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.cm
\(\chi_{1600}(3,\cdot)\) \(\chi_{1600}(27,\cdot)\) \(\chi_{1600}(83,\cdot)\) \(\chi_{1600}(163,\cdot)\) \(\chi_{1600}(187,\cdot)\) \(\chi_{1600}(267,\cdot)\) \(\chi_{1600}(323,\cdot)\) \(\chi_{1600}(347,\cdot)\) \(\chi_{1600}(403,\cdot)\) \(\chi_{1600}(427,\cdot)\) \(\chi_{1600}(483,\cdot)\) \(\chi_{1600}(563,\cdot)\) \(\chi_{1600}(587,\cdot)\) \(\chi_{1600}(667,\cdot)\) \(\chi_{1600}(723,\cdot)\) \(\chi_{1600}(747,\cdot)\) \(\chi_{1600}(803,\cdot)\) \(\chi_{1600}(827,\cdot)\) \(\chi_{1600}(883,\cdot)\) \(\chi_{1600}(963,\cdot)\) \(\chi_{1600}(987,\cdot)\) \(\chi_{1600}(1067,\cdot)\) \(\chi_{1600}(1123,\cdot)\) \(\chi_{1600}(1147,\cdot)\) \(\chi_{1600}(1203,\cdot)\) \(\chi_{1600}(1227,\cdot)\) \(\chi_{1600}(1283,\cdot)\) \(\chi_{1600}(1363,\cdot)\) \(\chi_{1600}(1387,\cdot)\) \(\chi_{1600}(1467,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{9}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1600 }(1387, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) |