Properties

Label 11.162
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 14.82740
Fricke sign 1-1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 14.8274044216704387574107898134±810814.8274044216704387574107898134 \pm 8 \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=1.83574704±1.1103a_{2}= -1.83574704 \pm 1.1 \cdot 10^{-3} a3=+0.01781603±9.7104a_{3}= +0.01781603 \pm 9.7 \cdot 10^{-4}
a4=+2.36996720±1.3103a_{4}= +2.36996720 \pm 1.3 \cdot 10^{-3} a5=0.23274490±1.0103a_{5}= -0.23274490 \pm 1.0 \cdot 10^{-3} a6=0.03270573±1.2103a_{6}= -0.03270573 \pm 1.2 \cdot 10^{-3}
a7=1.29577121±1.0103a_{7}= -1.29577121 \pm 1.0 \cdot 10^{-3} a8=2.51491324±1.1103a_{8}= -2.51491324 \pm 1.1 \cdot 10^{-3} a9=0.99968259±1.0103a_{9}= -0.99968259 \pm 1.0 \cdot 10^{-3}
a10=+0.42726076±1.2103a_{10}= +0.42726076 \pm 1.2 \cdot 10^{-3} a11=+0.30151134±1.0108a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} a12=+0.04222341±1.2103a_{12}= +0.04222341 \pm 1.2 \cdot 10^{-3}
a13=0.79493299±8.0104a_{13}= -0.79493299 \pm 8.0 \cdot 10^{-4} a14=+2.37870817±8.4104a_{14}= +2.37870817 \pm 8.4 \cdot 10^{-4} a15=0.00414659±7.7104a_{15}= -0.00414659 \pm 7.7 \cdot 10^{-4}
a16=+2.24677734±1.0103a_{16}= +2.24677734 \pm 1.0 \cdot 10^{-3} a17=1.03699708±1.0103a_{17}= -1.03699708 \pm 1.0 \cdot 10^{-3} a18=+1.83516436±1.1103a_{18}= +1.83516436 \pm 1.1 \cdot 10^{-3}
a19=+0.93345291±7.3104a_{19}= +0.93345291 \pm 7.3 \cdot 10^{-4} a20=0.55159778±1.3103a_{20}= -0.55159778 \pm 1.3 \cdot 10^{-3} a21=0.02308550±7.8104a_{21}= -0.02308550 \pm 7.8 \cdot 10^{-4}
a22=0.55349856±1.1103a_{22}= -0.55349856 \pm 1.1 \cdot 10^{-3} a23=1.29188712±9.4104a_{23}= -1.29188712 \pm 9.4 \cdot 10^{-4} a24=0.04480577±1.3103a_{24}= -0.04480577 \pm 1.3 \cdot 10^{-3}
a25=0.94582981±8.4104a_{25}= -0.94582981 \pm 8.4 \cdot 10^{-4} a26=+1.45929589±6.2104a_{26}= +1.45929589 \pm 6.2 \cdot 10^{-4} a27=0.03562641±9.3104a_{27}= -0.03562641 \pm 9.3 \cdot 10^{-4}
a28=3.07093528±1.0103a_{28}= -3.07093528 \pm 1.0 \cdot 10^{-3} a29=0.22668458±9.3104a_{29}= -0.22668458 \pm 9.3 \cdot 10^{-4} a30=+0.00761209±7.1104a_{30}= +0.00761209 \pm 7.1 \cdot 10^{-4}
a31=0.93905401±9.9104a_{31}= -0.93905401 \pm 9.9 \cdot 10^{-4} a32=1.60960161±8.5104a_{32}= -1.60960161 \pm 8.5 \cdot 10^{-4} a33=+0.00537174±9.7104a_{33}= +0.00537174 \pm 9.7 \cdot 10^{-4}
a34=+1.90366432±1.2103a_{34}= +1.90366432 \pm 1.2 \cdot 10^{-3} a35=+0.30158414±9.6104a_{35}= +0.30158414 \pm 9.6 \cdot 10^{-4} a36=2.36921495±1.1103a_{36}= -2.36921495 \pm 1.1 \cdot 10^{-3}
a37=1.59962290±1.0103a_{37}= -1.59962290 \pm 1.0 \cdot 10^{-3} a38=1.71358342±1.0103a_{38}= -1.71358342 \pm 1.0 \cdot 10^{-3} a39=0.01416255±5.8104a_{39}= -0.01416255 \pm 5.8 \cdot 10^{-4}
a40=+0.58533323±9.5104a_{40}= +0.58533323 \pm 9.5 \cdot 10^{-4} a41=+0.42371092±6.6104a_{41}= +0.42371092 \pm 6.6 \cdot 10^{-4} a42=+0.04237914±8.6104a_{42}= +0.04237914 \pm 8.6 \cdot 10^{-4}
a43=+0.16705464±9.6104a_{43}= +0.16705464 \pm 9.6 \cdot 10^{-4} a44=+0.71457200±1.3103a_{44}= +0.71457200 \pm 1.3 \cdot 10^{-3} a45=+0.23267102±1.0103a_{45}= +0.23267102 \pm 1.0 \cdot 10^{-3}
a46=+2.37157796±1.3103a_{46}= +2.37157796 \pm 1.3 \cdot 10^{-3} a47=1.96608973±8.0104a_{47}= -1.96608973 \pm 8.0 \cdot 10^{-4} a48=+0.04002865±1.0103a_{48}= +0.04002865 \pm 1.0 \cdot 10^{-3}
a49=+0.67902304±8.9104a_{49}= +0.67902304 \pm 8.9 \cdot 10^{-4} a50=+1.73630428±1.2103a_{50}= +1.73630428 \pm 1.2 \cdot 10^{-3} a51=0.01847517±9.9104a_{51}= -0.01847517 \pm 9.9 \cdot 10^{-4}
a52=1.88396512±8.4104a_{52}= -1.88396512 \pm 8.4 \cdot 10^{-4} a53=+0.25747578±7.7104a_{53}= +0.25747578 \pm 7.7 \cdot 10^{-4} a54=+0.06540107±8.0104a_{54}= +0.06540107 \pm 8.0 \cdot 10^{-4}
a55=0.07017523±1.0103a_{55}= -0.07017523 \pm 1.0 \cdot 10^{-3} a56=+3.25875218±6.9104a_{56}= +3.25875218 \pm 6.9 \cdot 10^{-4} a57=+0.01663043±6.5104a_{57}= +0.01663043 \pm 6.5 \cdot 10^{-4}
a58=+0.41613555±9.0104a_{58}= +0.41613555 \pm 9.0 \cdot 10^{-4} a59=+0.17526237±1.1103a_{59}= +0.17526237 \pm 1.1 \cdot 10^{-3} a60=0.00982728±6.1104a_{60}= -0.00982728 \pm 6.1 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000