Basic properties
| Modulus: | \(5610\) | |
| Conductor: | \(561\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{561}(14,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fd
\(\chi_{5610}(71,\cdot)\) \(\chi_{5610}(311,\cdot)\) \(\chi_{5610}(401,\cdot)\) \(\chi_{5610}(521,\cdot)\) \(\chi_{5610}(581,\cdot)\) \(\chi_{5610}(641,\cdot)\) \(\chi_{5610}(911,\cdot)\) \(\chi_{5610}(1061,\cdot)\) \(\chi_{5610}(1391,\cdot)\) \(\chi_{5610}(1571,\cdot)\) \(\chi_{5610}(1841,\cdot)\) \(\chi_{5610}(1901,\cdot)\) \(\chi_{5610}(1961,\cdot)\) \(\chi_{5610}(2051,\cdot)\) \(\chi_{5610}(2171,\cdot)\) \(\chi_{5610}(2561,\cdot)\) \(\chi_{5610}(2621,\cdot)\) \(\chi_{5610}(2951,\cdot)\) \(\chi_{5610}(3371,\cdot)\) \(\chi_{5610}(3491,\cdot)\) \(\chi_{5610}(3611,\cdot)\) \(\chi_{5610}(3701,\cdot)\) \(\chi_{5610}(3881,\cdot)\) \(\chi_{5610}(3941,\cdot)\) \(\chi_{5610}(4151,\cdot)\) \(\chi_{5610}(4211,\cdot)\) \(\chi_{5610}(4481,\cdot)\) \(\chi_{5610}(4601,\cdot)\) \(\chi_{5610}(5021,\cdot)\) \(\chi_{5610}(5141,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,1,e\left(\frac{4}{5}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(3941, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) |