Properties

Label 2.3
Level 22
Weight 00
Character 2.1
Symmetry odd
RR 8.273665
Fricke sign 1-1

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Maass form invariants

Level: 2 2
Weight: 0 0
Character: 2.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 8.27366588958609552472525333895±410128.27366588958609552472525333895 \pm 4 \cdot 10^{-12}

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=+1.19821271±1108a_{3}= +1.19821271 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=0.21310644±1108a_{5}= -0.21310644 \pm 1 \cdot 10^{-8} a6=+0.84726433±1.0108a_{6}= +0.84726433 \pm 1.0 \cdot 10^{-8}
a7=0.94143619±1108a_{7}= -0.94143619 \pm 1 \cdot 10^{-8} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=+0.43571370±1108a_{9}= +0.43571370 \pm 1 \cdot 10^{-8}
a10=0.15068901±1.0108a_{10}= -0.15068901 \pm 1.0 \cdot 10^{-8} a11=0.84862842±1108a_{11}= -0.84862842 \pm 1 \cdot 10^{-8} a12=+0.59910636±1.0108a_{12}= +0.59910636 \pm 1.0 \cdot 10^{-8}
a13=+0.68598475±1108a_{13}= +0.68598475 \pm 1 \cdot 10^{-8} a14=0.66569591±1.0108a_{14}= -0.66569591 \pm 1.0 \cdot 10^{-8} a15=0.25534684±1108a_{15}= -0.25534684 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.24707993±1108a_{17}= -0.24707993 \pm 1 \cdot 10^{-8} a18=+0.30809611±1.0108a_{18}= +0.30809611 \pm 1.0 \cdot 10^{-8}
a19=+0.58731713±1108a_{19}= +0.58731713 \pm 1 \cdot 10^{-8} a20=0.10655322±1.0108a_{20}= -0.10655322 \pm 1.0 \cdot 10^{-8} a21=1.12804081±1108a_{21}= -1.12804081 \pm 1 \cdot 10^{-8}
a22=0.60007091±1.0108a_{22}= -0.60007091 \pm 1.0 \cdot 10^{-8} a23=+1.67606999±1108a_{23}= +1.67606999 \pm 1 \cdot 10^{-8} a24=+0.42363217±1.0108a_{24}= +0.42363217 \pm 1.0 \cdot 10^{-8}
a25=0.95458565±1108a_{25}= -0.95458565 \pm 1 \cdot 10^{-8} a26=+0.48506447±1.0108a_{26}= +0.48506447 \pm 1.0 \cdot 10^{-8} a27=0.67613502±1108a_{27}= -0.67613502 \pm 1 \cdot 10^{-8}
a28=0.47071809±1.0108a_{28}= -0.47071809 \pm 1.0 \cdot 10^{-8} a29=+0.58885986±1108a_{29}= +0.58885986 \pm 1 \cdot 10^{-8} a30=0.18055748±1.0108a_{30}= -0.18055748 \pm 1.0 \cdot 10^{-8}
a31=+1.01294005±1108a_{31}= +1.01294005 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.01683735±1108a_{33}= -1.01683735 \pm 1 \cdot 10^{-8}
a34=0.17471189±1.0108a_{34}= -0.17471189 \pm 1.0 \cdot 10^{-8} a35=+0.20062611±1108a_{35}= +0.20062611 \pm 1 \cdot 10^{-8} a36=+0.21785685±1.0108a_{36}= +0.21785685 \pm 1.0 \cdot 10^{-8}
a37=0.90102046±1108a_{37}= -0.90102046 \pm 1 \cdot 10^{-8} a38=+0.41529593±1.0108a_{38}= +0.41529593 \pm 1.0 \cdot 10^{-8} a39=+0.82195565±1108a_{39}= +0.82195565 \pm 1 \cdot 10^{-8}
a40=0.07534450±1.0108a_{40}= -0.07534450 \pm 1.0 \cdot 10^{-8} a41=+0.93939000±1108a_{41}= +0.93939000 \pm 1 \cdot 10^{-8} a42=0.79764530±1.0108a_{42}= -0.79764530 \pm 1.0 \cdot 10^{-8}
a43=1.13741790±1108a_{43}= -1.13741790 \pm 1 \cdot 10^{-8} a44=0.42431421±1.0108a_{44}= -0.42431421 \pm 1.0 \cdot 10^{-8} a45=0.09285339±1108a_{45}= -0.09285339 \pm 1 \cdot 10^{-8}
a46=+1.18516046±1.0108a_{46}= +1.18516046 \pm 1.0 \cdot 10^{-8} a47=+0.50068856±1108a_{47}= +0.50068856 \pm 1 \cdot 10^{-8} a48=+0.29955318±1.0108a_{48}= +0.29955318 \pm 1.0 \cdot 10^{-8}
a49=0.11369791±1108a_{49}= -0.11369791 \pm 1 \cdot 10^{-8} a50=0.67499398±1.0108a_{50}= -0.67499398 \pm 1.0 \cdot 10^{-8} a51=0.29605431±1108a_{51}= -0.29605431 \pm 1 \cdot 10^{-8}
a52=+0.34299237±1.0108a_{52}= +0.34299237 \pm 1.0 \cdot 10^{-8} a53=0.18007065±1108a_{53}= -0.18007065 \pm 1 \cdot 10^{-8} a54=0.47809966±1.0108a_{54}= -0.47809966 \pm 1.0 \cdot 10^{-8}
a55=+0.18084818±1108a_{55}= +0.18084818 \pm 1 \cdot 10^{-8} a56=0.33284796±1.0108a_{56}= -0.33284796 \pm 1.0 \cdot 10^{-8} a57=+0.70373085±1108a_{57}= +0.70373085 \pm 1 \cdot 10^{-8}
a58=+0.41638680±1.0108a_{58}= +0.41638680 \pm 1.0 \cdot 10^{-8} a59=+0.74562420±1108a_{59}= +0.74562420 \pm 1 \cdot 10^{-8} a60=0.12767342±1.0108a_{60}= -0.12767342 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000