Properties

Label 7.44
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 10.64569
Fricke sign +1+1

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Maass form invariants

Level: 7 7
Weight: 0 0
Character: 7.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 10.6456998610881626671684696437±10101110.6456998610881626671684696437 \pm 10 \cdot 10^{-11}

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=0.50376920±4.6107a_{2}= -0.50376920 \pm 4.6 \cdot 10^{-7} a3=1.80106382±3.0107a_{3}= -1.80106382 \pm 3.0 \cdot 10^{-7}
a4=0.74621660±2.7107a_{4}= -0.74621660 \pm 2.7 \cdot 10^{-7} a5=+1.49735757±3.2107a_{5}= +1.49735757 \pm 3.2 \cdot 10^{-7} a6=+0.90732047±3.6107a_{6}= +0.90732047 \pm 3.6 \cdot 10^{-7}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=+0.87969013±3.0107a_{8}= +0.87969013 \pm 3.0 \cdot 10^{-7} a9=+2.24383089±2.9107a_{9}= +2.24383089 \pm 2.9 \cdot 10^{-7}
a10=0.75432262±3.3107a_{10}= -0.75432262 \pm 3.3 \cdot 10^{-7} a11=0.34690316±2.7107a_{11}= -0.34690316 \pm 2.7 \cdot 10^{-7} a12=+1.34398372±2.4107a_{12}= +1.34398372 \pm 2.4 \cdot 10^{-7}
a13=+0.18010998±3.3107a_{13}= +0.18010998 \pm 3.3 \cdot 10^{-7} a14=+0.19040686±4.7107a_{14}= +0.19040686 \pm 4.7 \cdot 10^{-7} a15=2.69683655±2.5107a_{15}= -2.69683655 \pm 2.5 \cdot 10^{-7}
a16=+0.30305581±3.8107a_{16}= +0.30305581 \pm 3.8 \cdot 10^{-7} a17=+0.09654488±2.5107a_{17}= +0.09654488 \pm 2.5 \cdot 10^{-7} a18=1.13037288±2.7107a_{18}= -1.13037288 \pm 2.7 \cdot 10^{-7}
a19=0.38277255±3.2107a_{19}= -0.38277255 \pm 3.2 \cdot 10^{-7} a20=1.11735307±2.1107a_{20}= -1.11735307 \pm 2.1 \cdot 10^{-7} a21=+0.68073814±3.1107a_{21}= +0.68073814 \pm 3.1 \cdot 10^{-7}
a22=+0.17475913±2.7107a_{22}= +0.17475913 \pm 2.7 \cdot 10^{-7} a23=0.11414604±4.1107a_{23}= -0.11414604 \pm 4.1 \cdot 10^{-7} a24=1.58437807±2.0107a_{24}= -1.58437807 \pm 2.0 \cdot 10^{-7}
a25=+1.24207970±3.1107a_{25}= +1.24207970 \pm 3.1 \cdot 10^{-7} a26=0.09073386±4.1107a_{26}= -0.09073386 \pm 4.1 \cdot 10^{-7} a27=2.24021881±3.3107a_{27}= -2.24021881 \pm 3.3 \cdot 10^{-7}
a28=+0.28204336±2.8107a_{28}= +0.28204336 \pm 2.8 \cdot 10^{-7} a29=+0.26151215±3.0107a_{29}= +0.26151215 \pm 3.0 \cdot 10^{-7} a30=+1.35858318±2.9107a_{30}= +1.35858318 \pm 2.9 \cdot 10^{-7}
a31=+0.52560445±2.5107a_{31}= +0.52560445 \pm 2.5 \cdot 10^{-7} a32=1.03236031±4.0107a_{32}= -1.03236031 \pm 4.0 \cdot 10^{-7} a33=+0.62479474±2.3107a_{33}= +0.62479474 \pm 2.3 \cdot 10^{-7}
a34=0.04863634±2.9107a_{34}= -0.04863634 \pm 2.9 \cdot 10^{-7} a35=0.56594797±3.3107a_{35}= -0.56594797 \pm 3.3 \cdot 10^{-7} a36=1.67438385±1.6107a_{36}= -1.67438385 \pm 1.6 \cdot 10^{-7}
a37=+1.40023940±3.1107a_{37}= +1.40023940 \pm 3.1 \cdot 10^{-7} a38=+0.19282902±3.2107a_{38}= +0.19282902 \pm 3.2 \cdot 10^{-7} a39=0.32438958±2.5107a_{39}= -0.32438958 \pm 2.5 \cdot 10^{-7}
a40=+1.31721068±3.1107a_{40}= +1.31721068 \pm 3.1 \cdot 10^{-7} a41=1.71375614±4.0107a_{41}= -1.71375614 \pm 4.0 \cdot 10^{-7} a42=0.34293490±7.8107a_{42}= -0.34293490 \pm 7.8 \cdot 10^{-7}
a43=0.81463946±2.4107a_{43}= -0.81463946 \pm 2.4 \cdot 10^{-7} a44=+0.25886490±2.0107a_{44}= +0.25886490 \pm 2.0 \cdot 10^{-7} a45=+3.35981718±2.6107a_{45}= +3.35981718 \pm 2.6 \cdot 10^{-7}
a46=+0.05750326±4.9107a_{46}= +0.05750326 \pm 4.9 \cdot 10^{-7} a47=0.74773270±3.7107a_{47}= -0.74773270 \pm 3.7 \cdot 10^{-7} a48=0.54582285±2.9107a_{48}= -0.54582285 \pm 2.9 \cdot 10^{-7}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.62572149±3.7107a_{50}= -0.62572149 \pm 3.7 \cdot 10^{-7} a51=0.17388349±1.8107a_{51}= -0.17388349 \pm 1.8 \cdot 10^{-7}
a52=0.13440106±2.2107a_{52}= -0.13440106 \pm 2.2 \cdot 10^{-7} a53=1.51277851±2.5107a_{53}= -1.51277851 \pm 2.5 \cdot 10^{-7} a54=+1.12855323±4.2107a_{54}= +1.12855323 \pm 4.2 \cdot 10^{-7}
a55=0.51943808±2.7107a_{55}= -0.51943808 \pm 2.7 \cdot 10^{-7} a56=0.33249162±3.1107a_{56}= -0.33249162 \pm 3.1 \cdot 10^{-7} a57=+0.68939780±1.6107a_{57}= +0.68939780 \pm 1.6 \cdot 10^{-7}
a58=0.13174177±3.1107a_{58}= -0.13174177 \pm 3.1 \cdot 10^{-7} a59=+0.97360644±5.0107a_{59}= +0.97360644 \pm 5.0 \cdot 10^{-7} a60=+2.01242420±2.0107a_{60}= +2.01242420 \pm 2.0 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000