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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1600.ct
\(\chi_{1600}(53,\cdot)\) \(\chi_{1600}(77,\cdot)\) \(\chi_{1600}(133,\cdot)\) \(\chi_{1600}(213,\cdot)\) \(\chi_{1600}(237,\cdot)\) \(\chi_{1600}(317,\cdot)\) \(\chi_{1600}(373,\cdot)\) \(\chi_{1600}(397,\cdot)\) \(\chi_{1600}(453,\cdot)\) \(\chi_{1600}(477,\cdot)\) \(\chi_{1600}(533,\cdot)\) \(\chi_{1600}(613,\cdot)\) \(\chi_{1600}(637,\cdot)\) \(\chi_{1600}(717,\cdot)\) \(\chi_{1600}(773,\cdot)\) \(\chi_{1600}(797,\cdot)\) \(\chi_{1600}(853,\cdot)\) \(\chi_{1600}(877,\cdot)\) \(\chi_{1600}(933,\cdot)\) \(\chi_{1600}(1013,\cdot)\) \(\chi_{1600}(1037,\cdot)\) \(\chi_{1600}(1117,\cdot)\) \(\chi_{1600}(1173,\cdot)\) \(\chi_{1600}(1197,\cdot)\) \(\chi_{1600}(1253,\cdot)\) \(\chi_{1600}(1277,\cdot)\) \(\chi_{1600}(1333,\cdot)\) \(\chi_{1600}(1413,\cdot)\) \(\chi_{1600}(1437,\cdot)\) \(\chi_{1600}(1517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((1,e\left(\frac{5}{16}\right),e\left(\frac{7}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1600 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{80}\right)\) |