Properties

Label 7.2
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 3.190858
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: 3.1908587629390006224343617764±1010143.1908587629390006224343617764 \pm 10 \cdot 10^{-14}

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=+0.83625991±1108a_{2}= +0.83625991 \pm 1 \cdot 10^{-8} a3=0.26984682±1108a_{3}= -0.26984682 \pm 1 \cdot 10^{-8}
a4=0.30066936±1108a_{4}= -0.30066936 \pm 1 \cdot 10^{-8} a5=+1.13127327±1108a_{5}= +1.13127327 \pm 1 \cdot 10^{-8} a6=0.22566208±1108a_{6}= -0.22566208 \pm 1 \cdot 10^{-8}
a7=+0.37796447±1.0108a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} a8=1.08769764±1108a_{8}= -1.08769764 \pm 1 \cdot 10^{-8} a9=0.92718269±1108a_{9}= -0.92718269 \pm 1 \cdot 10^{-8}
a10=+0.94603848±1108a_{10}= +0.94603848 \pm 1 \cdot 10^{-8} a11=+0.99072323±1108a_{11}= +0.99072323 \pm 1 \cdot 10^{-8} a12=+0.08113467±1108a_{12}= +0.08113467 \pm 1 \cdot 10^{-8}
a13=0.42786634±1108a_{13}= -0.42786634 \pm 1 \cdot 10^{-8} a14=+0.31607654±1.0108a_{14}= +0.31607654 \pm 1.0 \cdot 10^{-8} a15=0.30527050±1108a_{15}= -0.30527050 \pm 1 \cdot 10^{-8}
a16=0.60892858±1108a_{16}= -0.60892858 \pm 1 \cdot 10^{-8} a17=0.11183765±1108a_{17}= -0.11183765 \pm 1 \cdot 10^{-8} a18=0.77536572±1108a_{18}= -0.77536572 \pm 1 \cdot 10^{-8}
a19=+1.44527991±1108a_{19}= +1.44527991 \pm 1 \cdot 10^{-8} a20=0.34013921±1108a_{20}= -0.34013921 \pm 1 \cdot 10^{-8} a21=0.10199251±1.0108a_{21}= -0.10199251 \pm 1.0 \cdot 10^{-8}
a22=+0.82850212±1108a_{22}= +0.82850212 \pm 1 \cdot 10^{-8} a23=0.56069614±1108a_{23}= -0.56069614 \pm 1 \cdot 10^{-8} a24=+0.29351175±1108a_{24}= +0.29351175 \pm 1 \cdot 10^{-8}
a25=+0.27977921±1108a_{25}= +0.27977921 \pm 1 \cdot 10^{-8} a26=0.35780747±1108a_{26}= -0.35780747 \pm 1 \cdot 10^{-8} a27=+0.52004413±1108a_{27}= +0.52004413 \pm 1 \cdot 10^{-8}
a28=0.11364234±1.0108a_{28}= -0.11364234 \pm 1.0 \cdot 10^{-8} a29=1.18936259±1108a_{29}= -1.18936259 \pm 1 \cdot 10^{-8} a30=0.25528548±1108a_{30}= -0.25528548 \pm 1 \cdot 10^{-8}
a31=0.29775645±1108a_{31}= -0.29775645 \pm 1 \cdot 10^{-8} a32=+0.57847509±1108a_{32}= +0.57847509 \pm 1 \cdot 10^{-8} a33=0.26734352±1108a_{33}= -0.26734352 \pm 1 \cdot 10^{-8}
a34=0.09352534±1108a_{34}= -0.09352534 \pm 1 \cdot 10^{-8} a35=+0.42758110±1.0108a_{35}= +0.42758110 \pm 1.0 \cdot 10^{-8} a36=+0.27877543±1108a_{36}= +0.27877543 \pm 1 \cdot 10^{-8}
a37=+1.02114130±1108a_{37}= +1.02114130 \pm 1 \cdot 10^{-8} a38=+1.20862965±1108a_{38}= +1.20862965 \pm 1 \cdot 10^{-8} a39=+0.11545837±1108a_{39}= +0.11545837 \pm 1 \cdot 10^{-8}
a40=1.23048327±1108a_{40}= -1.23048327 \pm 1 \cdot 10^{-8} a41=0.99343549±1108a_{41}= -0.99343549 \pm 1 \cdot 10^{-8} a42=0.08529225±1.0108a_{42}= -0.08529225 \pm 1.0 \cdot 10^{-8}
a43=+0.04182029±1108a_{43}= +0.04182029 \pm 1 \cdot 10^{-8} a44=0.29788012±1108a_{44}= -0.29788012 \pm 1 \cdot 10^{-8} a45=1.04889699±1108a_{45}= -1.04889699 \pm 1 \cdot 10^{-8}
a46=0.46888770±1108a_{46}= -0.46888770 \pm 1 \cdot 10^{-8} a47=+1.28721012±1108a_{47}= +1.28721012 \pm 1 \cdot 10^{-8} a48=+0.16431744±1108a_{48}= +0.16431744 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.23396813±1108a_{50}= +0.23396813 \pm 1 \cdot 10^{-8} a51=+0.03017903±1108a_{51}= +0.03017903 \pm 1 \cdot 10^{-8}
a52=+0.12864630±1108a_{52}= +0.12864630 \pm 1 \cdot 10^{-8} a53=+0.02689712±1108a_{53}= +0.02689712 \pm 1 \cdot 10^{-8} a54=+0.43489206±1108a_{54}= +0.43489206 \pm 1 \cdot 10^{-8}
a55=+1.12077870±1108a_{55}= +1.12077870 \pm 1 \cdot 10^{-8} a56=0.41111107±1.0108a_{56}= -0.41111107 \pm 1.0 \cdot 10^{-8} a57=0.39000419±1108a_{57}= -0.39000419 \pm 1 \cdot 10^{-8}
a58=0.99461626±1108a_{58}= -0.99461626 \pm 1 \cdot 10^{-8} a59=0.02583187±1108a_{59}= -0.02583187 \pm 1 \cdot 10^{-8} a60=+0.09178549±1108a_{60}= +0.09178549 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000