Properties

Label 3.17
Level 33
Weight 00
Character 3.1
Symmetry even
RR 11.88997
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: 11.8899755746457276696737304641±5101011.8899755746457276696737304641 \pm 5 \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=+1.48875054±1108a_{2}= +1.48875054 \pm 1 \cdot 10^{-8} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+1.21637817±1108a_{4}= +1.21637817 \pm 1 \cdot 10^{-8} a5=+1.05751345±1108a_{5}= +1.05751345 \pm 1 \cdot 10^{-8} a6=0.85953053±1.0108a_{6}= -0.85953053 \pm 1.0 \cdot 10^{-8}
a7=+1.38681493±1108a_{7}= +1.38681493 \pm 1 \cdot 10^{-8} a8=+0.32213312±1108a_{8}= +0.32213312 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+1.57437372±1108a_{10}= +1.57437372 \pm 1 \cdot 10^{-8} a11=+0.86133456±1108a_{11}= +0.86133456 \pm 1 \cdot 10^{-8} a12=0.70227626±1.0108a_{12}= -0.70227626 \pm 1.0 \cdot 10^{-8}
a13=0.35392162±1108a_{13}= -0.35392162 \pm 1 \cdot 10^{-8} a14=+2.06462147±1108a_{14}= +2.06462147 \pm 1 \cdot 10^{-8} a15=0.61055567±1.0108a_{15}= -0.61055567 \pm 1.0 \cdot 10^{-8}
a16=0.73680232±1108a_{16}= -0.73680232 \pm 1 \cdot 10^{-8} a17=+0.46036502±1108a_{17}= +0.46036502 \pm 1 \cdot 10^{-8} a18=+0.49625018±1.0108a_{18}= +0.49625018 \pm 1.0 \cdot 10^{-8}
a19=1.26693887±1108a_{19}= -1.26693887 \pm 1 \cdot 10^{-8} a20=+1.28633627±1108a_{20}= +1.28633627 \pm 1 \cdot 10^{-8} a21=0.80067797±1.0108a_{21}= -0.80067797 \pm 1.0 \cdot 10^{-8}
a22=+1.28231229±1108a_{22}= +1.28231229 \pm 1 \cdot 10^{-8} a23=0.95212914±1108a_{23}= -0.95212914 \pm 1 \cdot 10^{-8} a24=0.18598364±1.0108a_{24}= -0.18598364 \pm 1.0 \cdot 10^{-8}
a25=+0.11833469±1108a_{25}= +0.11833469 \pm 1 \cdot 10^{-8} a26=0.52690101±1108a_{26}= -0.52690101 \pm 1 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+1.68689140±1108a_{28}= +1.68689140 \pm 1 \cdot 10^{-8} a29=+0.26788428±1108a_{29}= +0.26788428 \pm 1 \cdot 10^{-8} a30=0.90896509±1.0108a_{30}= -0.90896509 \pm 1.0 \cdot 10^{-8}
a31=+0.24009795±1108a_{31}= +0.24009795 \pm 1 \cdot 10^{-8} a32=1.41904797±1108a_{32}= -1.41904797 \pm 1 \cdot 10^{-8} a33=0.49729174±1.0108a_{33}= -0.49729174 \pm 1.0 \cdot 10^{-8}
a34=+0.68536868±1108a_{34}= +0.68536868 \pm 1 \cdot 10^{-8} a35=+1.46657544±1108a_{35}= +1.46657544 \pm 1 \cdot 10^{-8} a36=+0.40545939±1.0108a_{36}= +0.40545939 \pm 1.0 \cdot 10^{-8}
a37=+0.22069137±1108a_{37}= +0.22069137 \pm 1 \cdot 10^{-8} a38=1.88615592±1108a_{38}= -1.88615592 \pm 1 \cdot 10^{-8} a39=+0.20433675±1.0108a_{39}= +0.20433675 \pm 1.0 \cdot 10^{-8}
a40=+0.34066010±1108a_{40}= +0.34066010 \pm 1 \cdot 10^{-8} a41=+0.02289290±1108a_{41}= +0.02289290 \pm 1 \cdot 10^{-8} a42=1.19200976±1.0108a_{42}= -1.19200976 \pm 1.0 \cdot 10^{-8}
a43=+0.77379092±1108a_{43}= +0.77379092 \pm 1 \cdot 10^{-8} a44=+1.04770855±1108a_{44}= +1.04770855 \pm 1 \cdot 10^{-8} a45=+0.35250448±1.0108a_{45}= +0.35250448 \pm 1.0 \cdot 10^{-8}
a46=1.41748278±1108a_{46}= -1.41748278 \pm 1 \cdot 10^{-8} a47=0.16073558±1108a_{47}= -0.16073558 \pm 1 \cdot 10^{-8} a48=+0.42539302±1.0108a_{48}= +0.42539302 \pm 1.0 \cdot 10^{-8}
a49=+0.92325564±1108a_{49}= +0.92325564 \pm 1 \cdot 10^{-8} a50=+0.17617084±1108a_{50}= +0.17617084 \pm 1 \cdot 10^{-8} a51=0.26579187±1.0108a_{51}= -0.26579187 \pm 1.0 \cdot 10^{-8}
a52=0.43050254±1108a_{52}= -0.43050254 \pm 1 \cdot 10^{-8} a53=1.60254607±1108a_{53}= -1.60254607 \pm 1 \cdot 10^{-8} a54=0.28651018±1.0108a_{54}= -0.28651018 \pm 1.0 \cdot 10^{-8}
a55=+0.91087288±1108a_{55}= +0.91087288 \pm 1 \cdot 10^{-8} a56=+0.44673902±1108a_{56}= +0.44673902 \pm 1 \cdot 10^{-8} a57=+0.73146750±1.0108a_{57}= +0.73146750 \pm 1.0 \cdot 10^{-8}
a58=+0.39881287±1108a_{58}= +0.39881287 \pm 1 \cdot 10^{-8} a59=+0.79376959±1108a_{59}= +0.79376959 \pm 1 \cdot 10^{-8} a60=0.74266659±1.0108a_{60}= -0.74266659 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000