Properties

Label 15.6
Level 1515
Weight 00
Character 15.1
Symmetry odd
RR 3.104500
Fricke sign 1-1

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Maass form invariants

Level: 15=35 15 = 3 \cdot 5
Weight: 0 0
Character: 15.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 3.10450058521073190818804678447±710123.10450058521073190818804678447 \pm 7 \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=+1.40057911±1108a_{2}= +1.40057911 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.96162184±1108a_{4}= +0.96162184 \pm 1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.80862472±1.2108a_{6}= +0.80862472 \pm 1.2 \cdot 10^{-8}
a7=0.79844062±1108a_{7}= -0.79844062 \pm 1 \cdot 10^{-8} a8=0.05375165±1108a_{8}= -0.05375165 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.62635802±1.2108a_{10}= -0.62635802 \pm 1.2 \cdot 10^{-8} a11=+0.68234362±1108a_{11}= +0.68234362 \pm 1 \cdot 10^{-8} a12=+0.55519263±1.2108a_{12}= +0.55519263 \pm 1.2 \cdot 10^{-8}
a13=+1.95752907±1108a_{13}= +1.95752907 \pm 1 \cdot 10^{-8} a14=1.11827925±1108a_{14}= -1.11827925 \pm 1 \cdot 10^{-8} a15=0.25819889±1.0108a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8}
a16=1.03690528±1108a_{16}= -1.03690528 \pm 1 \cdot 10^{-8} a17=1.18150975±1108a_{17}= -1.18150975 \pm 1 \cdot 10^{-8} a18=+0.46685970±1.2108a_{18}= +0.46685970 \pm 1.2 \cdot 10^{-8}
a19=+0.23992205±1108a_{19}= +0.23992205 \pm 1 \cdot 10^{-8} a20=0.43005036±1.2108a_{20}= -0.43005036 \pm 1.2 \cdot 10^{-8} a21=0.46097990±1.2108a_{21}= -0.46097990 \pm 1.2 \cdot 10^{-8}
a22=+0.95567622±1108a_{22}= +0.95567622 \pm 1 \cdot 10^{-8} a23=+0.00554965±1108a_{23}= +0.00554965 \pm 1 \cdot 10^{-8} a24=0.03103353±1.2108a_{24}= -0.03103353 \pm 1.2 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+2.74167431±1108a_{26}= +2.74167431 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.76779793±1108a_{28}= -0.76779793 \pm 1 \cdot 10^{-8} a29=0.63881725±1108a_{29}= -0.63881725 \pm 1 \cdot 10^{-8} a30=0.36162797±1.2108a_{30}= -0.36162797 \pm 1.2 \cdot 10^{-8}
a31=0.15346815±1108a_{31}= -0.15346815 \pm 1 \cdot 10^{-8} a32=1.39851622±1108a_{32}= -1.39851622 \pm 1 \cdot 10^{-8} a33=+0.39395127±1.2108a_{33}= +0.39395127 \pm 1.2 \cdot 10^{-8}
a34=1.65479788±1108a_{34}= -1.65479788 \pm 1 \cdot 10^{-8} a35=+0.35707350±1.2108a_{35}= +0.35707350 \pm 1.2 \cdot 10^{-8} a36=+0.32054061±1.2108a_{36}= +0.32054061 \pm 1.2 \cdot 10^{-8}
a37=+0.66994276±1108a_{37}= +0.66994276 \pm 1 \cdot 10^{-8} a38=+0.33602981±1108a_{38}= +0.33602981 \pm 1 \cdot 10^{-8} a39=+1.13017993±1.2108a_{39}= +1.13017993 \pm 1.2 \cdot 10^{-8}
a40=+0.02403847±1.2108a_{40}= +0.02403847 \pm 1.2 \cdot 10^{-8} a41=1.23681028±1108a_{41}= -1.23681028 \pm 1 \cdot 10^{-8} a42=0.64563882±1.5108a_{42}= -0.64563882 \pm 1.5 \cdot 10^{-8}
a43=+1.03784093±1108a_{43}= +1.03784093 \pm 1 \cdot 10^{-8} a44=+0.65615653±1108a_{44}= +0.65615653 \pm 1 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=+0.00777272±1108a_{46}= +0.00777272 \pm 1 \cdot 10^{-8} a47=0.54921153±1108a_{47}= -0.54921153 \pm 1 \cdot 10^{-8} a48=0.59865754±1.2108a_{48}= -0.59865754 \pm 1.2 \cdot 10^{-8}
a49=0.36249258±1108a_{49}= -0.36249258 \pm 1 \cdot 10^{-8} a50=+0.28011582±1.2108a_{50}= +0.28011582 \pm 1.2 \cdot 10^{-8} a51=0.68214497±1.2108a_{51}= -0.68214497 \pm 1.2 \cdot 10^{-8}
a52=+1.88240269±1108a_{52}= +1.88240269 \pm 1 \cdot 10^{-8} a53=+1.12073576±1108a_{53}= +1.12073576 \pm 1 \cdot 10^{-8} a54=+0.26954157±1.2108a_{54}= +0.26954157 \pm 1.2 \cdot 10^{-8}
a55=0.30515335±1.2108a_{55}= -0.30515335 \pm 1.2 \cdot 10^{-8} a56=+0.04291750±1108a_{56}= +0.04291750 \pm 1 \cdot 10^{-8} a57=+0.13851906±1.2108a_{57}= +0.13851906 \pm 1.2 \cdot 10^{-8}
a58=0.89471409±1108a_{58}= -0.89471409 \pm 1 \cdot 10^{-8} a59=0.09045217±1108a_{59}= -0.09045217 \pm 1 \cdot 10^{-8} a60=0.24828969±1.2108a_{60}= -0.24828969 \pm 1.2 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000