Properties

Label 15.40
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 7.562171
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: even
Fricke sign: 1-1
Spectral parameter: 7.56217196142289907783685343164±1010117.56217196142289907783685343164 \pm 10 \cdot 10^{-11}

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=0.92302105±1108a_{2}= -0.92302105 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.14803215±1108a_{4}= -0.14803215 \pm 1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.53290645±1.1108a_{6}= -0.53290645 \pm 1.1 \cdot 10^{-8}
a7=+0.33505200±1108a_{7}= +0.33505200 \pm 1 \cdot 10^{-8} a8=+1.05965783±1108a_{8}= +1.05965783 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.41278756±1.1108a_{10}= +0.41278756 \pm 1.1 \cdot 10^{-8} a11=+0.09873737±1108a_{11}= +0.09873737 \pm 1 \cdot 10^{-8} a12=0.08546640±1.1108a_{12}= -0.08546640 \pm 1.1 \cdot 10^{-8}
a13=+0.87026032±1108a_{13}= +0.87026032 \pm 1 \cdot 10^{-8} a14=0.30926004±1108a_{14}= -0.30926004 \pm 1 \cdot 10^{-8} a15=0.25819889±1.0108a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8}
a16=0.83005434±1108a_{16}= -0.83005434 \pm 1 \cdot 10^{-8} a17=0.37810037±1108a_{17}= -0.37810037 \pm 1 \cdot 10^{-8} a18=0.30767368±1.1108a_{18}= -0.30767368 \pm 1.1 \cdot 10^{-8}
a19=1.90554406±1108a_{19}= -1.90554406 \pm 1 \cdot 10^{-8} a20=+0.06620199±1.1108a_{20}= +0.06620199 \pm 1.1 \cdot 10^{-8} a21=+0.19344236±1.1108a_{21}= +0.19344236 \pm 1.1 \cdot 10^{-8}
a22=0.09113667±1108a_{22}= -0.09113667 \pm 1 \cdot 10^{-8} a23=0.26149453±1108a_{23}= -0.26149453 \pm 1 \cdot 10^{-8} a24=+0.61179374±1.1108a_{24}= +0.61179374 \pm 1.1 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=0.80326859±1108a_{26}= -0.80326859 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.04959847±1108a_{28}= -0.04959847 \pm 1 \cdot 10^{-8} a29=0.48929170±1108a_{29}= -0.48929170 \pm 1 \cdot 10^{-8} a30=+0.23832301±1.1108a_{30}= +0.23832301 \pm 1.1 \cdot 10^{-8}
a31=1.53573291±1108a_{31}= -1.53573291 \pm 1 \cdot 10^{-8} a32=0.29350021±1108a_{32}= -0.29350021 \pm 1 \cdot 10^{-8} a33=+0.05700605±1.1108a_{33}= +0.05700605 \pm 1.1 \cdot 10^{-8}
a34=+0.34899460±1108a_{34}= +0.34899460 \pm 1 \cdot 10^{-8} a35=0.14983981±1.1108a_{35}= -0.14983981 \pm 1.1 \cdot 10^{-8} a36=0.04934405±1.1108a_{36}= -0.04934405 \pm 1.1 \cdot 10^{-8}
a37=1.09065642±1108a_{37}= -1.09065642 \pm 1 \cdot 10^{-8} a38=+1.75885727±1108a_{38}= +1.75885727 \pm 1 \cdot 10^{-8} a39=+0.50244503±1.1108a_{39}= +0.50244503 \pm 1.1 \cdot 10^{-8}
a40=0.47389339±1.1108a_{40}= -0.47389339 \pm 1.1 \cdot 10^{-8} a41=+1.28160014±1108a_{41}= +1.28160014 \pm 1 \cdot 10^{-8} a42=0.17855137±1.2108a_{42}= -0.17855137 \pm 1.2 \cdot 10^{-8}
a43=+0.13175545±1108a_{43}= +0.13175545 \pm 1 \cdot 10^{-8} a44=0.01461630±1108a_{44}= -0.01461630 \pm 1 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=+0.24136495±1108a_{46}= +0.24136495 \pm 1 \cdot 10^{-8} a47=1.10040937±1108a_{47}= -1.10040937 \pm 1 \cdot 10^{-8} a48=0.47923210±1.1108a_{48}= -0.47923210 \pm 1.1 \cdot 10^{-8}
a49=0.88774016±1108a_{49}= -0.88774016 \pm 1 \cdot 10^{-8} a50=0.18460421±1.1108a_{50}= -0.18460421 \pm 1.1 \cdot 10^{-8} a51=0.21829635±1.1108a_{51}= -0.21829635 \pm 1.1 \cdot 10^{-8}
a52=0.12882650±1108a_{52}= -0.12882650 \pm 1 \cdot 10^{-8} a53=+1.30641856±1108a_{53}= +1.30641856 \pm 1 \cdot 10^{-8} a54=0.17763548±1.1108a_{54}= -0.17763548 \pm 1.1 \cdot 10^{-8}
a55=0.04415669±1.1108a_{55}= -0.04415669 \pm 1.1 \cdot 10^{-8} a56=+0.35504047±1108a_{56}= +0.35504047 \pm 1 \cdot 10^{-8} a57=1.10016638±1.1108a_{57}= -1.10016638 \pm 1.1 \cdot 10^{-8}
a58=+0.45162654±1108a_{58}= +0.45162654 \pm 1 \cdot 10^{-8} a59=+1.28967818±1108a_{59}= +1.28967818 \pm 1 \cdot 10^{-8} a60=+0.03822174±1.1108a_{60}= +0.03822174 \pm 1.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000