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 \(\chi_{1600}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.ez
\(\chi_{4800}(163,\cdot)\) \(\chi_{4800}(187,\cdot)\) \(\chi_{4800}(403,\cdot)\) \(\chi_{4800}(427,\cdot)\) \(\chi_{4800}(667,\cdot)\) \(\chi_{4800}(883,\cdot)\) \(\chi_{4800}(1123,\cdot)\) \(\chi_{4800}(1147,\cdot)\) \(\chi_{4800}(1363,\cdot)\) \(\chi_{4800}(1387,\cdot)\) \(\chi_{4800}(1603,\cdot)\) \(\chi_{4800}(1627,\cdot)\) \(\chi_{4800}(1867,\cdot)\) \(\chi_{4800}(2083,\cdot)\) \(\chi_{4800}(2323,\cdot)\) \(\chi_{4800}(2347,\cdot)\) \(\chi_{4800}(2563,\cdot)\) \(\chi_{4800}(2587,\cdot)\) \(\chi_{4800}(2803,\cdot)\) \(\chi_{4800}(2827,\cdot)\) \(\chi_{4800}(3067,\cdot)\) \(\chi_{4800}(3283,\cdot)\) \(\chi_{4800}(3523,\cdot)\) \(\chi_{4800}(3547,\cdot)\) \(\chi_{4800}(3763,\cdot)\) \(\chi_{4800}(3787,\cdot)\) \(\chi_{4800}(4003,\cdot)\) \(\chi_{4800}(4027,\cdot)\) \(\chi_{4800}(4267,\cdot)\) \(\chi_{4800}(4483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((-1,e\left(\frac{11}{16}\right),1,e\left(\frac{19}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4800 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) |