Basic properties
| Modulus: | \(4224\) | |
| Conductor: | \(2112\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2112}(1229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4224.dj
\(\chi_{4224}(41,\cdot)\) \(\chi_{4224}(233,\cdot)\) \(\chi_{4224}(281,\cdot)\) \(\chi_{4224}(425,\cdot)\) \(\chi_{4224}(569,\cdot)\) \(\chi_{4224}(761,\cdot)\) \(\chi_{4224}(809,\cdot)\) \(\chi_{4224}(953,\cdot)\) \(\chi_{4224}(1097,\cdot)\) \(\chi_{4224}(1289,\cdot)\) \(\chi_{4224}(1337,\cdot)\) \(\chi_{4224}(1481,\cdot)\) \(\chi_{4224}(1625,\cdot)\) \(\chi_{4224}(1817,\cdot)\) \(\chi_{4224}(1865,\cdot)\) \(\chi_{4224}(2009,\cdot)\) \(\chi_{4224}(2153,\cdot)\) \(\chi_{4224}(2345,\cdot)\) \(\chi_{4224}(2393,\cdot)\) \(\chi_{4224}(2537,\cdot)\) \(\chi_{4224}(2681,\cdot)\) \(\chi_{4224}(2873,\cdot)\) \(\chi_{4224}(2921,\cdot)\) \(\chi_{4224}(3065,\cdot)\) \(\chi_{4224}(3209,\cdot)\) \(\chi_{4224}(3401,\cdot)\) \(\chi_{4224}(3449,\cdot)\) \(\chi_{4224}(3593,\cdot)\) \(\chi_{4224}(3737,\cdot)\) \(\chi_{4224}(3929,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2047,133,1409,3841)\) → \((1,e\left(\frac{15}{16}\right),-1,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4224 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{80}\right)\) |