Properties

Label 11.131
Level 1111
Weight 00
Character 11.1
Symmetry even
RR 13.46378
Fricke sign +1+1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 13.4637893382526451096086714008±210813.4637893382526451096086714008 \pm 2 \cdot 10^{-8}

Maass form coefficients

The coefficients here are shown to at most 88 digits of precision. Full precision coefficients are available in the downloads.

a1=+1a_{1}= +1 a2=1.17423596±1.5107a_{2}= -1.17423596 \pm 1.5 \cdot 10^{-7} a3=0.13743090±1.6107a_{3}= -0.13743090 \pm 1.6 \cdot 10^{-7}
a4=+0.37883010±1.1107a_{4}= +0.37883010 \pm 1.1 \cdot 10^{-7} a5=0.32132566±1.2107a_{5}= -0.32132566 \pm 1.2 \cdot 10^{-7} a6=+0.16137630±1.7107a_{6}= +0.16137630 \pm 1.7 \cdot 10^{-7}
a7=0.60231504±9.5108a_{7}= -0.60231504 \pm 9.5 \cdot 10^{-8} a8=+0.72940004±1.5107a_{8}= +0.72940004 \pm 1.5 \cdot 10^{-7} a9=0.98111275±1.6107a_{9}= -0.98111275 \pm 1.6 \cdot 10^{-7}
a10=+0.37731214±1.4107a_{10}= +0.37731214 \pm 1.4 \cdot 10^{-7} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=0.05206296±1.0107a_{12}= -0.05206296 \pm 1.0 \cdot 10^{-7}
a13=+0.89969709±1.3107a_{13}= +0.89969709 \pm 1.3 \cdot 10^{-7} a14=+0.70725998±1.0107a_{14}= +0.70725998 \pm 1.0 \cdot 10^{-7} a15=+0.04416007±1.3107a_{15}= +0.04416007 \pm 1.3 \cdot 10^{-7}
a16=1.23531785±1.6107a_{16}= -1.23531785 \pm 1.6 \cdot 10^{-7} a17=0.40030830±1.1107a_{17}= -0.40030830 \pm 1.1 \cdot 10^{-7} a18=+1.15205787±1.6107a_{18}= +1.15205787 \pm 1.6 \cdot 10^{-7}
a19=1.02579385±1.2107a_{19}= -1.02579385 \pm 1.2 \cdot 10^{-7} a20=0.12172783±1.4107a_{20}= -0.12172783 \pm 1.4 \cdot 10^{-7} a21=+0.08277670±1.3107a_{21}= +0.08277670 \pm 1.3 \cdot 10^{-7}
a22=+0.35404546±1.6107a_{22}= +0.35404546 \pm 1.6 \cdot 10^{-7} a23=1.50816262±1.2107a_{23}= -1.50816262 \pm 1.2 \cdot 10^{-7} a24=0.10024210±1.6107a_{24}= -0.10024210 \pm 1.6 \cdot 10^{-7}
a25=0.89674982±1.0107a_{25}= -0.89674982 \pm 1.0 \cdot 10^{-7} a26=1.05645667±1.4107a_{26}= -1.05645667 \pm 1.4 \cdot 10^{-7} a27=+0.27226611±1.0107a_{27}= +0.27226611 \pm 1.0 \cdot 10^{-7}
a28=0.22817506±7.6108a_{28}= -0.22817506 \pm 7.6 \cdot 10^{-8} a29=1.24812960±1.4107a_{29}= -1.24812960 \pm 1.4 \cdot 10^{-7} a30=0.05185435±1.4107a_{30}= -0.05185435 \pm 1.4 \cdot 10^{-7}
a31=1.15178777±1.1107a_{31}= -1.15178777 \pm 1.1 \cdot 10^{-7} a32=+0.72115461±1.0107a_{32}= +0.72115461 \pm 1.0 \cdot 10^{-7} a33=+0.04143698±1.7107a_{33}= +0.04143698 \pm 1.7 \cdot 10^{-7}
a34=+0.47005641±1.1107a_{34}= +0.47005641 \pm 1.1 \cdot 10^{-7} a35=+0.19353928±8.1108a_{35}= +0.19353928 \pm 8.1 \cdot 10^{-8} a36=0.37167504±7.7108a_{36}= -0.37167504 \pm 7.7 \cdot 10^{-8}
a37=0.00309026±1.2107a_{37}= -0.00309026 \pm 1.2 \cdot 10^{-7} a38=+1.20452403±1.2107a_{38}= +1.20452403 \pm 1.2 \cdot 10^{-7} a39=0.12364618±1.2107a_{39}= -0.12364618 \pm 1.2 \cdot 10^{-7}
a40=0.23437495±1.6107a_{40}= -0.23437495 \pm 1.6 \cdot 10^{-7} a41=+0.50626780±1.4107a_{41}= +0.50626780 \pm 1.4 \cdot 10^{-7} a42=0.09719937±1.4107a_{42}= -0.09719937 \pm 1.4 \cdot 10^{-7}
a43=+1.41103813±1.1107a_{43}= +1.41103813 \pm 1.1 \cdot 10^{-7} a44=0.11422157±1.2107a_{44}= -0.11422157 \pm 1.2 \cdot 10^{-7} a45=+0.31525670±1.2107a_{45}= +0.31525670 \pm 1.2 \cdot 10^{-7}
a46=+1.77093879±1.3107a_{46}= +1.77093879 \pm 1.3 \cdot 10^{-7} a47=+0.85264322±1.4107a_{47}= +0.85264322 \pm 1.4 \cdot 10^{-7} a48=+0.16977084±1.8107a_{48}= +0.16977084 \pm 1.8 \cdot 10^{-7}
a49=0.63721660±9.9108a_{49}= -0.63721660 \pm 9.9 \cdot 10^{-8} a50=+1.05299589±1.2107a_{50}= +1.05299589 \pm 1.2 \cdot 10^{-7} a51=+0.05501473±1.3107a_{51}= +0.05501473 \pm 1.3 \cdot 10^{-7}
a52=+0.34083233±6.7108a_{52}= +0.34083233 \pm 6.7 \cdot 10^{-8} a53=0.74661814±1.4107a_{53}= -0.74661814 \pm 1.4 \cdot 10^{-7} a54=0.31970465±1.2107a_{54}= -0.31970465 \pm 1.2 \cdot 10^{-7}
a55=+0.09688333±1.3107a_{55}= +0.09688333 \pm 1.3 \cdot 10^{-7} a56=0.43932861±1.0107a_{56}= -0.43932861 \pm 1.0 \cdot 10^{-7} a57=+0.14097577±1.6107a_{57}= +0.14097577 \pm 1.6 \cdot 10^{-7}
a58=+1.46559866±1.5107a_{58}= +1.46559866 \pm 1.5 \cdot 10^{-7} a59=0.29293821±1.8107a_{59}= -0.29293821 \pm 1.8 \cdot 10^{-7} a60=+0.01672917±1.3107a_{60}= +0.01672917 \pm 1.3 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000