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 \(\chi_{2805}(1754,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fg
\(\chi_{5610}(269,\cdot)\) \(\chi_{5610}(449,\cdot)\) \(\chi_{5610}(719,\cdot)\) \(\chi_{5610}(779,\cdot)\) \(\chi_{5610}(839,\cdot)\) \(\chi_{5610}(929,\cdot)\) \(\chi_{5610}(1049,\cdot)\) \(\chi_{5610}(1439,\cdot)\) \(\chi_{5610}(1499,\cdot)\) \(\chi_{5610}(1829,\cdot)\) \(\chi_{5610}(2249,\cdot)\) \(\chi_{5610}(2369,\cdot)\) \(\chi_{5610}(2489,\cdot)\) \(\chi_{5610}(2579,\cdot)\) \(\chi_{5610}(2759,\cdot)\) \(\chi_{5610}(2819,\cdot)\) \(\chi_{5610}(3029,\cdot)\) \(\chi_{5610}(3089,\cdot)\) \(\chi_{5610}(3359,\cdot)\) \(\chi_{5610}(3479,\cdot)\) \(\chi_{5610}(3899,\cdot)\) \(\chi_{5610}(4019,\cdot)\) \(\chi_{5610}(4349,\cdot)\) \(\chi_{5610}(4409,\cdot)\) \(\chi_{5610}(4559,\cdot)\) \(\chi_{5610}(4799,\cdot)\) \(\chi_{5610}(4889,\cdot)\) \(\chi_{5610}(5009,\cdot)\) \(\chi_{5610}(5069,\cdot)\) \(\chi_{5610}(5129,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(4559, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{20}\right)\) |