Basic properties
| Modulus: | \(4800\) | |
| 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 \(\chi_{1600}(1483,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.fl
\(\chi_{4800}(67,\cdot)\) \(\chi_{4800}(283,\cdot)\) \(\chi_{4800}(523,\cdot)\) \(\chi_{4800}(547,\cdot)\) \(\chi_{4800}(763,\cdot)\) \(\chi_{4800}(787,\cdot)\) \(\chi_{4800}(1003,\cdot)\) \(\chi_{4800}(1027,\cdot)\) \(\chi_{4800}(1267,\cdot)\) \(\chi_{4800}(1483,\cdot)\) \(\chi_{4800}(1723,\cdot)\) \(\chi_{4800}(1747,\cdot)\) \(\chi_{4800}(1963,\cdot)\) \(\chi_{4800}(1987,\cdot)\) \(\chi_{4800}(2203,\cdot)\) \(\chi_{4800}(2227,\cdot)\) \(\chi_{4800}(2467,\cdot)\) \(\chi_{4800}(2683,\cdot)\) \(\chi_{4800}(2923,\cdot)\) \(\chi_{4800}(2947,\cdot)\) \(\chi_{4800}(3163,\cdot)\) \(\chi_{4800}(3187,\cdot)\) \(\chi_{4800}(3403,\cdot)\) \(\chi_{4800}(3427,\cdot)\) \(\chi_{4800}(3667,\cdot)\) \(\chi_{4800}(3883,\cdot)\) \(\chi_{4800}(4123,\cdot)\) \(\chi_{4800}(4147,\cdot)\) \(\chi_{4800}(4363,\cdot)\) \(\chi_{4800}(4387,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((-1,e\left(\frac{5}{16}\right),1,e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4800 }(1483, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) |