Properties

Label 11.86
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 11.14723
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(11.1472353004277571201830219459 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.93346949 \pm 1.1 \cdot 10^{-7} \) \(a_{3}= +0.62589405 \pm 1.2 \cdot 10^{-7} \)
\(a_{4}= +2.73830428 \pm 8.7 \cdot 10^{-8} \) \(a_{5}= +1.16458706 \pm 9.3 \cdot 10^{-8} \) \(a_{6}= -1.21014706 \pm 1.3 \cdot 10^{-7} \)
\(a_{7}= +0.43442801 \pm 7.3 \cdot 10^{-8} \) \(a_{8}= -3.36095830 \pm 1.1 \cdot 10^{-7} \) \(a_{9}= -0.60825663 \pm 1.2 \cdot 10^{-7} \)
\(a_{10}= -2.25169356 \pm 1.0 \cdot 10^{-7} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.71388837 \pm 8.2 \cdot 10^{-8} \)
\(a_{13}= -0.89466811 \pm 1.0 \cdot 10^{-7} \) \(a_{14}= -0.83995331 \pm 8.4 \cdot 10^{-8} \) \(a_{15}= +0.72890812 \pm 1.0 \cdot 10^{-7} \)
\(a_{16}= +3.76000606 \pm 1.2 \cdot 10^{-7} \) \(a_{17}= -0.09690602 \pm 9.2 \cdot 10^{-8} \) \(a_{18}= +1.17604565 \pm 1.3 \cdot 10^{-7} \)
\(a_{19}= -1.51591912 \pm 9.8 \cdot 10^{-8} \) \(a_{20}= +3.18899374 \pm 1.1 \cdot 10^{-7} \) \(a_{21}= +0.27190591 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= -0.58296299 \pm 1.2 \cdot 10^{-7} \) \(a_{23}= -0.90296129 \pm 9.4 \cdot 10^{-8} \) \(a_{24}= -2.10360382 \pm 1.2 \cdot 10^{-7} \)
\(a_{25}= +0.35626303 \pm 8.3 \cdot 10^{-8} \) \(a_{26}= +1.72981350 \pm 1.1 \cdot 10^{-7} \) \(a_{27}= -1.00659826 \pm 8.1 \cdot 10^{-8} \)
\(a_{28}= +1.18959609 \pm 5.9 \cdot 10^{-8} \) \(a_{29}= -0.77054171 \pm 1.1 \cdot 10^{-7} \) \(a_{30}= -1.40932161 \pm 1.0 \cdot 10^{-7} \)
\(a_{31}= +0.81396168 \pm 8.8 \cdot 10^{-8} \) \(a_{32}= -3.90889872 \pm 7.9 \cdot 10^{-8} \) \(a_{33}= +0.18871416 \pm 1.3 \cdot 10^{-7} \)
\(a_{34}= +0.18736484 \pm 8.8 \cdot 10^{-8} \) \(a_{35}= +0.50592924 \pm 6.2 \cdot 10^{-8} \) \(a_{36}= -1.66559175 \pm 5.9 \cdot 10^{-8} \)
\(a_{37}= +1.52071528 \pm 9.3 \cdot 10^{-8} \) \(a_{38}= +2.93098337 \pm 9.6 \cdot 10^{-8} \) \(a_{39}= -0.55996745 \pm 9.3 \cdot 10^{-8} \)
\(a_{40}= -3.91412856 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -1.15877393 \pm 1.0 \cdot 10^{-7} \) \(a_{42}= -0.52572178 \pm 1.1 \cdot 10^{-7} \)
\(a_{43}= +1.18166369 \pm 9.0 \cdot 10^{-8} \) \(a_{44}= +0.82562981 \pm 9.8 \cdot 10^{-8} \) \(a_{45}= -0.70836781 \pm 9.5 \cdot 10^{-8} \)
\(a_{46}= +1.74584811 \pm 1.0 \cdot 10^{-7} \) \(a_{47}= -1.10413803 \pm 1.1 \cdot 10^{-7} \) \(a_{48}= +2.35336544 \pm 1.4 \cdot 10^{-7} \)
\(a_{49}= -0.81127230 \pm 7.6 \cdot 10^{-8} \) \(a_{50}= -0.68882370 \pm 9.2 \cdot 10^{-8} \) \(a_{51}= -0.06065290 \pm 1.0 \cdot 10^{-7} \)
\(a_{52}= -2.44987351 \pm 5.1 \cdot 10^{-8} \) \(a_{53}= -0.75526324 \pm 1.1 \cdot 10^{-7} \) \(a_{54}= +1.94622704 \pm 9.6 \cdot 10^{-8} \)
\(a_{55}= +0.35113621 \pm 1.0 \cdot 10^{-7} \) \(a_{56}= -1.46009444 \pm 7.7 \cdot 10^{-8} \) \(a_{57}= -0.94880476 \pm 1.2 \cdot 10^{-7} \)
\(a_{58}= +1.48981888 \pm 1.1 \cdot 10^{-7} \) \(a_{59}= -0.24035578 \pm 1.4 \cdot 10^{-7} \) \(a_{60}= +1.99597222 \pm 1.0 \cdot 10^{-7} \)

Displaying $a_n$ with $n$ up to: 60 180 1000