\cdot)\) \(\chi_{4224}(1879,\cdot)\) \(\chi_{4224}(2071,\cdot)\) \(\chi_{4224}(2215,\cdot)\) \(\chi_{4224}(2359,\cdot)\) \(\chi_{4224}(2407,\cdot)\) \(\chi_{4224}(2599,\cdot)\) \(\chi_{4224}(2743,\cdot)\) \(\chi_{4224}(2887,\cdot)\) \(\chi_{4224}(2935,\cdot)\) \(\chi_{4224}(3127,\cdot)\) \(\chi_{4224}(3271,\cdot)\) \(\chi_{4224}(3415,\cdot)\) \(\chi_{4224}(3463,\cdot)\) \(\chi_{4224}(3655,\cdot)\) \(\chi_{4224}(3799,\cdot)\) \(\chi_{4224}(3943,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2047,133,1409,3841)\) → \((-1,e\left(\frac{1}{16}\right),1,e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4224 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{31}{80}\right)\) |