Properties

Label 15.8
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 3.492902
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: 3.49290270259253829669762604106±810123.49290270259253829669762604106 \pm 8 \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=0.88183811±1108a_{2}= -0.88183811 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.22236155±1108a_{4}= -0.22236155 \pm 1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.50912947±1.0108a_{6}= -0.50912947 \pm 1.0 \cdot 10^{-8}
a7=1.74020519±1108a_{7}= -1.74020519 \pm 1 \cdot 10^{-8} a8=+1.07792500±1108a_{8}= +1.07792500 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.39436999±1.0108a_{10}= +0.39436999 \pm 1.0 \cdot 10^{-8} a11=+0.05890722±1108a_{11}= +0.05890722 \pm 1 \cdot 10^{-8} a12=0.12838050±1.0108a_{12}= -0.12838050 \pm 1.0 \cdot 10^{-8}
a13=1.08130549±1108a_{13}= -1.08130549 \pm 1 \cdot 10^{-8} a14=+1.53457926±1108a_{14}= +1.53457926 \pm 1 \cdot 10^{-8} a15=0.25819889±1.0108a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8}
a16=0.72819380±1108a_{16}= -0.72819380 \pm 1 \cdot 10^{-8} a17=0.26911202±1108a_{17}= -0.26911202 \pm 1 \cdot 10^{-8} a18=0.29394604±1.0108a_{18}= -0.29394604 \pm 1.0 \cdot 10^{-8}
a19=+0.92144269±1108a_{19}= +0.92144269 \pm 1 \cdot 10^{-8} a20=+0.09944311±1.0108a_{20}= +0.09944311 \pm 1.0 \cdot 10^{-8} a21=1.00470793±1.0108a_{21}= -1.00470793 \pm 1.0 \cdot 10^{-8}
a22=0.05194663±1108a_{22}= -0.05194663 \pm 1 \cdot 10^{-8} a23=0.73293349±1108a_{23}= -0.73293349 \pm 1 \cdot 10^{-8} a24=+0.62234029±1.0108a_{24}= +0.62234029 \pm 1.0 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+0.95353639±1108a_{26}= +0.95353639 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.38695472±1108a_{28}= +0.38695472 \pm 1 \cdot 10^{-8} a29=+0.11349613±1108a_{29}= +0.11349613 \pm 1 \cdot 10^{-8} a30=+0.22768962±1.0108a_{30}= +0.22768962 \pm 1.0 \cdot 10^{-8}
a31=0.69257519±1108a_{31}= -0.69257519 \pm 1 \cdot 10^{-8} a32=0.43577595±1108a_{32}= -0.43577595 \pm 1 \cdot 10^{-8} a33=+0.03401010±1.0108a_{33}= +0.03401010 \pm 1.0 \cdot 10^{-8}
a34=+0.23731324±1108a_{34}= +0.23731324 \pm 1 \cdot 10^{-8} a35=+0.77824342±1.0108a_{35}= +0.77824342 \pm 1.0 \cdot 10^{-8} a36=0.07412052±1.0108a_{36}= -0.07412052 \pm 1.0 \cdot 10^{-8}
a37=1.50999645±1108a_{37}= -1.50999645 \pm 1 \cdot 10^{-8} a38=0.81256328±1108a_{38}= -0.81256328 \pm 1 \cdot 10^{-8} a39=0.62429201±1.0108a_{39}= -0.62429201 \pm 1.0 \cdot 10^{-8}
a40=0.48206271±1.0108a_{40}= -0.48206271 \pm 1.0 \cdot 10^{-8} a41=+0.96172487±1108a_{41}= +0.96172487 \pm 1 \cdot 10^{-8} a42=+0.88598975±1.0108a_{42}= +0.88598975 \pm 1.0 \cdot 10^{-8}
a43=0.36548642±1108a_{43}= -0.36548642 \pm 1 \cdot 10^{-8} a44=0.01309870±1108a_{44}= -0.01309870 \pm 1 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=+0.64632869±1108a_{46}= +0.64632869 \pm 1 \cdot 10^{-8} a47=+0.16451821±1108a_{47}= +0.16451821 \pm 1 \cdot 10^{-8} a48=0.42042288±1.0108a_{48}= -0.42042288 \pm 1.0 \cdot 10^{-8}
a49=+2.02831410±1108a_{49}= +2.02831410 \pm 1 \cdot 10^{-8} a50=0.17636762±1.0108a_{50}= -0.17636762 \pm 1.0 \cdot 10^{-8} a51=0.15537190±1.0108a_{51}= -0.15537190 \pm 1.0 \cdot 10^{-8}
a52=+0.24044076±1108a_{52}= +0.24044076 \pm 1 \cdot 10^{-8} a53=+1.03521137±1108a_{53}= +1.03521137 \pm 1 \cdot 10^{-8} a54=0.16970982±1.0108a_{54}= -0.16970982 \pm 1.0 \cdot 10^{-8}
a55=0.02634411±1.0108a_{55}= -0.02634411 \pm 1.0 \cdot 10^{-8} a56=1.87581067±1108a_{56}= -1.87581067 \pm 1 \cdot 10^{-8} a57=+0.53199519±1.0108a_{57}= +0.53199519 \pm 1.0 \cdot 10^{-8}
a58=0.10008521±1108a_{58}= -0.10008521 \pm 1 \cdot 10^{-8} a59=1.76396140±1108a_{59}= -1.76396140 \pm 1 \cdot 10^{-8} a60=+0.05741350±1.0108a_{60}= +0.05741350 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000