Basic properties
Modulus: | \(2624\) | |
Conductor: | \(2624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2624.ep
\(\chi_{2624}(275,\cdot)\) \(\chi_{2624}(347,\cdot)\) \(\chi_{2624}(363,\cdot)\) \(\chi_{2624}(499,\cdot)\) \(\chi_{2624}(539,\cdot)\) \(\chi_{2624}(555,\cdot)\) \(\chi_{2624}(563,\cdot)\) \(\chi_{2624}(643,\cdot)\) \(\chi_{2624}(915,\cdot)\) \(\chi_{2624}(995,\cdot)\) \(\chi_{2624}(1051,\cdot)\) \(\chi_{2624}(1059,\cdot)\) \(\chi_{2624}(1083,\cdot)\) \(\chi_{2624}(1131,\cdot)\) \(\chi_{2624}(1163,\cdot)\) \(\chi_{2624}(1283,\cdot)\) \(\chi_{2624}(1587,\cdot)\) \(\chi_{2624}(1659,\cdot)\) \(\chi_{2624}(1675,\cdot)\) \(\chi_{2624}(1811,\cdot)\) \(\chi_{2624}(1851,\cdot)\) \(\chi_{2624}(1867,\cdot)\) \(\chi_{2624}(1875,\cdot)\) \(\chi_{2624}(1955,\cdot)\) \(\chi_{2624}(2227,\cdot)\) \(\chi_{2624}(2307,\cdot)\) \(\chi_{2624}(2363,\cdot)\) \(\chi_{2624}(2371,\cdot)\) \(\chi_{2624}(2395,\cdot)\) \(\chi_{2624}(2443,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(1083, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) |