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 \(\chi_{935}(878,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fa
\(\chi_{5610}(37,\cdot)\) \(\chi_{5610}(97,\cdot)\) \(\chi_{5610}(163,\cdot)\) \(\chi_{5610}(313,\cdot)\) \(\chi_{5610}(823,\cdot)\) \(\chi_{5610}(1213,\cdot)\) \(\chi_{5610}(1303,\cdot)\) \(\chi_{5610}(1357,\cdot)\) \(\chi_{5610}(1567,\cdot)\) \(\chi_{5610}(1807,\cdot)\) \(\chi_{5610}(1813,\cdot)\) \(\chi_{5610}(2077,\cdot)\) \(\chi_{5610}(2137,\cdot)\) \(\chi_{5610}(2203,\cdot)\) \(\chi_{5610}(2743,\cdot)\) \(\chi_{5610}(2863,\cdot)\) \(\chi_{5610}(2887,\cdot)\) \(\chi_{5610}(3337,\cdot)\) \(\chi_{5610}(3397,\cdot)\) \(\chi_{5610}(3667,\cdot)\) \(\chi_{5610}(3733,\cdot)\) \(\chi_{5610}(3853,\cdot)\) \(\chi_{5610}(4117,\cdot)\) \(\chi_{5610}(4273,\cdot)\) \(\chi_{5610}(4393,\cdot)\) \(\chi_{5610}(4783,\cdot)\) \(\chi_{5610}(4867,\cdot)\) \(\chi_{5610}(5197,\cdot)\) \(\chi_{5610}(5263,\cdot)\) \(\chi_{5610}(5377,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((1,-i,e\left(\frac{3}{5}\right),e\left(\frac{7}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(1813, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) |