Properties

Label 11.79
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 10.64668
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(10.6466817416048577250326557316 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.15875754 \pm 9.3 \cdot 10^{-8} \) \(a_{3}= -1.50974332 \pm 9.9 \cdot 10^{-8} \)
\(a_{4}= -0.97479604 \pm 6.9 \cdot 10^{-8} \) \(a_{5}= -0.87992865 \pm 7.3 \cdot 10^{-8} \) \(a_{6}= +0.23968314 \pm 1.0 \cdot 10^{-7} \)
\(a_{7}= +1.72672168 \pm 5.7 \cdot 10^{-8} \) \(a_{8}= +0.31351376 \pm 9.4 \cdot 10^{-8} \) \(a_{9}= +1.27932489 \pm 1.0 \cdot 10^{-7} \)
\(a_{10}= +0.13969531 \pm 8.5 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.47169181 \pm 6.5 \cdot 10^{-8} \)
\(a_{13}= -1.27847499 \pm 8.2 \cdot 10^{-8} \) \(a_{14}= -0.27413009 \pm 6.6 \cdot 10^{-8} \) \(a_{15}= +1.32846640 \pm 8.1 \cdot 10^{-8} \)
\(a_{16}= +0.92502337 \pm 9.8 \cdot 10^{-8} \) \(a_{17}= +0.98531391 \pm 7.2 \cdot 10^{-8} \) \(a_{18}= -0.20310247 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= -0.37115082 \pm 7.7 \cdot 10^{-8} \) \(a_{20}= +0.85775097 \pm 9.0 \cdot 10^{-8} \) \(a_{21}= -2.60690652 \pm 8.0 \cdot 10^{-8} \)
\(a_{22}= -0.04786720 \pm 1.0 \cdot 10^{-7} \) \(a_{23}= +0.64628233 \pm 7.4 \cdot 10^{-8} \) \(a_{24}= -0.47332531 \pm 9.8 \cdot 10^{-8} \)
\(a_{25}= -0.22572557 \pm 6.5 \cdot 10^{-8} \) \(a_{26}= +0.20296755 \pm 9.0 \cdot 10^{-8} \) \(a_{27}= -0.42170889 \pm 6.3 \cdot 10^{-8} \)
\(a_{28}= -1.68320146 \pm 4.6 \cdot 10^{-8} \) \(a_{29}= -1.02522627 \pm 8.9 \cdot 10^{-8} \) \(a_{30}= -0.21090406 \pm 8.6 \cdot 10^{-8} \)
\(a_{31}= +1.56938848 \pm 6.9 \cdot 10^{-8} \) \(a_{32}= -0.46036820 \pm 6.2 \cdot 10^{-8} \) \(a_{33}= -0.45520474 \pm 1.0 \cdot 10^{-7} \)
\(a_{34}= -0.15642601 \pm 7.0 \cdot 10^{-8} \) \(a_{35}= -1.51939188 \pm 4.9 \cdot 10^{-8} \) \(a_{36}= -1.24708084 \pm 4.7 \cdot 10^{-8} \)
\(a_{37}= -0.21412008 \pm 7.3 \cdot 10^{-8} \) \(a_{38}= +0.05892299 \pm 7.6 \cdot 10^{-8} \) \(a_{39}= +1.93016907 \pm 7.3 \cdot 10^{-8} \)
\(a_{40}= -0.27586974 \pm 9.7 \cdot 10^{-8} \) \(a_{41}= +0.12113544 \pm 8.5 \cdot 10^{-8} \) \(a_{42}= +0.41386607 \pm 8.9 \cdot 10^{-8} \)
\(a_{43}= +0.65982502 \pm 7.1 \cdot 10^{-8} \) \(a_{44}= -0.29391207 \pm 7.9 \cdot 10^{-8} \) \(a_{45}= -1.12571463 \pm 7.5 \cdot 10^{-8} \)
\(a_{46}= -0.10260219 \pm 8.4 \cdot 10^{-8} \) \(a_{47}= -0.96200393 \pm 8.8 \cdot 10^{-8} \) \(a_{48}= -1.39654785 \pm 1.1 \cdot 10^{-7} \)
\(a_{49}= +1.98156776 \pm 6.0 \cdot 10^{-8} \) \(a_{50}= +0.03583564 \pm 7.3 \cdot 10^{-8} \) \(a_{51}= -1.48757109 \pm 8.2 \cdot 10^{-8} \)
\(a_{52}= +1.24625236 \pm 4.1 \cdot 10^{-8} \) \(a_{53}= -0.37182494 \pm 9.1 \cdot 10^{-8} \) \(a_{54}= +0.06694947 \pm 7.6 \cdot 10^{-8} \)
\(a_{55}= -0.26530847 \pm 8.4 \cdot 10^{-8} \) \(a_{56}= +0.54135101 \pm 6.1 \cdot 10^{-8} \) \(a_{57}= +0.56034247 \pm 1.0 \cdot 10^{-7} \)
\(a_{58}= +0.16276240 \pm 9.3 \cdot 10^{-8} \) \(a_{59}= +0.97910691 \pm 1.1 \cdot 10^{-7} \) \(a_{60}= -1.29498379 \pm 8.4 \cdot 10^{-8} \)

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