Properties

Label 7.23
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 8.071618
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: 8.07161868258754741647199140303±710128.07161868258754741647199140303 \pm 7 \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=0.78095261±1108a_{2}= -0.78095261 \pm 1 \cdot 10^{-8} a3=+0.26104362±1108a_{3}= +0.26104362 \pm 1 \cdot 10^{-8}
a4=0.39011303±1108a_{4}= -0.39011303 \pm 1 \cdot 10^{-8} a5=1.40488222±1108a_{5}= -1.40488222 \pm 1 \cdot 10^{-8} a6=0.20386270±1108a_{6}= -0.20386270 \pm 1 \cdot 10^{-8}
a7=+0.37796447±1.0108a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} a8=+1.08561239±1108a_{8}= +1.08561239 \pm 1 \cdot 10^{-8} a9=0.93185623±1108a_{9}= -0.93185623 \pm 1 \cdot 10^{-8}
a10=+1.09714643±1108a_{10}= +1.09714643 \pm 1 \cdot 10^{-8} a11=+1.05965744±1108a_{11}= +1.05965744 \pm 1 \cdot 10^{-8} a12=0.10183652±1108a_{12}= -0.10183652 \pm 1 \cdot 10^{-8}
a13=+1.34568407±1108a_{13}= +1.34568407 \pm 1 \cdot 10^{-8} a14=0.29517234±1.5108a_{14}= -0.29517234 \pm 1.5 \cdot 10^{-8} a15=0.36673555±1108a_{15}= -0.36673555 \pm 1 \cdot 10^{-8}
a16=0.45769880±1108a_{16}= -0.45769880 \pm 1 \cdot 10^{-8} a17=0.21730688±1108a_{17}= -0.21730688 \pm 1 \cdot 10^{-8} a18=+0.72773555±1108a_{18}= +0.72773555 \pm 1 \cdot 10^{-8}
a19=+0.70636310±1108a_{19}= +0.70636310 \pm 1 \cdot 10^{-8} a20=+0.54806285±1108a_{20}= +0.54806285 \pm 1 \cdot 10^{-8} a21=+0.09866522±1.3108a_{21}= +0.09866522 \pm 1.3 \cdot 10^{-8}
a22=0.82754224±1108a_{22}= -0.82754224 \pm 1 \cdot 10^{-8} a23=0.80915214±1108a_{23}= -0.80915214 \pm 1 \cdot 10^{-8} a24=+0.28339219±1108a_{24}= +0.28339219 \pm 1 \cdot 10^{-8}
a25=+0.97369406±1108a_{25}= +0.97369406 \pm 1 \cdot 10^{-8} a26=1.05091549±1108a_{26}= -1.05091549 \pm 1 \cdot 10^{-8} a27=0.50429875±1108a_{27}= -0.50429875 \pm 1 \cdot 10^{-8}
a28=0.14744886±1.3108a_{28}= -0.14744886 \pm 1.3 \cdot 10^{-8} a29=+1.74010349±1108a_{29}= +1.74010349 \pm 1 \cdot 10^{-8} a30=+0.28640308±1108a_{30}= +0.28640308 \pm 1 \cdot 10^{-8}
a31=0.27967797±1108a_{31}= -0.27967797 \pm 1 \cdot 10^{-8} a32=0.72817132±1108a_{32}= -0.72817132 \pm 1 \cdot 10^{-8} a33=+0.27661682±1108a_{33}= +0.27661682 \pm 1 \cdot 10^{-8}
a34=+0.16970638±1108a_{34}= +0.16970638 \pm 1 \cdot 10^{-8} a35=0.53099557±1.3108a_{35}= -0.53099557 \pm 1.3 \cdot 10^{-8} a36=+0.36352925±1108a_{36}= +0.36352925 \pm 1 \cdot 10^{-8}
a37=+0.41526614±1108a_{37}= +0.41526614 \pm 1 \cdot 10^{-8} a38=0.55163610±1108a_{38}= -0.55163610 \pm 1 \cdot 10^{-8} a39=+0.35128225±1108a_{39}= +0.35128225 \pm 1 \cdot 10^{-8}
a40=1.52515755±1108a_{40}= -1.52515755 \pm 1 \cdot 10^{-8} a41=0.09704787±1108a_{41}= -0.09704787 \pm 1 \cdot 10^{-8} a42=0.07705286±1.8108a_{42}= -0.07705286 \pm 1.8 \cdot 10^{-8}
a43=+1.05932709±1108a_{43}= +1.05932709 \pm 1 \cdot 10^{-8} a44=0.41338617±1108a_{44}= -0.41338617 \pm 1 \cdot 10^{-8} a45=+1.30914825±1108a_{45}= +1.30914825 \pm 1 \cdot 10^{-8}
a46=+0.63190947±1108a_{46}= +0.63190947 \pm 1 \cdot 10^{-8} a47=0.18264642±1108a_{47}= -0.18264642 \pm 1 \cdot 10^{-8} a48=0.11947935±1108a_{48}= -0.11947935 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.76040891±1108a_{50}= -0.76040891 \pm 1 \cdot 10^{-8} a51=0.05672658±1108a_{51}= -0.05672658 \pm 1 \cdot 10^{-8}
a52=0.52496889±1108a_{52}= -0.52496889 \pm 1 \cdot 10^{-8} a53=0.09420467±1108a_{53}= -0.09420467 \pm 1 \cdot 10^{-8} a54=+0.39383342±1108a_{54}= +0.39383342 \pm 1 \cdot 10^{-8}
a55=1.48869390±1108a_{55}= -1.48869390 \pm 1 \cdot 10^{-8} a56=+0.41032292±1.3108a_{56}= +0.41032292 \pm 1.3 \cdot 10^{-8} a57=+0.18439158±1108a_{57}= +0.18439158 \pm 1 \cdot 10^{-8}
a58=1.35893836±1108a_{58}= -1.35893836 \pm 1 \cdot 10^{-8} a59=+1.50945843±1108a_{59}= +1.50945843 \pm 1 \cdot 10^{-8} a60=+0.14306831±1108a_{60}= +0.14306831 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000