Basic properties
Modulus: | \(1600\) | |
Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1600.cs
\(\chi_{1600}(67,\cdot)\) \(\chi_{1600}(123,\cdot)\) \(\chi_{1600}(147,\cdot)\) \(\chi_{1600}(203,\cdot)\) \(\chi_{1600}(227,\cdot)\) \(\chi_{1600}(283,\cdot)\) \(\chi_{1600}(363,\cdot)\) \(\chi_{1600}(387,\cdot)\) \(\chi_{1600}(467,\cdot)\) \(\chi_{1600}(523,\cdot)\) \(\chi_{1600}(547,\cdot)\) \(\chi_{1600}(603,\cdot)\) \(\chi_{1600}(627,\cdot)\) \(\chi_{1600}(683,\cdot)\) \(\chi_{1600}(763,\cdot)\) \(\chi_{1600}(787,\cdot)\) \(\chi_{1600}(867,\cdot)\) \(\chi_{1600}(923,\cdot)\) \(\chi_{1600}(947,\cdot)\) \(\chi_{1600}(1003,\cdot)\) \(\chi_{1600}(1027,\cdot)\) \(\chi_{1600}(1083,\cdot)\) \(\chi_{1600}(1163,\cdot)\) \(\chi_{1600}(1187,\cdot)\) \(\chi_{1600}(1267,\cdot)\) \(\chi_{1600}(1323,\cdot)\) \(\chi_{1600}(1347,\cdot)\) \(\chi_{1600}(1403,\cdot)\) \(\chi_{1600}(1427,\cdot)\) \(\chi_{1600}(1483,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{1}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1600 }(1027, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) |