Properties

Label 6.25
Level 66
Weight 00
Character 6.1
Symmetry even
RR 12.35443
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: 12.3544320764145925864501458165±7101012.3544320764145925864501458165 \pm 7 \cdot 10^{-10}

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=+0.15375910±1108a_{5}= +0.15375910 \pm 1 \cdot 10^{-8} a6=+0.40824829±1.0108a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8}
a7=0.63080242±1108a_{7}= -0.63080242 \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=0.10872411±1.1108a_{10}= -0.10872411 \pm 1.1 \cdot 10^{-8} a11=1.39010958±1108a_{11}= -1.39010958 \pm 1 \cdot 10^{-8} a12=0.28867513±5.2108a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8}
a13=1.19311603±1108a_{13}= -1.19311603 \pm 1 \cdot 10^{-8} a14=+0.44604467±1.0108a_{14}= +0.44604467 \pm 1.0 \cdot 10^{-8} a15=0.08877286±1.1108a_{15}= -0.08877286 \pm 1.1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.59084470±1108a_{17}= +0.59084470 \pm 1 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+1.39361270±1108a_{19}= +1.39361270 \pm 1 \cdot 10^{-8} a20=+0.07687955±1.1108a_{20}= +0.07687955 \pm 1.1 \cdot 10^{-8} a21=+0.36419395±1.0108a_{21}= +0.36419395 \pm 1.0 \cdot 10^{-8}
a22=+0.98295591±1.1108a_{22}= +0.98295591 \pm 1.1 \cdot 10^{-8} a23=+1.17196879±1108a_{23}= +1.17196879 \pm 1 \cdot 10^{-8} a24=+0.20412415±9.4108a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.97635814±1108a_{25}= -0.97635814 \pm 1 \cdot 10^{-8} a26=+0.84366043±1.1108a_{26}= +0.84366043 \pm 1.1 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.31540121±1.0108a_{28}= -0.31540121 \pm 1.0 \cdot 10^{-8} a29=+0.77742728±1108a_{29}= +0.77742728 \pm 1 \cdot 10^{-8} a30=+0.06277189±1.1108a_{30}= +0.06277189 \pm 1.1 \cdot 10^{-8}
a31=+0.54113220±1108a_{31}= +0.54113220 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.80258014±1.1108a_{33}= +0.80258014 \pm 1.1 \cdot 10^{-8}
a34=0.41779030±1.0108a_{34}= -0.41779030 \pm 1.0 \cdot 10^{-8} a35=0.09699162±1108a_{35}= -0.09699162 \pm 1 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.94225178±1108a_{37}= -0.94225178 \pm 1 \cdot 10^{-8} a38=0.98543299±1.0108a_{38}= -0.98543299 \pm 1.0 \cdot 10^{-8} a39=+0.68884586±1.1108a_{39}= +0.68884586 \pm 1.1 \cdot 10^{-8}
a40=0.05436205±1.1108a_{40}= -0.05436205 \pm 1.1 \cdot 10^{-8} a41=+1.05991310±1108a_{41}= +1.05991310 \pm 1 \cdot 10^{-8} a42=0.25752401±1.0108a_{42}= -0.25752401 \pm 1.0 \cdot 10^{-8}
a43=+1.78298098±1108a_{43}= +1.78298098 \pm 1 \cdot 10^{-8} a44=0.69505479±1.1108a_{44}= -0.69505479 \pm 1.1 \cdot 10^{-8} a45=+0.05125303±1.1108a_{45}= +0.05125303 \pm 1.1 \cdot 10^{-8}
a46=0.82870708±1.0108a_{46}= -0.82870708 \pm 1.0 \cdot 10^{-8} a47=0.47895242±1108a_{47}= -0.47895242 \pm 1 \cdot 10^{-8} a48=0.14433757±1.5107a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7}
a49=0.60208830±1108a_{49}= -0.60208830 \pm 1 \cdot 10^{-8} a50=+0.69038946±1.0108a_{50}= +0.69038946 \pm 1.0 \cdot 10^{-8} a51=0.34112435±1.0108a_{51}= -0.34112435 \pm 1.0 \cdot 10^{-8}
a52=0.59655801±1.1108a_{52}= -0.59655801 \pm 1.1 \cdot 10^{-8} a53=+1.64402471±1108a_{53}= +1.64402471 \pm 1 \cdot 10^{-8} a54=+0.13608276±1.6107a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7}
a55=0.21374200±1108a_{55}= -0.21374200 \pm 1 \cdot 10^{-8} a56=+0.22302234±1.0108a_{56}= +0.22302234 \pm 1.0 \cdot 10^{-8} a57=0.80460267±1.0108a_{57}= -0.80460267 \pm 1.0 \cdot 10^{-8}
a58=0.54972410±1.1108a_{58}= -0.54972410 \pm 1.1 \cdot 10^{-8} a59=+1.76826089±1108a_{59}= +1.76826089 \pm 1 \cdot 10^{-8} a60=0.04438643±1.1108a_{60}= -0.04438643 \pm 1.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000