Properties

Label 5.48
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 13.57514
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: 13.5751469722125384701318658932±610913.5751469722125384701318658932 \pm 6 \cdot 10^{-9}

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=1.77264780±7.1106a_{2}= -1.77264780 \pm 7.1 \cdot 10^{-6} a3=+1.65091832±7.7106a_{3}= +1.65091832 \pm 7.7 \cdot 10^{-6}
a4=+2.14228021±6.2106a_{4}= +2.14228021 \pm 6.2 \cdot 10^{-6} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=2.92649673±7.3106a_{6}= -2.92649673 \pm 7.3 \cdot 10^{-6}
a7=0.37903577±2.9106a_{7}= -0.37903577 \pm 2.9 \cdot 10^{-6} a8=2.02486051±6.6106a_{8}= -2.02486051 \pm 6.6 \cdot 10^{-6} a9=+1.72553131±3.7106a_{9}= +1.72553131 \pm 3.7 \cdot 10^{-6}
a10=+0.79275220±7.1106a_{10}= +0.79275220 \pm 7.1 \cdot 10^{-6} a11=1.17938046±3.9106a_{11}= -1.17938046 \pm 3.9 \cdot 10^{-6} a12=+3.53672966±6.4106a_{12}= +3.53672966 \pm 6.4 \cdot 10^{-6}
a13=0.12677608±5.0106a_{13}= -0.12677608 \pm 5.0 \cdot 10^{-6} a14=+0.67189693±3.0106a_{14}= +0.67189693 \pm 3.0 \cdot 10^{-6} a15=0.73831312±7.7106a_{15}= -0.73831312 \pm 7.7 \cdot 10^{-6}
a16=+1.44708430±3.1106a_{16}= +1.44708430 \pm 3.1 \cdot 10^{-6} a17=+0.22158530±7.9106a_{17}= +0.22158530 \pm 7.9 \cdot 10^{-6} a18=3.05875927±3.3106a_{18}= -3.05875927 \pm 3.3 \cdot 10^{-6}
a19=+0.43589052±7.3106a_{19}= +0.43589052 \pm 7.3 \cdot 10^{-6} a20=0.95805684±6.2106a_{20}= -0.95805684 \pm 6.2 \cdot 10^{-6} a21=0.62575710±3.2106a_{21}= -0.62575710 \pm 3.2 \cdot 10^{-6}
a22=+2.09062617±4.2106a_{22}= +2.09062617 \pm 4.2 \cdot 10^{-6} a23=1.14188714±3.0106a_{23}= -1.14188714 \pm 3.0 \cdot 10^{-6} a24=3.34287931±6.9106a_{24}= -3.34287931 \pm 6.9 \cdot 10^{-6}
a25=+0.2a_{25}= +0.2 a26=+0.22472933±6.0106a_{26}= +0.22472933 \pm 6.0 \cdot 10^{-6} a27=+1.19779293±5.9106a_{27}= +1.19779293 \pm 5.9 \cdot 10^{-6}
a28=0.81200084±2.4106a_{28}= -0.81200084 \pm 2.4 \cdot 10^{-6} a29=0.34369638±3.6106a_{29}= -0.34369638 \pm 3.6 \cdot 10^{-6} a30=+1.30876912±1.4105a_{30}= +1.30876912 \pm 1.4 \cdot 10^{-5}
a31=0.32124002±7.6106a_{31}= -0.32124002 \pm 7.6 \cdot 10^{-6} a32=0.54031030±7.7106a_{32}= -0.54031030 \pm 7.7 \cdot 10^{-6} a33=1.94706080±2.8106a_{33}= -1.94706080 \pm 2.8 \cdot 10^{-6}
a34=0.39279269±7.5106a_{34}= -0.39279269 \pm 7.5 \cdot 10^{-6} a35=+0.16950995±2.9106a_{35}= +0.16950995 \pm 2.9 \cdot 10^{-6} a36=+3.69657158±1.7106a_{36}= +3.69657158 \pm 1.7 \cdot 10^{-6}
a37=1.30109525±9.4106a_{37}= -1.30109525 \pm 9.4 \cdot 10^{-6} a38=0.77268036±5.1106a_{38}= -0.77268036 \pm 5.1 \cdot 10^{-6} a39=0.20929695±4.0106a_{39}= -0.20929695 \pm 4.0 \cdot 10^{-6}
a40=+0.90554515±6.6106a_{40}= +0.90554515 \pm 6.6 \cdot 10^{-6} a41=1.58967132±8.1106a_{41}= -1.58967132 \pm 8.1 \cdot 10^{-6} a42=+1.10924695±3.0106a_{42}= +1.10924695 \pm 3.0 \cdot 10^{-6}
a43=+1.26867000±8.0106a_{43}= +1.26867000 \pm 8.0 \cdot 10^{-6} a44=2.52656342±3.0106a_{44}= -2.52656342 \pm 3.0 \cdot 10^{-6} a45=0.77168106±3.8106a_{45}= -0.77168106 \pm 3.8 \cdot 10^{-6}
a46=+2.02416373±3.7106a_{46}= +2.02416373 \pm 3.7 \cdot 10^{-6} a47=1.49696719±4.7106a_{47}= -1.49696719 \pm 4.7 \cdot 10^{-6} a48=+2.38901799±3.2106a_{48}= +2.38901799 \pm 3.2 \cdot 10^{-6}
a49=0.85633188±6.4106a_{49}= -0.85633188 \pm 6.4 \cdot 10^{-6} a50=0.35452956±7.1106a_{50}= -0.35452956 \pm 7.1 \cdot 10^{-6} a51=+0.36581923±7.7106a_{51}= +0.36581923 \pm 7.7 \cdot 10^{-6}
a52=0.27158988±4.8106a_{52}= -0.27158988 \pm 4.8 \cdot 10^{-6} a53=+0.91226476±7.5106a_{53}= +0.91226476 \pm 7.5 \cdot 10^{-6} a54=2.12326500±6.1106a_{54}= -2.12326500 \pm 6.1 \cdot 10^{-6}
a55=+0.52743497±3.9106a_{55}= +0.52743497 \pm 3.9 \cdot 10^{-6} a56=+0.76749457±2.6106a_{56}= +0.76749457 \pm 2.6 \cdot 10^{-6} a57=+0.71961964±8.5106a_{57}= +0.71961964 \pm 8.5 \cdot 10^{-6}
a58=+0.60925263±2.8106a_{58}= +0.60925263 \pm 2.8 \cdot 10^{-6} a59=0.66326051±6.0106a_{59}= -0.66326051 \pm 6.0 \cdot 10^{-6} a60=1.58167359±1.3105a_{60}= -1.58167359 \pm 1.3 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000