Properties

Label 11.43
Level 1111
Weight 00
Character 11.1
Symmetry even
RR 8.142021
Fricke sign +1+1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 8.14202179524998289176347244901±210118.14202179524998289176347244901 \pm 2 \cdot 10^{-11}

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=+1.59270770±1108a_{2}= +1.59270770 \pm 1 \cdot 10^{-8} a3=+0.85525842±1108a_{3}= +0.85525842 \pm 1 \cdot 10^{-8}
a4=+1.53671783±1108a_{4}= +1.53671783 \pm 1 \cdot 10^{-8} a5=+0.28038333±1108a_{5}= +0.28038333 \pm 1 \cdot 10^{-8} a6=+1.36217668±1108a_{6}= +1.36217668 \pm 1 \cdot 10^{-8}
a7=+1.13968858±1108a_{7}= +1.13968858 \pm 1 \cdot 10^{-8} a8=+0.85483463±1108a_{8}= +0.85483463 \pm 1 \cdot 10^{-8} a9=0.26853303±1108a_{9}= -0.26853303 \pm 1 \cdot 10^{-8}
a10=+0.44656869±1108a_{10}= +0.44656869 \pm 1 \cdot 10^{-8} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=+1.31429087±1108a_{12}= +1.31429087 \pm 1 \cdot 10^{-8}
a13=+0.59811165±1108a_{13}= +0.59811165 \pm 1 \cdot 10^{-8} a14=+1.81519079±1108a_{14}= +1.81519079 \pm 1 \cdot 10^{-8} a15=+0.23980021±1108a_{15}= +0.23980021 \pm 1 \cdot 10^{-8}
a16=0.17521614±1108a_{16}= -0.17521614 \pm 1 \cdot 10^{-8} a17=0.28555021±1108a_{17}= -0.28555021 \pm 1 \cdot 10^{-8} a18=0.42769463±1108a_{18}= -0.42769463 \pm 1 \cdot 10^{-8}
a19=+1.74176402±1108a_{19}= +1.74176402 \pm 1 \cdot 10^{-8} a20=+0.43087006±1108a_{20}= +0.43087006 \pm 1 \cdot 10^{-8} a21=+0.97472826±1108a_{21}= +0.97472826 \pm 1 \cdot 10^{-8}
a22=0.48021944±1.0108a_{22}= -0.48021944 \pm 1.0 \cdot 10^{-8} a23=0.62636712±1108a_{23}= -0.62636712 \pm 1 \cdot 10^{-8} a24=+0.73110451±1108a_{24}= +0.73110451 \pm 1 \cdot 10^{-8}
a25=0.92138519±1108a_{25}= -0.92138519 \pm 1 \cdot 10^{-8} a26=+0.95261703±1108a_{26}= +0.95261703 \pm 1 \cdot 10^{-8} a27=1.08492356±1108a_{27}= -1.08492356 \pm 1 \cdot 10^{-8}
a28=+1.75137977±1108a_{28}= +1.75137977 \pm 1 \cdot 10^{-8} a29=+0.94672410±1108a_{29}= +0.94672410 \pm 1 \cdot 10^{-8} a30=+0.38193163±1108a_{30}= +0.38193163 \pm 1 \cdot 10^{-8}
a31=1.12689637±1108a_{31}= -1.12689637 \pm 1 \cdot 10^{-8} a32=1.13390272±1108a_{32}= -1.13390272 \pm 1 \cdot 10^{-8} a33=0.25787012±1.0108a_{33}= -0.25787012 \pm 1.0 \cdot 10^{-8}
a34=0.45479802±1108a_{34}= -0.45479802 \pm 1 \cdot 10^{-8} a35=+0.31954968±1108a_{35}= +0.31954968 \pm 1 \cdot 10^{-8} a36=0.41265950±1108a_{36}= -0.41265950 \pm 1 \cdot 10^{-8}
a37=1.23957119±1108a_{37}= -1.23957119 \pm 1 \cdot 10^{-8} a38=+2.77412097±1108a_{38}= +2.77412097 \pm 1 \cdot 10^{-8} a39=+0.51154002±1108a_{39}= +0.51154002 \pm 1 \cdot 10^{-8}
a40=+0.23968138±1108a_{40}= +0.23968138 \pm 1 \cdot 10^{-8} a41=+0.11054708±1108a_{41}= +0.11054708 \pm 1 \cdot 10^{-8} a42=+1.55245721±1108a_{42}= +1.55245721 \pm 1 \cdot 10^{-8}
a43=1.82463327±1108a_{43}= -1.82463327 \pm 1 \cdot 10^{-8} a44=0.46333786±1.0108a_{44}= -0.46333786 \pm 1.0 \cdot 10^{-8} a45=0.07529219±1108a_{45}= -0.07529219 \pm 1 \cdot 10^{-8}
a46=0.99761974±1108a_{46}= -0.99761974 \pm 1 \cdot 10^{-8} a47=+1.09465477±1108a_{47}= +1.09465477 \pm 1 \cdot 10^{-8} a48=0.14985508±1108a_{48}= -0.14985508 \pm 1 \cdot 10^{-8}
a49=+0.29889006±1108a_{49}= +0.29889006 \pm 1 \cdot 10^{-8} a50=1.46749729±1108a_{50}= -1.46749729 \pm 1 \cdot 10^{-8} a51=0.24421922±1108a_{51}= -0.24421922 \pm 1 \cdot 10^{-8}
a52=+0.91912883±1108a_{52}= +0.91912883 \pm 1 \cdot 10^{-8} a53=0.56517750±1108a_{53}= -0.56517750 \pm 1 \cdot 10^{-8} a54=1.72796611±1108a_{54}= -1.72796611 \pm 1 \cdot 10^{-8}
a55=0.08453876±1.0108a_{55}= -0.08453876 \pm 1.0 \cdot 10^{-8} a56=+0.97424526±1108a_{56}= +0.97424526 \pm 1 \cdot 10^{-8} a57=+1.48965834±1108a_{57}= +1.48965834 \pm 1 \cdot 10^{-8}
a58=+1.50785476±1108a_{58}= +1.50785476 \pm 1 \cdot 10^{-8} a59=+0.48456164±1108a_{59}= +0.48456164 \pm 1 \cdot 10^{-8} a60=+0.36850525±1108a_{60}= +0.36850525 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000