Properties

Label 15.65
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 9.824178
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: 9.82417896066128541274978863687±910109.82417896066128541274978863687 \pm 9 \cdot 10^{-10}

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=0.83201443±3.1108a_{2}= -0.83201443 \pm 3.1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.30775199±3.3108a_{4}= -0.30775199 \pm 3.3 \cdot 10^{-8} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.48036376±4.1108a_{6}= -0.48036376 \pm 4.1 \cdot 10^{-8}
a7=1.15946452±2.1108a_{7}= -1.15946452 \pm 2.1 \cdot 10^{-8} a8=+1.08806853±3.3108a_{8}= +1.08806853 \pm 3.3 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.37208816±4.1108a_{10}= -0.37208816 \pm 4.1 \cdot 10^{-8} a11=+1.51253669±1.8108a_{11}= +1.51253669 \pm 1.8 \cdot 10^{-8} a12=0.17768069±4.3108a_{12}= -0.17768069 \pm 4.3 \cdot 10^{-8}
a13=1.59511180±1.9108a_{13}= -1.59511180 \pm 1.9 \cdot 10^{-8} a14=+0.96469121±2.1108a_{14}= +0.96469121 \pm 2.1 \cdot 10^{-8} a15=+0.25819889±1.0108a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8}
a16=0.59753673±2.6108a_{16}= -0.59753673 \pm 2.6 \cdot 10^{-8} a17=1.25518491±2.4108a_{17}= -1.25518491 \pm 2.4 \cdot 10^{-8} a18=0.27733814±4.1108a_{18}= -0.27733814 \pm 4.1 \cdot 10^{-8}
a19=0.53242184±2.0108a_{19}= -0.53242184 \pm 2.0 \cdot 10^{-8} a20=0.13763087±4.3108a_{20}= -0.13763087 \pm 4.3 \cdot 10^{-8} a21=0.66941715±3.2108a_{21}= -0.66941715 \pm 3.2 \cdot 10^{-8}
a22=1.25845235±2.0108a_{22}= -1.25845235 \pm 2.0 \cdot 10^{-8} a23=+0.99607643±2.7108a_{23}= +0.99607643 \pm 2.7 \cdot 10^{-8} a24=+0.62819666±4.4108a_{24}= +0.62819666 \pm 4.4 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+1.32715604±2.2108a_{26}= +1.32715604 \pm 2.2 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.35682751±1.9108a_{28}= +0.35682751 \pm 1.9 \cdot 10^{-8} a29=+0.88766924±2.7108a_{29}= +0.88766924 \pm 2.7 \cdot 10^{-8} a30=0.21482520±4.1108a_{30}= -0.21482520 \pm 4.1 \cdot 10^{-8}
a31=0.35798668±2.3108a_{31}= -0.35798668 \pm 2.3 \cdot 10^{-8} a32=0.59090935±2.3108a_{32}= -0.59090935 \pm 2.3 \cdot 10^{-8} a33=+0.87326346±2.9108a_{33}= +0.87326346 \pm 2.9 \cdot 10^{-8}
a34=+1.04433196±3.2108a_{34}= +1.04433196 \pm 3.2 \cdot 10^{-8} a35=0.51852829±3.2108a_{35}= -0.51852829 \pm 3.2 \cdot 10^{-8} a36=0.10258400±4.3108a_{36}= -0.10258400 \pm 4.3 \cdot 10^{-8}
a37=+1.48711680±2.2108a_{37}= +1.48711680 \pm 2.2 \cdot 10^{-8} a38=+0.44298266±1.9108a_{38}= +0.44298266 \pm 1.9 \cdot 10^{-8} a39=0.92093823±2.9108a_{39}= -0.92093823 \pm 2.9 \cdot 10^{-8}
a40=+0.48659904±4.4108a_{40}= +0.48659904 \pm 4.4 \cdot 10^{-8} a41=+1.49189814±2.1108a_{41}= +1.49189814 \pm 2.1 \cdot 10^{-8} a42=+0.55696473±6.3108a_{42}= +0.55696473 \pm 6.3 \cdot 10^{-8}
a43=+0.70822630±2.3108a_{43}= +0.70822630 \pm 2.3 \cdot 10^{-8} a44=0.46548617±1.9108a_{44}= -0.46548617 \pm 1.9 \cdot 10^{-8} a45=+0.14907120±1.4107a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7}
a46=0.82874996±4.2108a_{46}= -0.82874996 \pm 4.2 \cdot 10^{-8} a47=0.55768184±1.6108a_{47}= -0.55768184 \pm 1.6 \cdot 10^{-8} a48=0.34498799±3.6108a_{48}= -0.34498799 \pm 3.6 \cdot 10^{-8}
a49=+0.34435796±2.4108a_{49}= +0.34435796 \pm 2.4 \cdot 10^{-8} a50=0.16640289±4.1108a_{50}= -0.16640289 \pm 4.1 \cdot 10^{-8} a51=0.72468135±3.4108a_{51}= -0.72468135 \pm 3.4 \cdot 10^{-8}
a52=+0.49089883±2.5108a_{52}= +0.49089883 \pm 2.5 \cdot 10^{-8} a53=+1.60533090±1.7108a_{53}= +1.60533090 \pm 1.7 \cdot 10^{-8} a54=0.16012125±4.1108a_{54}= -0.16012125 \pm 4.1 \cdot 10^{-8}
a55=+0.67642697±2.9108a_{55}= +0.67642697 \pm 2.9 \cdot 10^{-8} a56=1.26157684±2.4108a_{56}= -1.26157684 \pm 2.4 \cdot 10^{-8} a57=0.30739390±3.1108a_{57}= -0.30739390 \pm 3.1 \cdot 10^{-8}
a58=0.73855361±4.0108a_{58}= -0.73855361 \pm 4.0 \cdot 10^{-8} a59=+1.13460463±2.5108a_{59}= +1.13460463 \pm 2.5 \cdot 10^{-8} a60=0.07946122±4.3108a_{60}= -0.07946122 \pm 4.3 \cdot 10^{-8}

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