Basic properties
| Modulus: | \(5610\) | |
| Conductor: | \(935\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{935}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.ez
\(\chi_{5610}(7,\cdot)\) \(\chi_{5610}(73,\cdot)\) \(\chi_{5610}(343,\cdot)\) \(\chi_{5610}(403,\cdot)\) \(\chi_{5610}(853,\cdot)\) \(\chi_{5610}(877,\cdot)\) \(\chi_{5610}(997,\cdot)\) \(\chi_{5610}(1537,\cdot)\) \(\chi_{5610}(1603,\cdot)\) \(\chi_{5610}(1663,\cdot)\) \(\chi_{5610}(1927,\cdot)\) \(\chi_{5610}(1933,\cdot)\) \(\chi_{5610}(2173,\cdot)\) \(\chi_{5610}(2383,\cdot)\) \(\chi_{5610}(2437,\cdot)\) \(\chi_{5610}(2527,\cdot)\) \(\chi_{5610}(2917,\cdot)\) \(\chi_{5610}(3427,\cdot)\) \(\chi_{5610}(3577,\cdot)\) \(\chi_{5610}(3643,\cdot)\) \(\chi_{5610}(3703,\cdot)\) \(\chi_{5610}(3913,\cdot)\) \(\chi_{5610}(3967,\cdot)\) \(\chi_{5610}(3973,\cdot)\) \(\chi_{5610}(4087,\cdot)\) \(\chi_{5610}(4153,\cdot)\) \(\chi_{5610}(4483,\cdot)\) \(\chi_{5610}(4567,\cdot)\) \(\chi_{5610}(4957,\cdot)\) \(\chi_{5610}(5077,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((1,i,e\left(\frac{7}{10}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) |