Properties

Label 13.42
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 7.266725
Fricke sign +1+1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 7.26672532739623709080258495332±210117.26672532739623709080258495332 \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=1.87204905±1108a_{2}= -1.87204905 \pm 1 \cdot 10^{-8} a3=0.00906733±1108a_{3}= -0.00906733 \pm 1 \cdot 10^{-8}
a4=+2.50456764±1108a_{4}= +2.50456764 \pm 1 \cdot 10^{-8} a5=1.53380582±1108a_{5}= -1.53380582 \pm 1 \cdot 10^{-8} a6=+0.01697448±1108a_{6}= +0.01697448 \pm 1 \cdot 10^{-8}
a7=0.29987619±1108a_{7}= -0.29987619 \pm 1 \cdot 10^{-8} a8=2.81662442±1108a_{8}= -2.81662442 \pm 1 \cdot 10^{-8} a9=0.99991778±1108a_{9}= -0.99991778 \pm 1 \cdot 10^{-8}
a10=+2.87135973±1108a_{10}= +2.87135973 \pm 1 \cdot 10^{-8} a11=1.40578733±1108a_{11}= -1.40578733 \pm 1 \cdot 10^{-8} a12=0.02270973±1108a_{12}= -0.02270973 \pm 1 \cdot 10^{-8}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.56138295±1108a_{14}= +0.56138295 \pm 1 \cdot 10^{-8} a15=+0.01390752±1108a_{15}= +0.01390752 \pm 1 \cdot 10^{-8}
a16=+2.76829143±1108a_{16}= +2.76829143 \pm 1 \cdot 10^{-8} a17=0.29609404±1108a_{17}= -0.29609404 \pm 1 \cdot 10^{-8} a18=+1.87189514±1108a_{18}= +1.87189514 \pm 1 \cdot 10^{-8}
a19=0.57987337±1108a_{19}= -0.57987337 \pm 1 \cdot 10^{-8} a20=3.84152043±1108a_{20}= -3.84152043 \pm 1 \cdot 10^{-8} a21=+0.00271908±1108a_{21}= +0.00271908 \pm 1 \cdot 10^{-8}
a22=+2.63170283±1108a_{22}= +2.63170283 \pm 1 \cdot 10^{-8} a23=0.35332279±1108a_{23}= -0.35332279 \pm 1 \cdot 10^{-8} a24=+0.02553925±1108a_{24}= +0.02553925 \pm 1 \cdot 10^{-8}
a25=+1.35256030±1108a_{25}= +1.35256030 \pm 1 \cdot 10^{-8} a26=+0.51921299±1.1108a_{26}= +0.51921299 \pm 1.1 \cdot 10^{-8} a27=+0.01813391±1108a_{27}= +0.01813391 \pm 1 \cdot 10^{-8}
a28=0.75106021±1108a_{28}= -0.75106021 \pm 1 \cdot 10^{-8} a29=+0.58967746±1108a_{29}= +0.58967746 \pm 1 \cdot 10^{-8} a30=0.02603556±1108a_{30}= -0.02603556 \pm 1 \cdot 10^{-8}
a31=+1.07637975±1108a_{31}= +1.07637975 \pm 1 \cdot 10^{-8} a32=2.36575292±1108a_{32}= -2.36575292 \pm 1 \cdot 10^{-8} a33=+0.01274673±1108a_{33}= +0.01274673 \pm 1 \cdot 10^{-8}
a34=+0.55430257±1108a_{34}= +0.55430257 \pm 1 \cdot 10^{-8} a35=+0.45995185±1108a_{35}= +0.45995185 \pm 1 \cdot 10^{-8} a36=2.50436173±1108a_{36}= -2.50436173 \pm 1 \cdot 10^{-8}
a37=1.21714047±1108a_{37}= -1.21714047 \pm 1 \cdot 10^{-8} a38=+1.08555140±1108a_{38}= +1.08555140 \pm 1 \cdot 10^{-8} a39=+0.00251482±1.0108a_{39}= +0.00251482 \pm 1.0 \cdot 10^{-8}
a40=+4.32015494±1108a_{40}= +4.32015494 \pm 1 \cdot 10^{-8} a41=0.55157820±1108a_{41}= -0.55157820 \pm 1 \cdot 10^{-8} a42=0.00509024±1108a_{42}= -0.00509024 \pm 1 \cdot 10^{-8}
a43=+1.23183534±1108a_{43}= +1.23183534 \pm 1 \cdot 10^{-8} a44=3.52088946±1108a_{44}= -3.52088946 \pm 1 \cdot 10^{-8} a45=+1.53367972±1108a_{45}= +1.53367972 \pm 1 \cdot 10^{-8}
a46=+0.66143759±1108a_{46}= +0.66143759 \pm 1 \cdot 10^{-8} a47=+0.12022168±1108a_{47}= +0.12022168 \pm 1 \cdot 10^{-8} a48=0.02510100±1108a_{48}= -0.02510100 \pm 1 \cdot 10^{-8}
a49=0.91007427±1108a_{49}= -0.91007427 \pm 1 \cdot 10^{-8} a50=2.53205922±1108a_{50}= -2.53205922 \pm 1 \cdot 10^{-8} a51=+0.00268478±1108a_{51}= +0.00268478 \pm 1 \cdot 10^{-8}
a52=0.69464208±1.1108a_{52}= -0.69464208 \pm 1.1 \cdot 10^{-8} a53=+0.97715152±1108a_{53}= +0.97715152 \pm 1 \cdot 10^{-8} a54=0.03394757±1108a_{54}= -0.03394757 \pm 1 \cdot 10^{-8}
a55=+2.15620479±1108a_{55}= +2.15620479 \pm 1 \cdot 10^{-8} a56=+0.84463861±1108a_{56}= +0.84463861 \pm 1 \cdot 10^{-8} a57=+0.00525790±1108a_{57}= +0.00525790 \pm 1 \cdot 10^{-8}
a58=1.10390513±1108a_{58}= -1.10390513 \pm 1 \cdot 10^{-8} a59=+0.86374070±1108a_{59}= +0.86374070 \pm 1 \cdot 10^{-8} a60=+0.03483232±1108a_{60}= +0.03483232 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000