Basic properties
Modulus: | \(5610\) | |
Conductor: | \(2805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2805}(1448,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fb
\(\chi_{5610}(173,\cdot)\) \(\chi_{5610}(227,\cdot)\) \(\chi_{5610}(233,\cdot)\) \(\chi_{5610}(347,\cdot)\) \(\chi_{5610}(413,\cdot)\) \(\chi_{5610}(743,\cdot)\) \(\chi_{5610}(827,\cdot)\) \(\chi_{5610}(1217,\cdot)\) \(\chi_{5610}(1337,\cdot)\) \(\chi_{5610}(1493,\cdot)\) \(\chi_{5610}(1757,\cdot)\) \(\chi_{5610}(1877,\cdot)\) \(\chi_{5610}(1943,\cdot)\) \(\chi_{5610}(2213,\cdot)\) \(\chi_{5610}(2273,\cdot)\) \(\chi_{5610}(2723,\cdot)\) \(\chi_{5610}(2747,\cdot)\) \(\chi_{5610}(2867,\cdot)\) \(\chi_{5610}(3407,\cdot)\) \(\chi_{5610}(3473,\cdot)\) \(\chi_{5610}(3533,\cdot)\) \(\chi_{5610}(3797,\cdot)\) \(\chi_{5610}(3803,\cdot)\) \(\chi_{5610}(4043,\cdot)\) \(\chi_{5610}(4253,\cdot)\) \(\chi_{5610}(4307,\cdot)\) \(\chi_{5610}(4397,\cdot)\) \(\chi_{5610}(4787,\cdot)\) \(\chi_{5610}(5297,\cdot)\) \(\chi_{5610}(5447,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,-i,e\left(\frac{7}{10}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(4253, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{10}\right)\) |