Properties

Label 3.18
Level 33
Weight 00
Character 3.1
Symmetry even
RR 12.58046
Fricke sign 1-1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 12.5804630570261302059900701126±210912.5804630570261302059900701126 \pm 2 \cdot 10^{-9}

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=+0.81992642±1108a_{2}= +0.81992642 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.32772066±1108a_{4}= -0.32772066 \pm 1 \cdot 10^{-8} a5=1.55378752±1108a_{5}= -1.55378752 \pm 1 \cdot 10^{-8} a6=+0.47338474±1.1108a_{6}= +0.47338474 \pm 1.1 \cdot 10^{-8}
a7=+0.32162885±1108a_{7}= +0.32162885 \pm 1 \cdot 10^{-8} a8=1.08863325±1108a_{8}= -1.08863325 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=1.27399144±1108a_{10}= -1.27399144 \pm 1 \cdot 10^{-8} a11=1.25679502±1108a_{11}= -1.25679502 \pm 1 \cdot 10^{-8} a12=0.18920961±1.1108a_{12}= -0.18920961 \pm 1.1 \cdot 10^{-8}
a13=0.29739046±1108a_{13}= -0.29739046 \pm 1 \cdot 10^{-8} a14=+0.26371199±1108a_{14}= +0.26371199 \pm 1 \cdot 10^{-8} a15=0.89707964±1.0108a_{15}= -0.89707964 \pm 1.0 \cdot 10^{-8}
a16=0.56487851±1108a_{16}= -0.56487851 \pm 1 \cdot 10^{-8} a17=+0.70455719±1108a_{17}= +0.70455719 \pm 1 \cdot 10^{-8} a18=+0.27330881±1.1108a_{18}= +0.27330881 \pm 1.1 \cdot 10^{-8}
a19=0.71743121±1108a_{19}= -0.71743121 \pm 1 \cdot 10^{-8} a20=+0.50920828±1108a_{20}= +0.50920828 \pm 1 \cdot 10^{-8} a21=+0.18569250±1.1108a_{21}= +0.18569250 \pm 1.1 \cdot 10^{-8}
a22=1.03047944±1108a_{22}= -1.03047944 \pm 1 \cdot 10^{-8} a23=+0.43930859±1108a_{23}= +0.43930859 \pm 1 \cdot 10^{-8} a24=0.62852270±1.0108a_{24}= -0.62852270 \pm 1.0 \cdot 10^{-8}
a25=+1.41425566±1108a_{25}= +1.41425566 \pm 1 \cdot 10^{-8} a26=0.24383830±1108a_{26}= -0.24383830 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.10540442±1108a_{28}= -0.10540442 \pm 1 \cdot 10^{-8} a29=1.37724240±1108a_{29}= -1.37724240 \pm 1 \cdot 10^{-8} a30=0.73553930±1.1108a_{30}= -0.73553930 \pm 1.1 \cdot 10^{-8}
a31=+1.83715693±1108a_{31}= +1.83715693 \pm 1 \cdot 10^{-8} a32=+0.62547444±1108a_{32}= +0.62547444 \pm 1 \cdot 10^{-8} a33=0.72561094±1.0108a_{33}= -0.72561094 \pm 1.0 \cdot 10^{-8}
a34=+0.57768505±1108a_{34}= +0.57768505 \pm 1 \cdot 10^{-8} a35=0.49974289±1108a_{35}= -0.49974289 \pm 1 \cdot 10^{-8} a36=0.10924022±1.1108a_{36}= -0.10924022 \pm 1.1 \cdot 10^{-8}
a37=0.34327806±1108a_{37}= -0.34327806 \pm 1 \cdot 10^{-8} a38=0.58824081±1108a_{38}= -0.58824081 \pm 1 \cdot 10^{-8} a39=0.17169846±1.0108a_{39}= -0.17169846 \pm 1.0 \cdot 10^{-8}
a40=+1.69150476±1108a_{40}= +1.69150476 \pm 1 \cdot 10^{-8} a41=0.50604504±1108a_{41}= -0.50604504 \pm 1 \cdot 10^{-8} a42=+0.15225419±1.2108a_{42}= +0.15225419 \pm 1.2 \cdot 10^{-8}
a43=0.19390637±1108a_{43}= -0.19390637 \pm 1 \cdot 10^{-8} a44=+0.41187770±1108a_{44}= +0.41187770 \pm 1 \cdot 10^{-8} a45=0.51792917±1.0108a_{45}= -0.51792917 \pm 1.0 \cdot 10^{-8}
a46=+0.36020072±1108a_{46}= +0.36020072 \pm 1 \cdot 10^{-8} a47=0.45467588±1108a_{47}= -0.45467588 \pm 1 \cdot 10^{-8} a48=0.32613276±1.1108a_{48}= -0.32613276 \pm 1.1 \cdot 10^{-8}
a49=0.89655488±1108a_{49}= -0.89655488 \pm 1 \cdot 10^{-8} a50=+1.15958558±1108a_{50}= +1.15958558 \pm 1 \cdot 10^{-8} a51=+0.40677628±1.1108a_{51}= +0.40677628 \pm 1.1 \cdot 10^{-8}
a52=+0.09746100±1108a_{52}= +0.09746100 \pm 1 \cdot 10^{-8} a53=0.89731312±1108a_{53}= -0.89731312 \pm 1 \cdot 10^{-8} a54=+0.15779491±1.1108a_{54}= +0.15779491 \pm 1.1 \cdot 10^{-8}
a55=+1.95279242±1108a_{55}= +1.95279242 \pm 1 \cdot 10^{-8} a56=0.35013586±1108a_{56}= -0.35013586 \pm 1 \cdot 10^{-8} a57=0.41420910±1.1108a_{57}= -0.41420910 \pm 1.1 \cdot 10^{-8}
a58=1.12923743±1108a_{58}= -1.12923743 \pm 1 \cdot 10^{-8} a59=0.89738720±1108a_{59}= -0.89738720 \pm 1 \cdot 10^{-8} a60=+0.29399153±1.1108a_{60}= +0.29399153 \pm 1.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000