Properties

Label 5.10
Level 55
Weight 00
Character 5.1
Symmetry even
RR 6.823526
Fricke sign +1+1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 6.82352699542004840638783053459±810136.82352699542004840638783053459 \pm 8 \cdot 10^{-13}

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=1.50239859±1108a_{2}= -1.50239859 \pm 1 \cdot 10^{-8} a3=1.44420778±1108a_{3}= -1.44420778 \pm 1 \cdot 10^{-8}
a4=+1.25720152±1108a_{4}= +1.25720152 \pm 1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=+2.16977574±1108a_{6}= +2.16977574 \pm 1 \cdot 10^{-8}
a7=1.01867775±1108a_{7}= -1.01867775 \pm 1 \cdot 10^{-8} a8=0.38641921±1108a_{8}= -0.38641921 \pm 1 \cdot 10^{-8} a9=+1.08573612±1108a_{9}= +1.08573612 \pm 1 \cdot 10^{-8}
a10=+0.67189308±1.0108a_{10}= +0.67189308 \pm 1.0 \cdot 10^{-8} a11=+0.27403754±1108a_{11}= +0.27403754 \pm 1 \cdot 10^{-8} a12=1.81566022±1108a_{12}= -1.81566022 \pm 1 \cdot 10^{-8}
a13=0.60090893±1108a_{13}= -0.60090893 \pm 1 \cdot 10^{-8} a14=+1.53046002±1108a_{14}= +1.53046002 \pm 1 \cdot 10^{-8} a15=+0.64586935±1.0108a_{15}= +0.64586935 \pm 1.0 \cdot 10^{-8}
a16=0.67664585±1108a_{16}= -0.67664585 \pm 1 \cdot 10^{-8} a17=+1.16850492±1108a_{17}= +1.16850492 \pm 1 \cdot 10^{-8} a18=1.63120841±1108a_{18}= -1.63120841 \pm 1 \cdot 10^{-8}
a19=+0.04373142±1108a_{19}= +0.04373142 \pm 1 \cdot 10^{-8} a20=0.56223761±1.0108a_{20}= -0.56223761 \pm 1.0 \cdot 10^{-8} a21=+1.47118233±1108a_{21}= +1.47118233 \pm 1 \cdot 10^{-8}
a22=0.41171361±1108a_{22}= -0.41171361 \pm 1 \cdot 10^{-8} a23=0.85617233±1108a_{23}= -0.85617233 \pm 1 \cdot 10^{-8} a24=+0.55806963±1108a_{24}= +0.55806963 \pm 1 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+0.90280472±1108a_{26}= +0.90280472 \pm 1 \cdot 10^{-8} a27=0.12382077±1108a_{27}= -0.12382077 \pm 1 \cdot 10^{-8}
a28=1.28068322±1108a_{28}= -1.28068322 \pm 1 \cdot 10^{-8} a29=+1.02771347±1108a_{29}= +1.02771347 \pm 1 \cdot 10^{-8} a30=0.97035321±1.0108a_{30}= -0.97035321 \pm 1.0 \cdot 10^{-8}
a31=0.46294828±1108a_{31}= -0.46294828 \pm 1 \cdot 10^{-8} a32=+1.40301098±1108a_{32}= +1.40301098 \pm 1 \cdot 10^{-8} a33=0.39576715±1108a_{33}= -0.39576715 \pm 1 \cdot 10^{-8}
a34=1.75556014±1108a_{34}= -1.75556014 \pm 1 \cdot 10^{-8} a35=+0.45556654±1.0108a_{35}= +0.45556654 \pm 1.0 \cdot 10^{-8} a36=+1.36498910±1108a_{36}= +1.36498910 \pm 1 \cdot 10^{-8}
a37=+0.61665958±1108a_{37}= +0.61665958 \pm 1 \cdot 10^{-8} a38=0.06570202±1108a_{38}= -0.06570202 \pm 1 \cdot 10^{-8} a39=+0.86783735±1108a_{39}= +0.86783735 \pm 1 \cdot 10^{-8}
a40=+0.17281192±1.0108a_{40}= +0.17281192 \pm 1.0 \cdot 10^{-8} a41=0.49940161±1108a_{41}= -0.49940161 \pm 1 \cdot 10^{-8} a42=2.21030226±1108a_{42}= -2.21030226 \pm 1 \cdot 10^{-8}
a43=1.26831230±1108a_{43}= -1.26831230 \pm 1 \cdot 10^{-8} a44=+0.34452041±1108a_{44}= +0.34452041 \pm 1 \cdot 10^{-8} a45=0.48555595±1.0108a_{45}= -0.48555595 \pm 1.0 \cdot 10^{-8}
a46=+1.28631210±1108a_{46}= +1.28631210 \pm 1 \cdot 10^{-8} a47=+1.82916469±1108a_{47}= +1.82916469 \pm 1 \cdot 10^{-8} a48=+0.97721721±1108a_{48}= +0.97721721 \pm 1 \cdot 10^{-8}
a49=+0.03770436±1108a_{49}= +0.03770436 \pm 1 \cdot 10^{-8} a50=0.30047972±1.0108a_{50}= -0.30047972 \pm 1.0 \cdot 10^{-8} a51=1.68756390±1108a_{51}= -1.68756390 \pm 1 \cdot 10^{-8}
a52=0.75546362±1108a_{52}= -0.75546362 \pm 1 \cdot 10^{-8} a53=+0.94964223±1108a_{53}= +0.94964223 \pm 1 \cdot 10^{-8} a54=+0.18602815±1108a_{54}= +0.18602815 \pm 1 \cdot 10^{-8}
a55=0.12255331±1.0108a_{55}= -0.12255331 \pm 1.0 \cdot 10^{-8} a56=+0.39363665±1108a_{56}= +0.39363665 \pm 1 \cdot 10^{-8} a57=0.06315725±1108a_{57}= -0.06315725 \pm 1 \cdot 10^{-8}
a58=1.54403527±1108a_{58}= -1.54403527 \pm 1 \cdot 10^{-8} a59=0.12799937±1108a_{59}= -0.12799937 \pm 1 \cdot 10^{-8} a60=+0.81198794±1.0108a_{60}= +0.81198794 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000