Properties

Label 6.23
Level 66
Weight 00
Character 6.1
Symmetry even
RR 11.70574
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: 11.7057493188922908818178031444±3101011.7057493188922908818178031444 \pm 3 \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=0.66850969±1108a_{5}= -0.66850969 \pm 1 \cdot 10^{-8} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=0.07206613±1108a_{7}= -0.07206613 \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=+0.47270773±1.0108a_{10}= +0.47270773 \pm 1.0 \cdot 10^{-8} a11=+1.67985412±1108a_{11}= +1.67985412 \pm 1 \cdot 10^{-8} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=0.94390003±1108a_{13}= -0.94390003 \pm 1 \cdot 10^{-8} a14=+0.05095845±1.0108a_{14}= +0.05095845 \pm 1.0 \cdot 10^{-8} a15=0.38596425±1.0108a_{15}= -0.38596425 \pm 1.0 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=1.25685865±1108a_{17}= -1.25685865 \pm 1 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=1.08123179±1108a_{19}= -1.08123179 \pm 1 \cdot 10^{-8} a20=0.33425484±1.0108a_{20}= -0.33425484 \pm 1.0 \cdot 10^{-8} a21=0.04160740±1.0108a_{21}= -0.04160740 \pm 1.0 \cdot 10^{-8}
a22=1.18783624±1.0108a_{22}= -1.18783624 \pm 1.0 \cdot 10^{-8} a23=+0.42557446±1108a_{23}= +0.42557446 \pm 1 \cdot 10^{-8} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.55309480±1108a_{25}= -0.55309480 \pm 1 \cdot 10^{-8} a26=+0.66743811±1.0108a_{26}= +0.66743811 \pm 1.0 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.03603307±1.0108a_{28}= -0.03603307 \pm 1.0 \cdot 10^{-8} a29=1.15829044±1108a_{29}= -1.15829044 \pm 1 \cdot 10^{-8} a30=+0.27291794±1.0108a_{30}= +0.27291794 \pm 1.0 \cdot 10^{-8}
a31=1.10192872±1108a_{31}= -1.10192872 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.96986423±1.0108a_{33}= +0.96986423 \pm 1.0 \cdot 10^{-8}
a34=+0.88873327±1.0108a_{34}= +0.88873327 \pm 1.0 \cdot 10^{-8} a35=+0.04817691±1108a_{35}= +0.04817691 \pm 1 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.81918702±1108a_{37}= -0.81918702 \pm 1 \cdot 10^{-8} a38=+0.76454633±1.0108a_{38}= +0.76454633 \pm 1.0 \cdot 10^{-8} a39=0.54496094±1.0108a_{39}= -0.54496094 \pm 1.0 \cdot 10^{-8}
a40=+0.23635387±1.0108a_{40}= +0.23635387 \pm 1.0 \cdot 10^{-8} a41=1.72746323±1108a_{41}= -1.72746323 \pm 1 \cdot 10^{-8} a42=+0.02942088±1.0108a_{42}= +0.02942088 \pm 1.0 \cdot 10^{-8}
a43=+0.24615773±1108a_{43}= +0.24615773 \pm 1 \cdot 10^{-8} a44=+0.83992706±1.0108a_{44}= +0.83992706 \pm 1.0 \cdot 10^{-8} a45=0.22283656±1.0108a_{45}= -0.22283656 \pm 1.0 \cdot 10^{-8}
a46=0.30092659±1.0108a_{46}= -0.30092659 \pm 1.0 \cdot 10^{-8} a47=+1.81532756±1108a_{47}= +1.81532756 \pm 1 \cdot 10^{-8} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=0.99480647±1108a_{49}= -0.99480647 \pm 1 \cdot 10^{-8} a50=+0.39109708±1.0108a_{50}= +0.39109708 \pm 1.0 \cdot 10^{-8} a51=0.72564768±1.0108a_{51}= -0.72564768 \pm 1.0 \cdot 10^{-8}
a52=0.47195002±1.0108a_{52}= -0.47195002 \pm 1.0 \cdot 10^{-8} a53=+1.02315543±1108a_{53}= +1.02315543 \pm 1 \cdot 10^{-8} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=1.12299875±1108a_{55}= -1.12299875 \pm 1 \cdot 10^{-8} a56=+0.02547923±1.0108a_{56}= +0.02547923 \pm 1.0 \cdot 10^{-8} a57=0.62424946±1.0108a_{57}= -0.62424946 \pm 1.0 \cdot 10^{-8}
a58=+0.81903502±1.0108a_{58}= +0.81903502 \pm 1.0 \cdot 10^{-8} a59=+0.31930564±1108a_{59}= +0.31930564 \pm 1 \cdot 10^{-8} a60=0.19298212±1.0108a_{60}= -0.19298212 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000