Properties

Label 13.91
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 10.31744
Fricke sign +1+1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 10.3174493943770964696347589092±4101010.3174493943770964696347589092 \pm 4 \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=0.98531349±1108a_{2}= -0.98531349 \pm 1 \cdot 10^{-8} a3=+1.01469006±1108a_{3}= +1.01469006 \pm 1 \cdot 10^{-8}
a4=0.02915733±1.0108a_{4}= -0.02915733 \pm 1.0 \cdot 10^{-8} a5=1.65020586±1108a_{5}= -1.65020586 \pm 1 \cdot 10^{-8} a6=0.99978780±1108a_{6}= -0.99978780 \pm 1 \cdot 10^{-8}
a7=1.89403345±1108a_{7}= -1.89403345 \pm 1 \cdot 10^{-8} a8=+1.01404260±1108a_{8}= +1.01404260 \pm 1 \cdot 10^{-8} a9=+0.02959591±1108a_{9}= +0.02959591 \pm 1 \cdot 10^{-8}
a10=+1.62597010±1108a_{10}= +1.62597010 \pm 1 \cdot 10^{-8} a11=0.81774040±1108a_{11}= -0.81774040 \pm 1 \cdot 10^{-8} a12=0.02958565±1108a_{12}= -0.02958565 \pm 1 \cdot 10^{-8}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=+1.86621671±1.0108a_{14}= +1.86621671 \pm 1.0 \cdot 10^{-8} a15=1.67444748±1108a_{15}= -1.67444748 \pm 1 \cdot 10^{-8}
a16=0.96999252±1108a_{16}= -0.96999252 \pm 1 \cdot 10^{-8} a17=0.90300182±1108a_{17}= -0.90300182 \pm 1 \cdot 10^{-8} a18=0.02916125±1108a_{18}= -0.02916125 \pm 1 \cdot 10^{-8}
a19=0.46664169±1108a_{19}= -0.46664169 \pm 1 \cdot 10^{-8} a20=+0.04811559±1108a_{20}= +0.04811559 \pm 1 \cdot 10^{-8} a21=1.92185691±1108a_{21}= -1.92185691 \pm 1 \cdot 10^{-8}
a22=+0.80573065±1108a_{22}= +0.80573065 \pm 1 \cdot 10^{-8} a23=+0.20150784±1108a_{23}= +0.20150784 \pm 1 \cdot 10^{-8} a24=+1.02893894±1108a_{24}= +1.02893894 \pm 1 \cdot 10^{-8}
a25=+1.72317938±1108a_{25}= +1.72317938 \pm 1 \cdot 10^{-8} a26=+0.27327679±2.0108a_{26}= +0.27327679 \pm 2.0 \cdot 10^{-8} a27=0.98465938±1108a_{27}= -0.98465938 \pm 1 \cdot 10^{-8}
a28=+0.05522495±1.1108a_{28}= +0.05522495 \pm 1.1 \cdot 10^{-8} a29=+0.16420408±1108a_{29}= +0.16420408 \pm 1 \cdot 10^{-8} a30=+1.64985569±1108a_{30}= +1.64985569 \pm 1 \cdot 10^{-8}
a31=0.84137374±1108a_{31}= -0.84137374 \pm 1 \cdot 10^{-8} a32=0.05829588±1108a_{32}= -0.05829588 \pm 1 \cdot 10^{-8} a33=0.82975306±1108a_{33}= -0.82975306 \pm 1 \cdot 10^{-8}
a34=+0.88973988±1108a_{34}= +0.88973988 \pm 1 \cdot 10^{-8} a35=+3.12554510±1108a_{35}= +3.12554510 \pm 1 \cdot 10^{-8} a36=0.00086294±1108a_{36}= -0.00086294 \pm 1 \cdot 10^{-8}
a37=+0.30551891±1108a_{37}= +0.30551891 \pm 1 \cdot 10^{-8} a38=+0.45978835±1.0108a_{38}= +0.45978835 \pm 1.0 \cdot 10^{-8} a39=0.28142439±1.7108a_{39}= -0.28142439 \pm 1.7 \cdot 10^{-8}
a40=1.67337904±1108a_{40}= -1.67337904 \pm 1 \cdot 10^{-8} a41=+0.32230748±1.0108a_{41}= +0.32230748 \pm 1.0 \cdot 10^{-8} a42=+1.89363154±1108a_{42}= +1.89363154 \pm 1 \cdot 10^{-8}
a43=0.94007302±1108a_{43}= -0.94007302 \pm 1 \cdot 10^{-8} a44=+0.02384312±1108a_{44}= +0.02384312 \pm 1 \cdot 10^{-8} a45=0.04883935±1108a_{45}= -0.04883935 \pm 1 \cdot 10^{-8}
a46=0.19854839±1108a_{46}= -0.19854839 \pm 1 \cdot 10^{-8} a47=+0.43012565±1108a_{47}= +0.43012565 \pm 1 \cdot 10^{-8} a48=0.98424177±1108a_{48}= -0.98424177 \pm 1 \cdot 10^{-8}
a49=+2.58736272±1108a_{49}= +2.58736272 \pm 1 \cdot 10^{-8} a50=1.69787189±1108a_{50}= -1.69787189 \pm 1 \cdot 10^{-8} a51=0.91626697±1108a_{51}= -0.91626697 \pm 1 \cdot 10^{-8}
a52=+0.00808679±2.0108a_{52}= +0.00808679 \pm 2.0 \cdot 10^{-8} a53=+1.27584131±1108a_{53}= +1.27584131 \pm 1 \cdot 10^{-8} a54=+0.97019817±1108a_{54}= +0.97019817 \pm 1 \cdot 10^{-8}
a55=+1.34944001±1108a_{55}= +1.34944001 \pm 1 \cdot 10^{-8} a56=1.92063060±1108a_{56}= -1.92063060 \pm 1 \cdot 10^{-8} a57=0.47349668±1108a_{57}= -0.47349668 \pm 1 \cdot 10^{-8}
a58=0.16179249±1.1108a_{58}= -0.16179249 \pm 1.1 \cdot 10^{-8} a59=0.46770093±1108a_{59}= -0.46770093 \pm 1 \cdot 10^{-8} a60=+0.04882241±1108a_{60}= +0.04882241 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000