Properties

Label 13.186
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 14.45835
Fricke sign +1+1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 14.4583560141038604331992208333±210714.4583560141038604331992208333 \pm 2 \cdot 10^{-7}

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=0.63993643±5.9103a_{2}= -0.63993643 \pm 5.9 \cdot 10^{-3} a3=1.02336159±5.7103a_{3}= -1.02336159 \pm 5.7 \cdot 10^{-3}
a4=0.59048137±5.4103a_{4}= -0.59048137 \pm 5.4 \cdot 10^{-3} a5=+0.55557033±5.1103a_{5}= +0.55557033 \pm 5.1 \cdot 10^{-3} a6=+0.65488636±6.6103a_{6}= +0.65488636 \pm 6.6 \cdot 10^{-3}
a7=0.76492561±5.2103a_{7}= -0.76492561 \pm 5.2 \cdot 10^{-3} a8=+1.01780697±4.5103a_{8}= +1.01780697 \pm 4.5 \cdot 10^{-3} a9=+0.04726894±5.6103a_{9}= +0.04726894 \pm 5.6 \cdot 10^{-3}
a10=0.35552970±5.8103a_{10}= -0.35552970 \pm 5.8 \cdot 10^{-3} a11=1.72927124±4.8103a_{11}= -1.72927124 \pm 4.8 \cdot 10^{-3} a12=+0.60427595±5.8103a_{12}= +0.60427595 \pm 5.8 \cdot 10^{-3}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.48950376±5.7103a_{14}= +0.48950376 \pm 5.7 \cdot 10^{-3} a15=0.56854934±6.2103a_{15}= -0.56854934 \pm 6.2 \cdot 10^{-3}
a16=0.06085039±4.7103a_{16}= -0.06085039 \pm 4.7 \cdot 10^{-3} a17=+1.06973512±5.2103a_{17}= +1.06973512 \pm 5.2 \cdot 10^{-3} a18=0.03024912±6.4103a_{18}= -0.03024912 \pm 6.4 \cdot 10^{-3}
a19=+0.01906219±4.3103a_{19}= +0.01906219 \pm 4.3 \cdot 10^{-3} a20=0.32805393±5.3103a_{20}= -0.32805393 \pm 5.3 \cdot 10^{-3} a21=+0.78279548±4.5103a_{21}= +0.78279548 \pm 4.5 \cdot 10^{-3}
a22=+1.10662367±5.3103a_{22}= +1.10662367 \pm 5.3 \cdot 10^{-3} a23=+1.87897865±4.3103a_{23}= +1.87897865 \pm 4.3 \cdot 10^{-3} a24=1.04158456±4.4103a_{24}= -1.04158456 \pm 4.4 \cdot 10^{-3}
a25=0.69134160±3.9103a_{25}= -0.69134160 \pm 3.9 \cdot 10^{-3} a26=+0.17748643±5.9103a_{26}= +0.17748643 \pm 5.9 \cdot 10^{-3} a27=+0.97498837±4.6103a_{27}= +0.97498837 \pm 4.6 \cdot 10^{-3}
a28=+0.45167432±4.9103a_{28}= +0.45167432 \pm 4.9 \cdot 10^{-3} a29=0.67032694±3.9103a_{29}= -0.67032694 \pm 3.9 \cdot 10^{-3} a30=+0.36383544±7.5103a_{30}= +0.36383544 \pm 7.5 \cdot 10^{-3}
a31=+0.83009116±5.6103a_{31}= +0.83009116 \pm 5.6 \cdot 10^{-3} a32=0.97886658±6.0103a_{32}= -0.97886658 \pm 6.0 \cdot 10^{-3} a33=+1.76966977±4.2103a_{33}= +1.76966977 \pm 4.2 \cdot 10^{-3}
a34=0.68456248±5.7103a_{34}= -0.68456248 \pm 5.7 \cdot 10^{-3} a35=0.42496997±4.2103a_{35}= -0.42496997 \pm 4.2 \cdot 10^{-3} a36=0.02791143±5.2103a_{36}= -0.02791143 \pm 5.2 \cdot 10^{-3}
a37=+1.35864801±6.5103a_{37}= +1.35864801 \pm 6.5 \cdot 10^{-3} a38=0.01219859±4.1103a_{38}= -0.01219859 \pm 4.1 \cdot 10^{-3} a39=+0.28382944±5.7103a_{39}= +0.28382944 \pm 5.7 \cdot 10^{-3}
a40=+0.56546336±4.5103a_{40}= +0.56546336 \pm 4.5 \cdot 10^{-3} a41=+1.16657830±4.7103a_{41}= +1.16657830 \pm 4.7 \cdot 10^{-3} a42=0.50093935±3.7103a_{42}= -0.50093935 \pm 3.7 \cdot 10^{-3}
a43=+0.81083656±5.2103a_{43}= +0.81083656 \pm 5.2 \cdot 10^{-3} a44=+1.02110244±5.0103a_{44}= +1.02110244 \pm 5.0 \cdot 10^{-3} a45=+0.02626122±5.6103a_{45}= +0.02626122 \pm 5.6 \cdot 10^{-3}
a46=1.20242689±5.6103a_{46}= -1.20242689 \pm 5.6 \cdot 10^{-3} a47=0.44118848±5.4103a_{47}= -0.44118848 \pm 5.4 \cdot 10^{-3} a48=+0.06227195±5.3103a_{48}= +0.06227195 \pm 5.3 \cdot 10^{-3}
a49=0.41488882±4.7103a_{49}= -0.41488882 \pm 4.7 \cdot 10^{-3} a50=+0.44241468±4.7103a_{50}= +0.44241468 \pm 4.7 \cdot 10^{-3} a51=1.09472584±6.1103a_{51}= -1.09472584 \pm 6.1 \cdot 10^{-3}
a52=+0.16377006±5.4103a_{52}= +0.16377006 \pm 5.4 \cdot 10^{-3} a53=0.03535638±4.0103a_{53}= -0.03535638 \pm 4.0 \cdot 10^{-3} a54=0.62393058±5.4103a_{54}= -0.62393058 \pm 5.4 \cdot 10^{-3}
a55=0.96073180±3.4103a_{55}= -0.96073180 \pm 3.4 \cdot 10^{-3} a56=0.77854661±3.9103a_{56}= -0.77854661 \pm 3.9 \cdot 10^{-3} a57=0.01950752±4.1103a_{57}= -0.01950752 \pm 4.1 \cdot 10^{-3}
a58=+0.42896663±3.8103a_{58}= +0.42896663 \pm 3.8 \cdot 10^{-3} a59=+0.24168906±4.8103a_{59}= +0.24168906 \pm 4.8 \cdot 10^{-3} a60=+0.33571779±6.2103a_{60}= +0.33571779 \pm 6.2 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000