Properties

Label 15.48
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 8.665011
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: 8.66501125743234703233038713886±210108.66501125743234703233038713886 \pm 2 \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=1.78430801±2.2108a_{2}= -1.78430801 \pm 2.2 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+2.18375508±2.3108a_{4}= +2.18375508 \pm 2.3 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=1.03017071±3.2108a_{6}= -1.03017071 \pm 3.2 \cdot 10^{-8}
a7=0.86471208±1.5108a_{7}= -0.86471208 \pm 1.5 \cdot 10^{-8} a8=2.11218367±2.3108a_{8}= -2.11218367 \pm 2.3 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.79796680±3.2108a_{10}= +0.79796680 \pm 3.2 \cdot 10^{-8} a11=+1.49839490±1.2108a_{11}= +1.49839490 \pm 1.2 \cdot 10^{-8} a12=+1.26079158±3.3108a_{12}= +1.26079158 \pm 3.3 \cdot 10^{-8}
a13=1.32980681±1.3108a_{13}= -1.32980681 \pm 1.3 \cdot 10^{-8} a14=+1.54291270±1.5108a_{14}= +1.54291270 \pm 1.5 \cdot 10^{-8} a15=0.25819889±1.0108a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8}
a16=+1.58503116±1.8108a_{16}= +1.58503116 \pm 1.8 \cdot 10^{-8} a17=+1.28573655±1.7108a_{17}= +1.28573655 \pm 1.7 \cdot 10^{-8} a18=0.59476934±3.2108a_{18}= -0.59476934 \pm 3.2 \cdot 10^{-8}
a19=+0.27539008±1.4108a_{19}= +0.27539008 \pm 1.4 \cdot 10^{-8} a20=0.97660496±3.3108a_{20}= -0.97660496 \pm 3.3 \cdot 10^{-8} a21=0.49924175±2.5108a_{21}= -0.49924175 \pm 2.5 \cdot 10^{-8}
a22=2.67359803±1.4108a_{22}= -2.67359803 \pm 1.4 \cdot 10^{-8} a23=+0.54590729±1.9108a_{23}= +0.54590729 \pm 1.9 \cdot 10^{-8} a24=1.21946981±3.4108a_{24}= -1.21946981 \pm 3.4 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+2.37278494±1.5108a_{26}= +2.37278494 \pm 1.5 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=1.88831940±1.3108a_{28}= -1.88831940 \pm 1.3 \cdot 10^{-8} a29=1.09434703±1.9108a_{29}= -1.09434703 \pm 1.9 \cdot 10^{-8} a30=+0.46070635±3.2108a_{30}= +0.46070635 \pm 3.2 \cdot 10^{-8}
a31=+0.59510980±1.6108a_{31}= +0.59510980 \pm 1.6 \cdot 10^{-8} a32=0.71600013±1.6108a_{32}= -0.71600013 \pm 1.6 \cdot 10^{-8} a33=+0.86509870±2.3108a_{33}= +0.86509870 \pm 2.3 \cdot 10^{-8}
a34=2.29415002±2.2108a_{34}= -2.29415002 \pm 2.2 \cdot 10^{-8} a35=+0.38671100±2.5108a_{35}= +0.38671100 \pm 2.5 \cdot 10^{-8} a36=+0.72791836±3.3108a_{36}= +0.72791836 \pm 3.3 \cdot 10^{-8}
a37=1.83037580±1.5108a_{37}= -1.83037580 \pm 1.5 \cdot 10^{-8} a38=0.49138073±1.3108a_{38}= -0.49138073 \pm 1.3 \cdot 10^{-8} a39=0.76776432±2.3108a_{39}= -0.76776432 \pm 2.3 \cdot 10^{-8}
a40=+0.94459725±3.4108a_{40}= +0.94459725 \pm 3.4 \cdot 10^{-8} a41=0.61025692±1.4108a_{41}= -0.61025692 \pm 1.4 \cdot 10^{-8} a42=+0.89080106±4.7108a_{42}= +0.89080106 \pm 4.7 \cdot 10^{-8}
a43=+0.20796810±1.6108a_{43}= +0.20796810 \pm 1.6 \cdot 10^{-8} a44=+3.27212748±1.3108a_{44}= +3.27212748 \pm 1.3 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=0.97406675±2.9108a_{46}= -0.97406675 \pm 2.9 \cdot 10^{-8} a47=1.16144440±1.1108a_{47}= -1.16144440 \pm 1.1 \cdot 10^{-8} a48=+0.91511817±2.8108a_{48}= +0.91511817 \pm 2.8 \cdot 10^{-8}
a49=0.25227301±1.7108a_{49}= -0.25227301 \pm 1.7 \cdot 10^{-8} a50=0.35686160±3.2108a_{50}= -0.35686160 \pm 3.2 \cdot 10^{-8} a51=+0.74232034±2.7108a_{51}= +0.74232034 \pm 2.7 \cdot 10^{-8}
a52=2.90397236±1.7108a_{52}= -2.90397236 \pm 1.7 \cdot 10^{-8} a53=0.80364722±1.2108a_{53}= -0.80364722 \pm 1.2 \cdot 10^{-8} a54=0.34339024±3.2108a_{54}= -0.34339024 \pm 3.2 \cdot 10^{-8}
a55=0.67010257±2.3108a_{55}= -0.67010257 \pm 2.3 \cdot 10^{-8} a56=+1.82643074±1.7108a_{56}= +1.82643074 \pm 1.7 \cdot 10^{-8} a57=+0.15899654±2.5108a_{57}= +0.15899654 \pm 2.5 \cdot 10^{-8}
a58=+1.95265216±2.8108a_{58}= +1.95265216 \pm 2.8 \cdot 10^{-8} a59=+0.29886782±1.7108a_{59}= +0.29886782 \pm 1.7 \cdot 10^{-8} a60=0.56384314±3.3108a_{60}= -0.56384314 \pm 3.3 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000