Properties

Label 6.30
Level 66
Weight 00
Character 6.1
Symmetry even
RR 13.25452
Fricke sign 1-1

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Maass form invariants

Level: 6=23 6 = 2 \cdot 3
Weight: 0 0
Character: 6.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 13.2545279009091376360016084446±310913.2545279009091376360016084446 \pm 3 \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=0.70710678±1.0108a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.25362063±2.6108a_{5}= +0.25362063 \pm 2.6 \cdot 10^{-8} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=0.92043812±1.2108a_{7}= -0.92043812 \pm 1.2 \cdot 10^{-8} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.17933687±3.6108a_{10}= -0.17933687 \pm 3.6 \cdot 10^{-8} a11=0.60127167±2.3108a_{11}= -0.60127167 \pm 2.3 \cdot 10^{-8} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=+1.21883607±2.2108a_{13}= +1.21883607 \pm 2.2 \cdot 10^{-8} a14=+0.65084804±2.2108a_{14}= +0.65084804 \pm 2.2 \cdot 10^{-8} a15=+0.14642794±3.6108a_{15}= +0.14642794 \pm 3.6 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.62990649±1108a_{17}= +0.62990649 \pm 1 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=1.02056651±1.0108a_{19}= -1.02056651 \pm 1.0 \cdot 10^{-8} a20=+0.12681032±3.6108a_{20}= +0.12681032 \pm 3.6 \cdot 10^{-8} a21=0.53141520±2.2108a_{21}= -0.53141520 \pm 2.2 \cdot 10^{-8}
a22=+0.42516328±3.4108a_{22}= +0.42516328 \pm 3.4 \cdot 10^{-8} a23=1.90228214±1.2108a_{23}= -1.90228214 \pm 1.2 \cdot 10^{-8} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.93567657±1.2108a_{25}= -0.93567657 \pm 1.2 \cdot 10^{-8} a26=0.86184725±3.2108a_{26}= -0.86184725 \pm 3.2 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.46021906±2.2108a_{28}= -0.46021906 \pm 2.2 \cdot 10^{-8} a29=+1.25185803±1.8108a_{29}= +1.25185803 \pm 1.8 \cdot 10^{-8} a30=0.10354019±3.6108a_{30}= -0.10354019 \pm 3.6 \cdot 10^{-8}
a31=1.33588283±1.1108a_{31}= -1.33588283 \pm 1.1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.34714436±3.4108a_{33}= -0.34714436 \pm 3.4 \cdot 10^{-8}
a34=0.44541115±2.0108a_{34}= -0.44541115 \pm 2.0 \cdot 10^{-8} a35=0.23344210±1.4108a_{35}= -0.23344210 \pm 1.4 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.08472825±3.3108a_{37}= -0.08472825 \pm 3.3 \cdot 10^{-8} a38=+0.72164950±2.0108a_{38}= +0.72164950 \pm 2.0 \cdot 10^{-8} a39=+0.70369533±3.2108a_{39}= +0.70369533 \pm 3.2 \cdot 10^{-8}
a40=0.08966843±3.6108a_{40}= -0.08966843 \pm 3.6 \cdot 10^{-8} a41=0.23770994±2.1108a_{41}= -0.23770994 \pm 2.1 \cdot 10^{-8} a42=+0.37576729±2.2108a_{42}= +0.37576729 \pm 2.2 \cdot 10^{-8}
a43=1.54088966±3.6108a_{43}= -1.54088966 \pm 3.6 \cdot 10^{-8} a44=0.30063584±3.4108a_{44}= -0.30063584 \pm 3.4 \cdot 10^{-8} a45=+0.08454021±3.6108a_{45}= +0.08454021 \pm 3.6 \cdot 10^{-8}
a46=+1.34511660±2.2108a_{46}= +1.34511660 \pm 2.2 \cdot 10^{-8} a47=1.39058236±1.1108a_{47}= -1.39058236 \pm 1.1 \cdot 10^{-8} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=0.15279366±1.6108a_{49}= -0.15279366 \pm 1.6 \cdot 10^{-8} a50=+0.66162325±2.3108a_{50}= +0.66162325 \pm 2.3 \cdot 10^{-8} a51=+0.36367668±2.0108a_{51}= +0.36367668 \pm 2.0 \cdot 10^{-8}
a52=+0.60941803±3.2108a_{52}= +0.60941803 \pm 3.2 \cdot 10^{-8} a53=0.24768209±1.3108a_{53}= -0.24768209 \pm 1.3 \cdot 10^{-8} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=0.15249490±2.7108a_{55}= -0.15249490 \pm 2.7 \cdot 10^{-8} a56=+0.32542402±2.2108a_{56}= +0.32542402 \pm 2.2 \cdot 10^{-8} a57=0.58922435±2.0108a_{57}= -0.58922435 \pm 2.0 \cdot 10^{-8}
a58=0.88519730±2.8108a_{58}= -0.88519730 \pm 2.8 \cdot 10^{-8} a59=+0.91644587±1108a_{59}= +0.91644587 \pm 1 \cdot 10^{-8} a60=+0.07321397±3.6108a_{60}= +0.07321397 \pm 3.6 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000