Properties

Label 3.26
Level 33
Weight 00
Character 3.1
Symmetry even
RR 14.62623
Fricke sign +1+1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 14.6262358403662403553443790824±510814.6262358403662403553443790824 \pm 5 \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=+0.55536200±3.0108a_{2}= +0.55536200 \pm 3.0 \cdot 10^{-8} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.69157305±1.8108a_{4}= -0.69157305 \pm 1.8 \cdot 10^{-8} a5=0.95281834±1108a_{5}= -0.95281834 \pm 1 \cdot 10^{-8} a6=0.32063840±4.0108a_{6}= -0.32063840 \pm 4.0 \cdot 10^{-8}
a7=+1.83744158±1.7108a_{7}= +1.83744158 \pm 1.7 \cdot 10^{-8} a8=0.93943539±1108a_{8}= -0.93943539 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.52915910±1108a_{10}= -0.52915910 \pm 1 \cdot 10^{-8} a11=0.01575162±1108a_{11}= -0.01575162 \pm 1 \cdot 10^{-8} a12=+0.39927988±2.9108a_{12}= +0.39927988 \pm 2.9 \cdot 10^{-8}
a13=+1.03096988±1.2108a_{13}= +1.03096988 \pm 1.2 \cdot 10^{-8} a14=+1.02044524±2.2108a_{14}= +1.02044524 \pm 2.2 \cdot 10^{-8} a15=+0.55010992±1.3108a_{15}= +0.55010992 \pm 1.3 \cdot 10^{-8}
a16=+0.16984632±2.6108a_{16}= +0.16984632 \pm 2.6 \cdot 10^{-8} a17=+0.64782636±2.1108a_{17}= +0.64782636 \pm 2.1 \cdot 10^{-8} a18=+0.18512067±4.0108a_{18}= +0.18512067 \pm 4.0 \cdot 10^{-8}
a19=+0.63339593±3.4108a_{19}= +0.63339593 \pm 3.4 \cdot 10^{-8} a20=+0.65894348±1108a_{20}= +0.65894348 \pm 1 \cdot 10^{-8} a21=1.06084739±2.7108a_{21}= -1.06084739 \pm 2.7 \cdot 10^{-8}
a22=0.00874785±1.2108a_{22}= -0.00874785 \pm 1.2 \cdot 10^{-8} a23=+0.20959728±1108a_{23}= +0.20959728 \pm 1 \cdot 10^{-8} a24=+0.54238328±1.7108a_{24}= +0.54238328 \pm 1.7 \cdot 10^{-8}
a25=0.09213721±2.2108a_{25}= -0.09213721 \pm 2.2 \cdot 10^{-8} a26=+0.57256150±1.7108a_{26}= +0.57256150 \pm 1.7 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=1.27072507±1.4108a_{28}= -1.27072507 \pm 1.4 \cdot 10^{-8} a29=+0.31961885±1108a_{29}= +0.31961885 \pm 1 \cdot 10^{-8} a30=+0.30551015±4.3108a_{30}= +0.30551015 \pm 4.3 \cdot 10^{-8}
a31=0.20102882±2.5108a_{31}= -0.20102882 \pm 2.5 \cdot 10^{-8} a32=+1.03376159±2.8108a_{32}= +1.03376159 \pm 2.8 \cdot 10^{-8} a33=+0.00909420±1.9108a_{33}= +0.00909420 \pm 1.9 \cdot 10^{-8}
a34=+0.35977815±2.9108a_{34}= +0.35977815 \pm 2.9 \cdot 10^{-8} a35=1.75074803±1108a_{35}= -1.75074803 \pm 1 \cdot 10^{-8} a36=0.23052435±2.9108a_{36}= -0.23052435 \pm 2.9 \cdot 10^{-8}
a37=+0.79454377±1108a_{37}= +0.79454377 \pm 1 \cdot 10^{-8} a38=+0.35176403±4.6108a_{38}= +0.35176403 \pm 4.6 \cdot 10^{-8} a39=0.59523074±2.3108a_{39}= -0.59523074 \pm 2.3 \cdot 10^{-8}
a40=+0.89511127±1108a_{40}= +0.89511127 \pm 1 \cdot 10^{-8} a41=0.17596149±2.4108a_{41}= -0.17596149 \pm 2.4 \cdot 10^{-8} a42=0.58915433±5.8108a_{42}= -0.58915433 \pm 5.8 \cdot 10^{-8}
a43=+0.77907495±1108a_{43}= +0.77907495 \pm 1 \cdot 10^{-8} a44=+0.01089339±1108a_{44}= +0.01089339 \pm 1 \cdot 10^{-8} a45=0.31760611±1.3108a_{45}= -0.31760611 \pm 1.3 \cdot 10^{-8}
a46=+0.11640236±1.1108a_{46}= +0.11640236 \pm 1.1 \cdot 10^{-8} a47=1.83642604±2.2108a_{47}= -1.83642604 \pm 2.2 \cdot 10^{-8} a48=0.09806082±3.6108a_{48}= -0.09806082 \pm 3.6 \cdot 10^{-8}
a49=+2.37619156±1108a_{49}= +2.37619156 \pm 1 \cdot 10^{-8} a50=0.05116951±3.0108a_{50}= -0.05116951 \pm 3.0 \cdot 10^{-8} a51=0.37402273±3.2108a_{51}= -0.37402273 \pm 3.2 \cdot 10^{-8}
a52=0.71299098±1.1108a_{52}= -0.71299098 \pm 1.1 \cdot 10^{-8} a53=+1.34409416±1108a_{53}= +1.34409416 \pm 1 \cdot 10^{-8} a54=0.10687947±4.0108a_{54}= -0.10687947 \pm 4.0 \cdot 10^{-8}
a55=+0.01500843±1108a_{55}= +0.01500843 \pm 1 \cdot 10^{-8} a56=1.72615766±1108a_{56}= -1.72615766 \pm 1 \cdot 10^{-8} a57=0.36569131±4.5108a_{57}= -0.36569131 \pm 4.5 \cdot 10^{-8}
a58=+0.17750416±1108a_{58}= +0.17750416 \pm 1 \cdot 10^{-8} a59=+1.01496206±1108a_{59}= +1.01496206 \pm 1 \cdot 10^{-8} a60=0.38044120±3.1108a_{60}= -0.38044120 \pm 3.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000