Basic properties
Modulus: | \(5610\) | |
Conductor: | \(935\) | 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 \(\chi_{935}(742,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fl
\(\chi_{5610}(367,\cdot)\) \(\chi_{5610}(487,\cdot)\) \(\chi_{5610}(643,\cdot)\) \(\chi_{5610}(907,\cdot)\) \(\chi_{5610}(1027,\cdot)\) \(\chi_{5610}(1093,\cdot)\) \(\chi_{5610}(1153,\cdot)\) \(\chi_{5610}(1417,\cdot)\) \(\chi_{5610}(1423,\cdot)\) \(\chi_{5610}(1873,\cdot)\) \(\chi_{5610}(1897,\cdot)\) \(\chi_{5610}(2017,\cdot)\) \(\chi_{5610}(2407,\cdot)\) \(\chi_{5610}(2557,\cdot)\) \(\chi_{5610}(2623,\cdot)\) \(\chi_{5610}(2953,\cdot)\) \(\chi_{5610}(3067,\cdot)\) \(\chi_{5610}(3133,\cdot)\) \(\chi_{5610}(3193,\cdot)\) \(\chi_{5610}(3403,\cdot)\) \(\chi_{5610}(3457,\cdot)\) \(\chi_{5610}(3463,\cdot)\) \(\chi_{5610}(3547,\cdot)\) \(\chi_{5610}(4057,\cdot)\) \(\chi_{5610}(4447,\cdot)\) \(\chi_{5610}(4723,\cdot)\) \(\chi_{5610}(4933,\cdot)\) \(\chi_{5610}(4987,\cdot)\) \(\chi_{5610}(5107,\cdot)\) \(\chi_{5610}(5173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((1,i,e\left(\frac{2}{5}\right),e\left(\frac{7}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(3547, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) |