Properties

Label 7.32
Level 77
Weight 00
Character 7.1
Symmetry even
RR 9.043174
Fricke sign +1+1

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Maass form invariants

Level: 7 7
Weight: 0 0
Character: 7.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 9.04317475934475316020212165607±810129.04317475934475316020212165607 \pm 8 \cdot 10^{-12}

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=1.76083825±1108a_{2}= -1.76083825 \pm 1 \cdot 10^{-8} a3=+0.40738712±1108a_{3}= +0.40738712 \pm 1 \cdot 10^{-8}
a4=+2.10055136±1108a_{4}= +2.10055136 \pm 1 \cdot 10^{-8} a5=1.65932682±1108a_{5}= -1.65932682 \pm 1 \cdot 10^{-8} a6=0.71734283±1108a_{6}= -0.71734283 \pm 1 \cdot 10^{-8}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=1.93789294±1108a_{8}= -1.93789294 \pm 1 \cdot 10^{-8} a9=0.83403573±1108a_{9}= -0.83403573 \pm 1 \cdot 10^{-8}
a10=+2.92180614±1108a_{10}= +2.92180614 \pm 1 \cdot 10^{-8} a11=0.57027487±1108a_{11}= -0.57027487 \pm 1 \cdot 10^{-8} a12=+0.85573758±1108a_{12}= +0.85573758 \pm 1 \cdot 10^{-8}
a13=0.15350800±1108a_{13}= -0.15350800 \pm 1 \cdot 10^{-8} a14=+0.66553430±1.0108a_{14}= +0.66553430 \pm 1.0 \cdot 10^{-8} a15=0.67598838±1108a_{15}= -0.67598838 \pm 1 \cdot 10^{-8}
a16=+1.31176465±1108a_{16}= +1.31176465 \pm 1 \cdot 10^{-8} a17=+0.04052070±1108a_{17}= +0.04052070 \pm 1 \cdot 10^{-8} a18=+1.46860202±1108a_{18}= +1.46860202 \pm 1 \cdot 10^{-8}
a19=+1.40714906±1108a_{19}= +1.40714906 \pm 1 \cdot 10^{-8} a20=3.48550121±1108a_{20}= -3.48550121 \pm 1 \cdot 10^{-8} a21=0.15397786±1.0108a_{21}= -0.15397786 \pm 1.0 \cdot 10^{-8}
a22=+1.00416181±1108a_{22}= +1.00416181 \pm 1 \cdot 10^{-8} a23=+0.43358674±1108a_{23}= +0.43358674 \pm 1 \cdot 10^{-8} a24=0.78947263±1108a_{24}= -0.78947263 \pm 1 \cdot 10^{-8}
a25=+1.75336550±1108a_{25}= +1.75336550 \pm 1 \cdot 10^{-8} a26=+0.27030275±1108a_{26}= +0.27030275 \pm 1 \cdot 10^{-8} a27=0.74716254±1108a_{27}= -0.74716254 \pm 1 \cdot 10^{-8}
a28=0.79393379±1.0108a_{28}= -0.79393379 \pm 1.0 \cdot 10^{-8} a29=0.67197674±1108a_{29}= -0.67197674 \pm 1 \cdot 10^{-8} a30=+1.19030620±1108a_{30}= +1.19030620 \pm 1 \cdot 10^{-8}
a31=+0.62738347±1108a_{31}= +0.62738347 \pm 1 \cdot 10^{-8} a32=0.37191245±1108a_{32}= -0.37191245 \pm 1 \cdot 10^{-8} a33=0.23232264±1108a_{33}= -0.23232264 \pm 1 \cdot 10^{-8}
a34=0.07135041±1108a_{34}= -0.07135041 \pm 1 \cdot 10^{-8} a35=+0.62716659±1.0108a_{35}= +0.62716659 \pm 1.0 \cdot 10^{-8} a36=1.75193489±1108a_{36}= -1.75193489 \pm 1 \cdot 10^{-8}
a37=+1.35660258±1108a_{37}= +1.35660258 \pm 1 \cdot 10^{-8} a38=2.47776189±1108a_{38}= -2.47776189 \pm 1 \cdot 10^{-8} a39=0.06253718±1108a_{39}= -0.06253718 \pm 1 \cdot 10^{-8}
a40=+3.21559772±1108a_{40}= +3.21559772 \pm 1 \cdot 10^{-8} a41=+0.78455291±1108a_{41}= +0.78455291 \pm 1 \cdot 10^{-8} a42=+0.27113011±1.0108a_{42}= +0.27113011 \pm 1.0 \cdot 10^{-8}
a43=1.32726359±1108a_{43}= -1.32726359 \pm 1 \cdot 10^{-8} a44=1.19789166±1108a_{44}= -1.19789166 \pm 1 \cdot 10^{-8} a45=+1.38393786±1108a_{45}= +1.38393786 \pm 1 \cdot 10^{-8}
a46=0.76347612±1108a_{46}= -0.76347612 \pm 1 \cdot 10^{-8} a47=+0.01412394±1108a_{47}= +0.01412394 \pm 1 \cdot 10^{-8} a48=+0.53439603±1108a_{48}= +0.53439603 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=3.08739304±1108a_{50}= -3.08739304 \pm 1 \cdot 10^{-8} a51=+0.01650761±1108a_{51}= +0.01650761 \pm 1 \cdot 10^{-8}
a52=0.32245143±1108a_{52}= -0.32245143 \pm 1 \cdot 10^{-8} a53=+1.16099364±1108a_{53}= +1.16099364 \pm 1 \cdot 10^{-8} a54=+1.31563238±1108a_{54}= +1.31563238 \pm 1 \cdot 10^{-8}
a55=+0.94627239±1108a_{55}= +0.94627239 \pm 1 \cdot 10^{-8} a56=+0.73245468±1.0108a_{56}= +0.73245468 \pm 1.0 \cdot 10^{-8} a57=+0.57325441±1108a_{57}= +0.57325441 \pm 1 \cdot 10^{-8}
a58=+1.18324234±1108a_{58}= +1.18324234 \pm 1 \cdot 10^{-8} a59=1.52629429±1108a_{59}= -1.52629429 \pm 1 \cdot 10^{-8} a60=1.41994831±1108a_{60}= -1.41994831 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000