Properties

Label 13.194
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 14.67181
Fricke sign 1-1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 14.6718170691001421911597173815±310714.6718170691001421911597173815 \pm 3 \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=0.85454918±6.8106a_{2}= -0.85454918 \pm 6.8 \cdot 10^{-6} a3=+1.18939602±5.2106a_{3}= +1.18939602 \pm 5.2 \cdot 10^{-6}
a4=0.26974569±7.3106a_{4}= -0.26974569 \pm 7.3 \cdot 10^{-6} a5=+0.75803629±5.7106a_{5}= +0.75803629 \pm 5.7 \cdot 10^{-6} a6=1.01639740±6.6106a_{6}= -1.01639740 \pm 6.6 \cdot 10^{-6}
a7=0.88638633±5.2106a_{7}= -0.88638633 \pm 5.2 \cdot 10^{-6} a8=+1.08506015±6.7106a_{8}= +1.08506015 \pm 6.7 \cdot 10^{-6} a9=+0.41466289±4.6106a_{9}= +0.41466289 \pm 4.6 \cdot 10^{-6}
a10=0.64777929±5.2106a_{10}= -0.64777929 \pm 5.2 \cdot 10^{-6} a11=+0.37806249±3.9106a_{11}= +0.37806249 \pm 3.9 \cdot 10^{-6} a12=0.32083445±6.5106a_{12}= -0.32083445 \pm 6.5 \cdot 10^{-6}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.75746072±7.4106a_{14}= +0.75746072 \pm 7.4 \cdot 10^{-6} a15=+0.90160535±4.2106a_{15}= +0.90160535 \pm 4.2 \cdot 10^{-6}
a16=0.65749157±4.7106a_{16}= -0.65749157 \pm 4.7 \cdot 10^{-6} a17=+0.37829645±5.1106a_{17}= +0.37829645 \pm 5.1 \cdot 10^{-6} a18=0.35434983±5.4106a_{18}= -0.35434983 \pm 5.4 \cdot 10^{-6}
a19=1.82298932±5.5106a_{19}= -1.82298932 \pm 5.5 \cdot 10^{-6} a20=0.20447702±6.3106a_{20}= -0.20447702 \pm 6.3 \cdot 10^{-6} a21=1.05426437±4.2106a_{21}= -1.05426437 \pm 4.2 \cdot 10^{-6}
a22=0.32307300±3.7106a_{22}= -0.32307300 \pm 3.7 \cdot 10^{-6} a23=0.06393740±3.7106a_{23}= -0.06393740 \pm 3.7 \cdot 10^{-6} a24=+1.29056622±6.1106a_{24}= +1.29056622 \pm 6.1 \cdot 10^{-6}
a25=0.42538098±6.3106a_{25}= -0.42538098 \pm 6.3 \cdot 10^{-6} a26=0.23700930±6.8106a_{26}= -0.23700930 \pm 6.8 \cdot 10^{-6} a27=0.69619763±5.6106a_{27}= -0.69619763 \pm 5.6 \cdot 10^{-6}
a28=+0.23909889±8.0106a_{28}= +0.23909889 \pm 8.0 \cdot 10^{-6} a29=+0.06231457±4.9106a_{29}= +0.06231457 \pm 4.9 \cdot 10^{-6} a30=0.77046611±3.5106a_{30}= -0.77046611 \pm 3.5 \cdot 10^{-6}
a31=+1.72167118±3.8106a_{31}= +1.72167118 \pm 3.8 \cdot 10^{-6} a32=0.52320126±5.1106a_{32}= -0.52320126 \pm 5.1 \cdot 10^{-6} a33=+0.44966603±4.6106a_{33}= +0.44966603 \pm 4.6 \cdot 10^{-6}
a34=0.32327292±6.5106a_{34}= -0.32327292 \pm 6.5 \cdot 10^{-6} a35=0.67191301±4.7106a_{35}= -0.67191301 \pm 4.7 \cdot 10^{-6} a36=0.11185353±4.5106a_{36}= -0.11185353 \pm 4.5 \cdot 10^{-6}
a37=+1.57690600±4.5106a_{37}= +1.57690600 \pm 4.5 \cdot 10^{-6} a38=+1.55783404±7.4106a_{38}= +1.55783404 \pm 7.4 \cdot 10^{-6} a39=+0.32987910±5.2106a_{39}= +0.32987910 \pm 5.2 \cdot 10^{-6}
a40=+0.82251497±6.1106a_{40}= +0.82251497 \pm 6.1 \cdot 10^{-6} a41=1.00557767±7.6106a_{41}= -1.00557767 \pm 7.6 \cdot 10^{-6} a42=+0.90092076±6.1106a_{42}= +0.90092076 \pm 6.1 \cdot 10^{-6}
a43=0.03451455±4.3106a_{43}= -0.03451455 \pm 4.3 \cdot 10^{-6} a44=0.10198073±3.0106a_{44}= -0.10198073 \pm 3.0 \cdot 10^{-6} a45=+0.31432952±3.9106a_{45}= +0.31432952 \pm 3.9 \cdot 10^{-6}
a46=+0.05463765±4.4106a_{46}= +0.05463765 \pm 4.4 \cdot 10^{-6} a47=+0.00747220±4.0106a_{47}= +0.00747220 \pm 4.0 \cdot 10^{-6} a48=0.78201786±4.2106a_{48}= -0.78201786 \pm 4.2 \cdot 10^{-6}
a49=0.21431927±3.9106a_{49}= -0.21431927 \pm 3.9 \cdot 10^{-6} a50=+0.36350897±5.1106a_{50}= +0.36350897 \pm 5.1 \cdot 10^{-6} a51=+0.44994429±5.5106a_{51}= +0.44994429 \pm 5.5 \cdot 10^{-6}
a52=0.07481399±7.3106a_{52}= -0.07481399 \pm 7.3 \cdot 10^{-6} a53=+0.41581193±5.4106a_{53}= +0.41581193 \pm 5.4 \cdot 10^{-6} a54=+0.59493512±5.9106a_{54}= +0.59493512 \pm 5.9 \cdot 10^{-6}
a55=+0.28658509±3.6106a_{55}= +0.28658509 \pm 3.6 \cdot 10^{-6} a56=0.96178248±6.3106a_{56}= -0.96178248 \pm 6.3 \cdot 10^{-6} a57=2.16825624±3.1106a_{57}= -2.16825624 \pm 3.1 \cdot 10^{-6}
a58=0.05325087±7.9106a_{58}= -0.05325087 \pm 7.9 \cdot 10^{-6} a59=1.56038292±4.5106a_{59}= -1.56038292 \pm 4.5 \cdot 10^{-6} a60=0.24320416±4.1106a_{60}= -0.24320416 \pm 4.1 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000