Properties

Label 13.175
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 13.99015
Fricke sign 1-1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 13.990151114539748168779049836±610813.990151114539748168779049836 \pm 6 \cdot 10^{-8}

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=0.98255203±1.6103a_{2}= -0.98255203 \pm 1.6 \cdot 10^{-3} a3=1.45695237±1.5103a_{3}= -1.45695237 \pm 1.5 \cdot 10^{-3}
a4=0.03459151±1.4103a_{4}= -0.03459151 \pm 1.4 \cdot 10^{-3} a5=1.49462642±1.3103a_{5}= -1.49462642 \pm 1.3 \cdot 10^{-3} a6=+1.43153151±1.7103a_{6}= +1.43153151 \pm 1.7 \cdot 10^{-3}
a7=+1.71204737±1.4103a_{7}= +1.71204737 \pm 1.4 \cdot 10^{-3} a8=+1.01653999±1.2103a_{8}= +1.01653999 \pm 1.2 \cdot 10^{-3} a9=+1.12271021±1.5103a_{9}= +1.12271021 \pm 1.5 \cdot 10^{-3}
a10=+1.46854822±1.5103a_{10}= +1.46854822 \pm 1.5 \cdot 10^{-3} a11=0.83527788±1.3103a_{11}= -0.83527788 \pm 1.3 \cdot 10^{-3} a12=+0.05039818±1.5103a_{12}= +0.05039818 \pm 1.5 \cdot 10^{-3}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=1.68217561±1.5103a_{14}= -1.68217561 \pm 1.5 \cdot 10^{-3} a15=+2.17759950±1.6103a_{15}= +2.17759950 \pm 1.6 \cdot 10^{-3}
a16=0.96421192±1.2103a_{16}= -0.96421192 \pm 1.2 \cdot 10^{-3} a17=1.15806476±1.4103a_{17}= -1.15806476 \pm 1.4 \cdot 10^{-3} a18=1.10312119±1.7103a_{18}= -1.10312119 \pm 1.7 \cdot 10^{-3}
a19=+1.00443703±1.1103a_{19}= +1.00443703 \pm 1.1 \cdot 10^{-3} a20=+0.05170139±1.4103a_{20}= +0.05170139 \pm 1.4 \cdot 10^{-3} a21=2.49437147±1.2103a_{21}= -2.49437147 \pm 1.2 \cdot 10^{-3}
a22=+0.82070397±1.4103a_{22}= +0.82070397 \pm 1.4 \cdot 10^{-3} a23=0.93441880±1.1103a_{23}= -0.93441880 \pm 1.1 \cdot 10^{-3} a24=1.48105034±1.1103a_{24}= -1.48105034 \pm 1.1 \cdot 10^{-3}
a25=+1.23390814±1.0103a_{25}= +1.23390814 \pm 1.0 \cdot 10^{-3} a26=0.27251090±1.6103a_{26}= -0.27251090 \pm 1.6 \cdot 10^{-3} a27=0.17878293±1.2103a_{27}= -0.17878293 \pm 1.2 \cdot 10^{-3}
a28=0.05922231±1.3103a_{28}= -0.05922231 \pm 1.3 \cdot 10^{-3} a29=+0.02523085±1.0103a_{29}= +0.02523085 \pm 1.0 \cdot 10^{-3} a30=2.13960481±2.0103a_{30}= -2.13960481 \pm 2.0 \cdot 10^{-3}
a31=0.96065549±1.5103a_{31}= -0.96065549 \pm 1.5 \cdot 10^{-3} a32=0.06915161±1.6103a_{32}= -0.06915161 \pm 1.6 \cdot 10^{-3} a33=+1.21696008±1.1103a_{33}= +1.21696008 \pm 1.1 \cdot 10^{-3}
a34=+1.13785888±1.5103a_{34}= +1.13785888 \pm 1.5 \cdot 10^{-3} a35=2.55887123±1.1103a_{35}= -2.55887123 \pm 1.1 \cdot 10^{-3} a36=0.03883624±1.4103a_{36}= -0.03883624 \pm 1.4 \cdot 10^{-3}
a37=0.16346245±1.7103a_{37}= -0.16346245 \pm 1.7 \cdot 10^{-3} a38=0.98691164±1.1103a_{38}= -0.98691164 \pm 1.1 \cdot 10^{-3} a39=0.40408588±1.5103a_{39}= -0.40408588 \pm 1.5 \cdot 10^{-3}
a40=1.51934752±1.2103a_{40}= -1.51934752 \pm 1.2 \cdot 10^{-3} a41=0.85362131±1.2103a_{41}= -0.85362131 \pm 1.2 \cdot 10^{-3} a42=+2.45084974±1.0103a_{42}= +2.45084974 \pm 1.0 \cdot 10^{-3}
a43=+0.31238335±1.4103a_{43}= +0.31238335 \pm 1.4 \cdot 10^{-3} a44=+0.02889352±1.3103a_{44}= +0.02889352 \pm 1.3 \cdot 10^{-3} a45=1.67803234±1.5103a_{45}= -1.67803234 \pm 1.5 \cdot 10^{-3}
a46=+0.91811508±1.5103a_{46}= +0.91811508 \pm 1.5 \cdot 10^{-3} a47=0.51211644±1.4103a_{47}= -0.51211644 \pm 1.4 \cdot 10^{-3} a48=+1.40481084±1.4103a_{48}= +1.40481084 \pm 1.4 \cdot 10^{-3}
a49=+1.93110618±1.2103a_{49}= +1.93110618 \pm 1.2 \cdot 10^{-3} a50=1.21237894±1.2103a_{50}= -1.21237894 \pm 1.2 \cdot 10^{-3} a51=+1.68724519±1.6103a_{51}= +1.68724519 \pm 1.6 \cdot 10^{-3}
a52=0.00959396±1.4103a_{52}= -0.00959396 \pm 1.4 \cdot 10^{-3} a53=1.27738153±1.0103a_{53}= -1.27738153 \pm 1.0 \cdot 10^{-3} a54=+0.17566353±1.4103a_{54}= +0.17566353 \pm 1.4 \cdot 10^{-3}
a55=+1.24842838±9.4104a_{55}= +1.24842838 \pm 9.4 \cdot 10^{-4} a56=+1.74036461±1.0103a_{56}= +1.74036461 \pm 1.0 \cdot 10^{-3} a57=1.46341691±1.1103a_{57}= -1.46341691 \pm 1.1 \cdot 10^{-3}
a58=0.02479062±1.0103a_{58}= -0.02479062 \pm 1.0 \cdot 10^{-3} a59=+1.25718691±1.3103a_{59}= +1.25718691 \pm 1.3 \cdot 10^{-3} a60=0.07532646±1.6103a_{60}= -0.07532646 \pm 1.6 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000