Properties

Label 5.47
Level 55
Weight 00
Character 5.1
Symmetry even
RR 13.46898
Fricke sign +1+1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 13.4689817279077632395708438097±510913.4689817279077632395708438097 \pm 5 \cdot 10^{-9}

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=+0.28850745±1.0108a_{2}= +0.28850745 \pm 1.0 \cdot 10^{-8} a3=+1.81176018±1108a_{3}= +1.81176018 \pm 1 \cdot 10^{-8}
a4=0.91676345±1.0108a_{4}= -0.91676345 \pm 1.0 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.52270631±1108a_{6}= +0.52270631 \pm 1 \cdot 10^{-8}
a7=+1.05569799±1.1108a_{7}= +1.05569799 \pm 1.1 \cdot 10^{-8} a8=0.55300054±1.3108a_{8}= -0.55300054 \pm 1.3 \cdot 10^{-8} a9=+2.28247495±1108a_{9}= +2.28247495 \pm 1 \cdot 10^{-8}
a10=0.12902446±2.1108a_{10}= -0.12902446 \pm 2.1 \cdot 10^{-8} a11=+0.66805106±1.3108a_{11}= +0.66805106 \pm 1.3 \cdot 10^{-8} a12=1.66095551±1108a_{12}= -1.66095551 \pm 1 \cdot 10^{-8}
a13=+0.43699604±1.0108a_{13}= +0.43699604 \pm 1.0 \cdot 10^{-8} a14=+0.30457674±1.0108a_{14}= +0.30457674 \pm 1.0 \cdot 10^{-8} a15=0.81024378±1.9108a_{15}= -0.81024378 \pm 1.9 \cdot 10^{-8}
a16=+0.75721867±1.0108a_{16}= +0.75721867 \pm 1.0 \cdot 10^{-8} a17=+0.20056032±1108a_{17}= +0.20056032 \pm 1 \cdot 10^{-8} a18=+0.65851103±1108a_{18}= +0.65851103 \pm 1 \cdot 10^{-8}
a19=+0.41978546±1108a_{19}= +0.41978546 \pm 1 \cdot 10^{-8} a20=+0.40998908±2.1108a_{20}= +0.40998908 \pm 2.1 \cdot 10^{-8} a21=+1.91267158±1108a_{21}= +1.91267158 \pm 1 \cdot 10^{-8}
a22=+0.19273771±1.0108a_{22}= +0.19273771 \pm 1.0 \cdot 10^{-8} a23=+0.43917938±1108a_{23}= +0.43917938 \pm 1 \cdot 10^{-8} a24=1.00190436±1108a_{24}= -1.00190436 \pm 1 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+0.12607661±1108a_{26}= +0.12607661 \pm 1 \cdot 10^{-8} a27=+2.32353704±1.2108a_{27}= +2.32353704 \pm 1.2 \cdot 10^{-8}
a28=0.96782533±1108a_{28}= -0.96782533 \pm 1 \cdot 10^{-8} a29=+0.89425740±1.3108a_{29}= +0.89425740 \pm 1.3 \cdot 10^{-8} a30=0.23376137±3.0108a_{30}= -0.23376137 \pm 3.0 \cdot 10^{-8}
a31=1.78704214±1108a_{31}= -1.78704214 \pm 1 \cdot 10^{-8} a32=+0.77146377±1108a_{32}= +0.77146377 \pm 1 \cdot 10^{-8} a33=+1.21034830±1.0108a_{33}= +1.21034830 \pm 1.0 \cdot 10^{-8}
a34=+0.05786315±1108a_{34}= +0.05786315 \pm 1 \cdot 10^{-8} a35=0.47212249±2.2108a_{35}= -0.47212249 \pm 2.2 \cdot 10^{-8} a36=2.09248961±1108a_{36}= -2.09248961 \pm 1 \cdot 10^{-8}
a37=+1.69406117±1.3108a_{37}= +1.69406117 \pm 1.3 \cdot 10^{-8} a38=+0.12111123±1108a_{38}= +0.12111123 \pm 1 \cdot 10^{-8} a39=+0.79173202±1108a_{39}= +0.79173202 \pm 1 \cdot 10^{-8}
a40=+0.24730936±2.4108a_{40}= +0.24730936 \pm 2.4 \cdot 10^{-8} a41=0.25467131±1108a_{41}= -0.25467131 \pm 1 \cdot 10^{-8} a42=+0.55182001±1108a_{42}= +0.55182001 \pm 1 \cdot 10^{-8}
a43=1.13084618±1108a_{43}= -1.13084618 \pm 1 \cdot 10^{-8} a44=0.61244479±1108a_{44}= -0.61244479 \pm 1 \cdot 10^{-8} a45=1.02075383±1.6108a_{45}= -1.02075383 \pm 1.6 \cdot 10^{-8}
a46=+0.12670652±1108a_{46}= +0.12670652 \pm 1 \cdot 10^{-8} a47=+0.60659433±1.2108a_{47}= +0.60659433 \pm 1.2 \cdot 10^{-8} a48=+1.37189864±1108a_{48}= +1.37189864 \pm 1 \cdot 10^{-8}
a49=+0.11449825±1108a_{49}= +0.11449825 \pm 1 \cdot 10^{-8} a50=+0.05770149±2.1108a_{50}= +0.05770149 \pm 2.1 \cdot 10^{-8} a51=+0.36336721±1108a_{51}= +0.36336721 \pm 1 \cdot 10^{-8}
a52=0.40062200±1.0108a_{52}= -0.40062200 \pm 1.0 \cdot 10^{-8} a53=1.05830836±1108a_{53}= -1.05830836 \pm 1 \cdot 10^{-8} a54=+0.67035775±1108a_{54}= +0.67035775 \pm 1 \cdot 10^{-8}
a55=0.29876151±2.4108a_{55}= -0.29876151 \pm 2.4 \cdot 10^{-8} a56=0.58380156±1.3108a_{56}= -0.58380156 \pm 1.3 \cdot 10^{-8} a57=+0.76055058±1108a_{57}= +0.76055058 \pm 1 \cdot 10^{-8}
a58=+0.25799992±1.3108a_{58}= +0.25799992 \pm 1.3 \cdot 10^{-8} a59=1.36745789±1108a_{59}= -1.36745789 \pm 1 \cdot 10^{-8} a60=+0.74280189±3.0108a_{60}= +0.74280189 \pm 3.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000