Properties

Label 7.17
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 7.054070
Fricke sign +1+1

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Maass form invariants

Level: 7 7
Weight: 0 0
Character: 7.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 7.05407006402443772681162287093±310127.05407006402443772681162287093 \pm 3 \cdot 10^{-12}

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=1.40005431±7.7108a_{2}= -1.40005431 \pm 7.7 \cdot 10^{-8} a3=+0.77754554±5.1108a_{3}= +0.77754554 \pm 5.1 \cdot 10^{-8}
a4=+0.96015208±4.6108a_{4}= +0.96015208 \pm 4.6 \cdot 10^{-8} a5=+0.34215209±5.4108a_{5}= +0.34215209 \pm 5.4 \cdot 10^{-8} a6=1.08860598±6.1108a_{6}= -1.08860598 \pm 6.1 \cdot 10^{-8}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=+0.05578925±5.0108a_{8}= +0.05578925 \pm 5.0 \cdot 10^{-8} a9=0.39542294±4.8108a_{9}= -0.39542294 \pm 4.8 \cdot 10^{-8}
a10=0.47903151±5.6108a_{10}= -0.47903151 \pm 5.6 \cdot 10^{-8} a11=1.64843106±4.6108a_{11}= -1.64843106 \pm 4.6 \cdot 10^{-8} a12=+0.74656197±4.0108a_{12}= +0.74656197 \pm 4.0 \cdot 10^{-8}
a13=+0.36765423±5.6108a_{13}= +0.36765423 \pm 5.6 \cdot 10^{-8} a14=+0.52917079±8.7108a_{14}= +0.52917079 \pm 8.7 \cdot 10^{-8} a15=+0.26603883±4.3108a_{15}= +0.26603883 \pm 4.3 \cdot 10^{-8}
a16=1.03826006±6.5108a_{16}= -1.03826006 \pm 6.5 \cdot 10^{-8} a17=0.30573775±4.2108a_{17}= -0.30573775 \pm 4.2 \cdot 10^{-8} a18=+0.55361359±4.6108a_{18}= +0.55361359 \pm 4.6 \cdot 10^{-8}
a19=1.46294233±5.4108a_{19}= -1.46294233 \pm 5.4 \cdot 10^{-8} a20=+0.32851804±3.5108a_{20}= +0.32851804 \pm 3.5 \cdot 10^{-8} a21=0.29388459±6.2108a_{21}= -0.29388459 \pm 6.2 \cdot 10^{-8}
a22=+2.30789302±4.6108a_{22}= +2.30789302 \pm 4.6 \cdot 10^{-8} a23=+0.15051419±6.9108a_{23}= +0.15051419 \pm 6.9 \cdot 10^{-8} a24=+0.04337868±3.3108a_{24}= +0.04337868 \pm 3.3 \cdot 10^{-8}
a25=0.88293195±5.1108a_{25}= -0.88293195 \pm 5.1 \cdot 10^{-8} a26=0.51473589±6.8108a_{26}= -0.51473589 \pm 6.8 \cdot 10^{-8} a27=1.08500488±5.6108a_{27}= -1.08500488 \pm 5.6 \cdot 10^{-8}
a28=0.36290338±5.6108a_{28}= -0.36290338 \pm 5.6 \cdot 10^{-8} a29=+1.80198246±5.1108a_{29}= +1.80198246 \pm 5.1 \cdot 10^{-8} a30=0.37246881±4.9108a_{30}= -0.37246881 \pm 4.9 \cdot 10^{-8}
a31=0.35875082±4.1108a_{31}= -0.35875082 \pm 4.1 \cdot 10^{-8} a32=+1.39783123±6.7108a_{32}= +1.39783123 \pm 6.7 \cdot 10^{-8} a33=1.28173021±3.8108a_{33}= -1.28173021 \pm 3.8 \cdot 10^{-8}
a34=+0.42804945±5.0108a_{34}= +0.42804945 \pm 5.0 \cdot 10^{-8} a35=0.12932133±6.5108a_{35}= -0.12932133 \pm 6.5 \cdot 10^{-8} a36=0.37966616±2.7108a_{36}= -0.37966616 \pm 2.7 \cdot 10^{-8}
a37=0.70779263±5.2108a_{37}= -0.70779263 \pm 5.2 \cdot 10^{-8} a38=+2.04819872±5.3108a_{38}= +2.04819872 \pm 5.3 \cdot 10^{-8} a39=+0.28586790±4.2108a_{39}= +0.28586790 \pm 4.2 \cdot 10^{-8}
a40=+0.01908841±5.2108a_{40}= +0.01908841 \pm 5.2 \cdot 10^{-8} a41=1.22347525±6.7108a_{41}= -1.22347525 \pm 6.7 \cdot 10^{-8} a42=+0.41145439±1.3107a_{42}= +0.41145439 \pm 1.3 \cdot 10^{-7}
a43=+0.10338373±4.0108a_{43}= +0.10338373 \pm 4.0 \cdot 10^{-8} a44=1.58274452±3.4108a_{44}= -1.58274452 \pm 3.4 \cdot 10^{-8} a45=0.13529478±4.3108a_{45}= -0.13529478 \pm 4.3 \cdot 10^{-8}
a46=0.21072804±8.2108a_{46}= -0.21072804 \pm 8.2 \cdot 10^{-8} a47=+1.03833078±6.2108a_{47}= +1.03833078 \pm 6.2 \cdot 10^{-8} a48=0.80729447±4.9108a_{48}= -0.80729447 \pm 4.9 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+1.23615268±6.3108a_{50}= +1.23615268 \pm 6.3 \cdot 10^{-8} a51=0.23772502±3.1108a_{51}= -0.23772502 \pm 3.1 \cdot 10^{-8}
a52=+0.35300397±3.6108a_{52}= +0.35300397 \pm 3.6 \cdot 10^{-8} a53=+0.70159950±4.2108a_{53}= +0.70159950 \pm 4.2 \cdot 10^{-8} a54=+1.51906576±7.1108a_{54}= +1.51906576 \pm 7.1 \cdot 10^{-8}
a55=0.56401413±4.5108a_{55}= -0.56401413 \pm 4.5 \cdot 10^{-8} a56=0.02108635±6.1108a_{56}= -0.02108635 \pm 6.1 \cdot 10^{-8} a57=1.13750428±2.7108a_{57}= -1.13750428 \pm 2.7 \cdot 10^{-8}
a58=2.52287331±5.2108a_{58}= -2.52287331 \pm 5.2 \cdot 10^{-8} a59=+0.56523109±8.4108a_{59}= +0.56523109 \pm 8.4 \cdot 10^{-8} a60=+0.25543774±3.5108a_{60}= +0.25543774 \pm 3.5 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000