Properties

Label 6.7
Level 66
Weight 00
Character 6.1
Symmetry even
RR 6.306363
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: 6.3063635862299167471318702404±410136.3063635862299167471318702404 \pm 4 \cdot 10^{-13}

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=+0.97192954±1108a_{5}= +0.97192954 \pm 1 \cdot 10^{-8} a6=+0.40824829±1.0108a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8}
a7=+0.44871333±1108a_{7}= +0.44871333 \pm 1 \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=0.68725797±1.0108a_{10}= -0.68725797 \pm 1.0 \cdot 10^{-8} a11=+1.97215658±1108a_{11}= +1.97215658 \pm 1 \cdot 10^{-8} a12=0.28867513±5.2108a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8}
a13=0.83800685±1108a_{13}= -0.83800685 \pm 1 \cdot 10^{-8} a14=0.31728824±1.0108a_{14}= -0.31728824 \pm 1.0 \cdot 10^{-8} a15=0.56114378±1.0108a_{15}= -0.56114378 \pm 1.0 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+1.25531527±1108a_{17}= +1.25531527 \pm 1 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+0.09576926±1108a_{19}= +0.09576926 \pm 1 \cdot 10^{-8} a20=+0.48596477±1.0108a_{20}= +0.48596477 \pm 1.0 \cdot 10^{-8} a21=0.25906476±1.0108a_{21}= -0.25906476 \pm 1.0 \cdot 10^{-8}
a22=1.39452529±1.0108a_{22}= -1.39452529 \pm 1.0 \cdot 10^{-8} a23=+0.13218023±1108a_{23}= +0.13218023 \pm 1 \cdot 10^{-8} a24=+0.20412415±9.4108a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.05535297±1108a_{25}= -0.05535297 \pm 1 \cdot 10^{-8} a26=+0.59256033±1.0108a_{26}= +0.59256033 \pm 1.0 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.22435667±1.0108a_{28}= +0.22435667 \pm 1.0 \cdot 10^{-8} a29=0.46591850±1108a_{29}= -0.46591850 \pm 1 \cdot 10^{-8} a30=+0.39678857±1.0108a_{30}= +0.39678857 \pm 1.0 \cdot 10^{-8}
a31=+1.32762435±1108a_{31}= +1.32762435 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.13862513±1.0108a_{33}= -1.13862513 \pm 1.0 \cdot 10^{-8}
a34=0.88764194±1.0108a_{34}= -0.88764194 \pm 1.0 \cdot 10^{-8} a35=+0.43611774±1108a_{35}= +0.43611774 \pm 1 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.31323642±1108a_{37}= -0.31323642 \pm 1 \cdot 10^{-8} a38=0.06771909±1.0108a_{38}= -0.06771909 \pm 1.0 \cdot 10^{-8} a39=+0.48382348±1.0108a_{39}= +0.48382348 \pm 1.0 \cdot 10^{-8}
a40=0.34362898±1.0108a_{40}= -0.34362898 \pm 1.0 \cdot 10^{-8} a41=0.18335567±1108a_{41}= -0.18335567 \pm 1 \cdot 10^{-8} a42=+0.18318645±1.0108a_{42}= +0.18318645 \pm 1.0 \cdot 10^{-8}
a43=+0.59489458±1108a_{43}= +0.59489458 \pm 1 \cdot 10^{-8} a44=+0.98607829±1.0108a_{44}= +0.98607829 \pm 1.0 \cdot 10^{-8} a45=+0.32397651±1.0108a_{45}= +0.32397651 \pm 1.0 \cdot 10^{-8}
a46=0.09346554±1.0108a_{46}= -0.09346554 \pm 1.0 \cdot 10^{-8} a47=0.71146143±1108a_{47}= -0.71146143 \pm 1 \cdot 10^{-8} a48=0.14433757±1.5107a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7}
a49=0.79865635±1108a_{49}= -0.79865635 \pm 1 \cdot 10^{-8} a50=+0.03914046±1.0108a_{50}= +0.03914046 \pm 1.0 \cdot 10^{-8} a51=0.72475661±1.0108a_{51}= -0.72475661 \pm 1.0 \cdot 10^{-8}
a52=0.41900343±1.0108a_{52}= -0.41900343 \pm 1.0 \cdot 10^{-8} a53=0.40990219±1108a_{53}= -0.40990219 \pm 1 \cdot 10^{-8} a54=+0.13608276±1.6107a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7}
a55=+1.91679723±1108a_{55}= +1.91679723 \pm 1 \cdot 10^{-8} a56=0.15864412±1.0108a_{56}= -0.15864412 \pm 1.0 \cdot 10^{-8} a57=0.05529241±1.0108a_{57}= -0.05529241 \pm 1.0 \cdot 10^{-8}
a58=+0.32945413±1.0108a_{58}= +0.32945413 \pm 1.0 \cdot 10^{-8} a59=+1.37683804±1108a_{59}= +1.37683804 \pm 1 \cdot 10^{-8} a60=0.28057189±1.0108a_{60}= -0.28057189 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000