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.cr
\(\chi_{1600}(21,\cdot)\) \(\chi_{1600}(61,\cdot)\) \(\chi_{1600}(141,\cdot)\) \(\chi_{1600}(181,\cdot)\) \(\chi_{1600}(221,\cdot)\) \(\chi_{1600}(261,\cdot)\) \(\chi_{1600}(341,\cdot)\) \(\chi_{1600}(381,\cdot)\) \(\chi_{1600}(421,\cdot)\) \(\chi_{1600}(461,\cdot)\) \(\chi_{1600}(541,\cdot)\) \(\chi_{1600}(581,\cdot)\) \(\chi_{1600}(621,\cdot)\) \(\chi_{1600}(661,\cdot)\) \(\chi_{1600}(741,\cdot)\) \(\chi_{1600}(781,\cdot)\) \(\chi_{1600}(821,\cdot)\) \(\chi_{1600}(861,\cdot)\) \(\chi_{1600}(941,\cdot)\) \(\chi_{1600}(981,\cdot)\) \(\chi_{1600}(1021,\cdot)\) \(\chi_{1600}(1061,\cdot)\) \(\chi_{1600}(1141,\cdot)\) \(\chi_{1600}(1181,\cdot)\) \(\chi_{1600}(1221,\cdot)\) \(\chi_{1600}(1261,\cdot)\) \(\chi_{1600}(1341,\cdot)\) \(\chi_{1600}(1381,\cdot)\) \(\chi_{1600}(1421,\cdot)\) \(\chi_{1600}(1461,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1600 }(741, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) |