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 \(\chi_{2805}(167,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fk
\(\chi_{5610}(107,\cdot)\) \(\chi_{5610}(167,\cdot)\) \(\chi_{5610}(437,\cdot)\) \(\chi_{5610}(503,\cdot)\) \(\chi_{5610}(623,\cdot)\) \(\chi_{5610}(677,\cdot)\) \(\chi_{5610}(887,\cdot)\) \(\chi_{5610}(1163,\cdot)\) \(\chi_{5610}(1553,\cdot)\) \(\chi_{5610}(2063,\cdot)\) \(\chi_{5610}(2147,\cdot)\) \(\chi_{5610}(2153,\cdot)\) \(\chi_{5610}(2207,\cdot)\) \(\chi_{5610}(2417,\cdot)\) \(\chi_{5610}(2477,\cdot)\) \(\chi_{5610}(2543,\cdot)\) \(\chi_{5610}(2657,\cdot)\) \(\chi_{5610}(2987,\cdot)\) \(\chi_{5610}(3053,\cdot)\) \(\chi_{5610}(3203,\cdot)\) \(\chi_{5610}(3593,\cdot)\) \(\chi_{5610}(3713,\cdot)\) \(\chi_{5610}(3737,\cdot)\) \(\chi_{5610}(4187,\cdot)\) \(\chi_{5610}(4193,\cdot)\) \(\chi_{5610}(4457,\cdot)\) \(\chi_{5610}(4517,\cdot)\) \(\chi_{5610}(4583,\cdot)\) \(\chi_{5610}(4703,\cdot)\) \(\chi_{5610}(4967,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,i,e\left(\frac{1}{10}\right),e\left(\frac{9}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(167, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) |