Properties

Label 5.30
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 11.09312
Fricke sign 1-1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 11.0931280004854038979726892996±3101011.0931280004854038979726892996 \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=0.31821009±3.9107a_{2}= -0.31821009 \pm 3.9 \cdot 10^{-7} a3=0.14985869±4.2107a_{3}= -0.14985869 \pm 4.2 \cdot 10^{-7}
a4=0.89874234±3.4107a_{4}= -0.89874234 \pm 3.4 \cdot 10^{-7} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.04768655±4.0107a_{6}= +0.04768655 \pm 4.0 \cdot 10^{-7}
a7=1.39569714±1.6107a_{7}= -1.39569714 \pm 1.6 \cdot 10^{-7} a8=+0.60419897±3.6107a_{8}= +0.60419897 \pm 3.6 \cdot 10^{-7} a9=0.97754237±2.0107a_{9}= -0.97754237 \pm 2.0 \cdot 10^{-7}
a10=0.14230788±4.0107a_{10}= -0.14230788 \pm 4.0 \cdot 10^{-7} a11=+0.94349242±2.1107a_{11}= +0.94349242 \pm 2.1 \cdot 10^{-7} a12=+0.13468435±3.5107a_{12}= +0.13468435 \pm 3.5 \cdot 10^{-7}
a13=+1.57536981±2.7107a_{13}= +1.57536981 \pm 2.7 \cdot 10^{-7} a14=+0.44412491±1.6107a_{14}= +0.44412491 \pm 1.6 \cdot 10^{-7} a15=0.06701884±4.3107a_{15}= -0.06701884 \pm 4.3 \cdot 10^{-7}
a16=+0.70648014±1.7107a_{16}= +0.70648014 \pm 1.7 \cdot 10^{-7} a17=0.27827180±4.3107a_{17}= -0.27827180 \pm 4.3 \cdot 10^{-7} a18=+0.31106384±1.8107a_{18}= +0.31106384 \pm 1.8 \cdot 10^{-7}
a19=+1.35632093±4.0107a_{19}= +1.35632093 \pm 4.0 \cdot 10^{-7} a20=0.40192979±3.5107a_{20}= -0.40192979 \pm 3.5 \cdot 10^{-7} a21=+0.20915734±1.8107a_{21}= +0.20915734 \pm 1.8 \cdot 10^{-7}
a22=0.30022881±2.3107a_{22}= -0.30022881 \pm 2.3 \cdot 10^{-7} a23=0.14379336±1.7107a_{23}= -0.14379336 \pm 1.7 \cdot 10^{-7} a24=0.09054447±3.8107a_{24}= -0.09054447 \pm 3.8 \cdot 10^{-7}
a25=+0.2a_{25}= +0.2 a26=0.50129857±3.3107a_{26}= -0.50129857 \pm 3.3 \cdot 10^{-7} a27=+0.29635191±3.2107a_{27}= +0.29635191 \pm 3.2 \cdot 10^{-7}
a28=+1.25437211±1.3107a_{28}= +1.25437211 \pm 1.3 \cdot 10^{-7} a29=0.25170097±1.9107a_{29}= -0.25170097 \pm 1.9 \cdot 10^{-7} a30=+0.02132607±8.3107a_{30}= +0.02132607 \pm 8.3 \cdot 10^{-7}
a31=0.24790308±4.2107a_{31}= -0.24790308 \pm 4.2 \cdot 10^{-7} a32=0.82900807±4.2107a_{32}= -0.82900807 \pm 4.2 \cdot 10^{-7} a33=0.14139054±1.5107a_{33}= -0.14139054 \pm 1.5 \cdot 10^{-7}
a34=+0.08854889±4.1107a_{34}= +0.08854889 \pm 4.1 \cdot 10^{-7} a35=0.62417473±1.7107a_{35}= -0.62417473 \pm 1.7 \cdot 10^{-7} a36=+0.87855872±9.7108a_{36}= +0.87855872 \pm 9.7 \cdot 10^{-8}
a37=+1.01274664±5.2107a_{37}= +1.01274664 \pm 5.2 \cdot 10^{-7} a38=0.43159500±2.8107a_{38}= -0.43159500 \pm 2.8 \cdot 10^{-7} a39=0.23608286±2.2107a_{39}= -0.23608286 \pm 2.2 \cdot 10^{-7}
a40=+0.27020599±3.7107a_{40}= +0.27020599 \pm 3.7 \cdot 10^{-7} a41=+0.51964696±4.4107a_{41}= +0.51964696 \pm 4.4 \cdot 10^{-7} a42=0.06655598±1.7107a_{42}= -0.06655598 \pm 1.7 \cdot 10^{-7}
a43=0.68912000±4.4107a_{43}= -0.68912000 \pm 4.4 \cdot 10^{-7} a44=0.84795659±1.6107a_{44}= -0.84795659 \pm 1.6 \cdot 10^{-7} a45=0.43717024±2.1107a_{45}= -0.43717024 \pm 2.1 \cdot 10^{-7}
a46=+0.04575650±2.0107a_{46}= +0.04575650 \pm 2.0 \cdot 10^{-7} a47=+0.83793176±2.6107a_{47}= +0.83793176 \pm 2.6 \cdot 10^{-7} a48=0.10587219±1.7107a_{48}= -0.10587219 \pm 1.7 \cdot 10^{-7}
a49=+0.94797049±3.5107a_{49}= +0.94797049 \pm 3.5 \cdot 10^{-7} a50=0.06364202±4.0107a_{50}= -0.06364202 \pm 4.0 \cdot 10^{-7} a51=+0.04170145±4.2107a_{51}= +0.04170145 \pm 4.2 \cdot 10^{-7}
a52=1.41585155±2.6107a_{52}= -1.41585155 \pm 2.6 \cdot 10^{-7} a53=+1.55839449±4.1107a_{53}= +1.55839449 \pm 4.1 \cdot 10^{-7} a54=0.09430217±3.3107a_{54}= -0.09430217 \pm 3.3 \cdot 10^{-7}
a55=+0.42194264±2.3107a_{55}= +0.42194264 \pm 2.3 \cdot 10^{-7} a56=0.84327876±1.4107a_{56}= -0.84327876 \pm 1.4 \cdot 10^{-7} a57=0.20325648±4.7107a_{57}= -0.20325648 \pm 4.7 \cdot 10^{-7}
a58=+0.08009379±1.5107a_{58}= +0.08009379 \pm 1.5 \cdot 10^{-7} a59=0.49169326±3.3107a_{59}= -0.49169326 \pm 3.3 \cdot 10^{-7} a60=+0.06023267±7.8107a_{60}= +0.06023267 \pm 7.8 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000