Properties

Label 5.61
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 14.98678
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: 14.9867895143026282497687488554±210714.9867895143026282497687488554 \pm 2 \cdot 10^{-7}

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=+0.96060755±3.3104a_{2}= +0.96060755 \pm 3.3 \cdot 10^{-4} a3=0.23968016±3.6104a_{3}= -0.23968016 \pm 3.6 \cdot 10^{-4}
a4=0.07723313±2.9104a_{4}= -0.07723313 \pm 2.9 \cdot 10^{-4} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.23023857±3.4104a_{6}= -0.23023857 \pm 3.4 \cdot 10^{-4}
a7=+0.94632982±1.3104a_{7}= +0.94632982 \pm 1.3 \cdot 10^{-4} a8=1.03479828±3.1104a_{8}= -1.03479828 \pm 3.1 \cdot 10^{-4} a9=0.94255342±1.7104a_{9}= -0.94255342 \pm 1.7 \cdot 10^{-4}
a10=+0.42959676±3.3104a_{10}= +0.42959676 \pm 3.3 \cdot 10^{-4} a11=+0.83684963±1.8104a_{11}= +0.83684963 \pm 1.8 \cdot 10^{-4} a12=+0.01851125±3.0104a_{12}= +0.01851125 \pm 3.0 \cdot 10^{-4}
a13=+1.29993484±2.3104a_{13}= +1.29993484 \pm 2.3 \cdot 10^{-4} a14=+0.90905157±1.4104a_{14}= +0.90905157 \pm 1.4 \cdot 10^{-4} a15=0.10718823±3.6104a_{15}= -0.10718823 \pm 3.6 \cdot 10^{-4}
a16=0.91680191±1.4104a_{16}= -0.91680191 \pm 1.4 \cdot 10^{-4} a17=0.12407729±3.7104a_{17}= -0.12407729 \pm 3.7 \cdot 10^{-4} a18=0.90542393±1.5104a_{18}= -0.90542393 \pm 1.5 \cdot 10^{-4}
a19=+1.47712782±3.4104a_{19}= +1.47712782 \pm 3.4 \cdot 10^{-4} a20=0.03453971±2.9104a_{20}= -0.03453971 \pm 2.9 \cdot 10^{-4} a21=0.22681648±1.5104a_{21}= -0.22681648 \pm 1.5 \cdot 10^{-4}
a22=+0.80388407±1.9104a_{22}= +0.80388407 \pm 1.9 \cdot 10^{-4} a23=+0.85717918±1.4104a_{23}= +0.85717918 \pm 1.4 \cdot 10^{-4} a24=+0.24802062±3.2104a_{24}= +0.24802062 \pm 3.2 \cdot 10^{-4}
a25=+0.2a_{25}= +0.2 a26=+1.24872723±2.8104a_{26}= +1.24872723 \pm 2.8 \cdot 10^{-4} a27=+0.46559151±2.7104a_{27}= +0.46559151 \pm 2.7 \cdot 10^{-4}
a28=0.07308802±1.1104a_{28}= -0.07308802 \pm 1.1 \cdot 10^{-4} a29=+1.50225644±1.6104a_{29}= +1.50225644 \pm 1.6 \cdot 10^{-4} a30=0.10296582±6.9104a_{30}= -0.10296582 \pm 6.9 \cdot 10^{-4}
a31=0.03240728±3.5104a_{31}= -0.03240728 \pm 3.5 \cdot 10^{-4} a32=+0.15411145±3.6104a_{32}= +0.15411145 \pm 3.6 \cdot 10^{-4} a33=0.20057625±1.3104a_{33}= -0.20057625 \pm 1.3 \cdot 10^{-4}
a34=0.11918958±3.5104a_{34}= -0.11918958 \pm 3.5 \cdot 10^{-4} a35=+0.42321156±1.3104a_{35}= +0.42321156 \pm 1.3 \cdot 10^{-4} a36=+0.07279636±8.2105a_{36}= +0.07279636 \pm 8.2 \cdot 10^{-5}
a37=+0.28178048±4.4104a_{37}= +0.28178048 \pm 4.4 \cdot 10^{-4} a38=+1.41894013±2.4104a_{38}= +1.41894013 \pm 2.4 \cdot 10^{-4} a39=0.31156859±1.8104a_{39}= -0.31156859 \pm 1.8 \cdot 10^{-4}
a40=0.46277586±3.1104a_{40}= -0.46277586 \pm 3.1 \cdot 10^{-4} a41=0.47520235±3.7104a_{41}= -0.47520235 \pm 3.7 \cdot 10^{-4} a42=0.21788163±1.4104a_{42}= -0.21788163 \pm 1.4 \cdot 10^{-4}
a43=0.32897076±3.7104a_{43}= -0.32897076 \pm 3.7 \cdot 10^{-4} a44=0.06463252±1.4104a_{44}= -0.06463252 \pm 1.4 \cdot 10^{-4} a45=0.42152270±1.7104a_{45}= -0.42152270 \pm 1.7 \cdot 10^{-4}
a46=+0.82341279±1.7104a_{46}= +0.82341279 \pm 1.7 \cdot 10^{-4} a47=+0.89230822±2.2104a_{47}= +0.89230822 \pm 2.2 \cdot 10^{-4} a48=+0.21973923±1.5104a_{48}= +0.21973923 \pm 1.5 \cdot 10^{-4}
a49=0.10445987±3.0104a_{49}= -0.10445987 \pm 3.0 \cdot 10^{-4} a50=+0.19212151±3.3104a_{50}= +0.19212151 \pm 3.3 \cdot 10^{-4} a51=+0.02973886±3.6104a_{51}= +0.02973886 \pm 3.6 \cdot 10^{-4}
a52=0.10039804±2.2104a_{52}= -0.10039804 \pm 2.2 \cdot 10^{-4} a53=1.82846460±3.5104a_{53}= -1.82846460 \pm 3.5 \cdot 10^{-4} a54=+0.44725072±2.8104a_{54}= +0.44725072 \pm 2.8 \cdot 10^{-4}
a55=+0.37425053±1.8104a_{55}= +0.37425053 \pm 1.8 \cdot 10^{-4} a56=0.97926048±1.2104a_{56}= -0.97926048 \pm 1.2 \cdot 10^{-4} a57=0.35403823±3.9104a_{57}= -0.35403823 \pm 3.9 \cdot 10^{-4}
a58=+1.44307888±1.3104a_{58}= +1.44307888 \pm 1.3 \cdot 10^{-4} a59=+1.37176601±2.8104a_{59}= +1.37176601 \pm 2.8 \cdot 10^{-4} a60=+0.00827848±6.5104a_{60}= +0.00827848 \pm 6.5 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000