Properties

Label 13.56
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 8.322577
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: 8.32257722261542143711892684188±510118.32257722261542143711892684188 \pm 5 \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=1.70965539±2.3108a_{2}= -1.70965539 \pm 2.3 \cdot 10^{-8} a3=0.51125795±1.7108a_{3}= -0.51125795 \pm 1.7 \cdot 10^{-8}
a4=+1.92292157±2.5108a_{4}= +1.92292157 \pm 2.5 \cdot 10^{-8} a5=+1.36477620±1.9108a_{5}= +1.36477620 \pm 1.9 \cdot 10^{-8} a6=+0.87407492±2.2108a_{6}= +0.87407492 \pm 2.2 \cdot 10^{-8}
a7=+0.48375874±1.7108a_{7}= +0.48375874 \pm 1.7 \cdot 10^{-8} a8=1.57787783±2.2108a_{8}= -1.57787783 \pm 2.2 \cdot 10^{-8} a9=0.73861530±1.5108a_{9}= -0.73861530 \pm 1.5 \cdot 10^{-8}
a10=2.33329699±1.7108a_{10}= -2.33329699 \pm 1.7 \cdot 10^{-8} a11=+1.17444023±1.3108a_{11}= +1.17444023 \pm 1.3 \cdot 10^{-8} a12=0.98310895±2.2108a_{12}= -0.98310895 \pm 2.2 \cdot 10^{-8}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=0.82706074±2.5108a_{14}= -0.82706074 \pm 2.5 \cdot 10^{-8} a15=0.69775269±1.4108a_{15}= -0.69775269 \pm 1.4 \cdot 10^{-8}
a16=+0.77470578±1.6108a_{16}= +0.77470578 \pm 1.6 \cdot 10^{-8} a17=+0.96804829±1.7108a_{17}= +0.96804829 \pm 1.7 \cdot 10^{-8} a18=+1.26277764±1.8108a_{18}= +1.26277764 \pm 1.8 \cdot 10^{-8}
a19=+0.00002203±1.8108a_{19}= +0.00002203 \pm 1.8 \cdot 10^{-8} a20=+2.62435758±2.1108a_{20}= +2.62435758 \pm 2.1 \cdot 10^{-8} a21=0.24732551±1.4108a_{21}= -0.24732551 \pm 1.4 \cdot 10^{-8}
a22=2.00788807±1.2108a_{22}= -2.00788807 \pm 1.2 \cdot 10^{-8} a23=1.27765062±1.2108a_{23}= -1.27765062 \pm 1.2 \cdot 10^{-8} a24=+0.80670259±2.0108a_{24}= +0.80670259 \pm 2.0 \cdot 10^{-8}
a25=+0.86261407±2.1108a_{25}= +0.86261407 \pm 2.1 \cdot 10^{-8} a26=+0.47417309±3.3108a_{26}= +0.47417309 \pm 3.3 \cdot 10^{-8} a27=+0.88888090±1.9108a_{27}= +0.88888090 \pm 1.9 \cdot 10^{-8}
a28=+0.93023012±2.7108a_{28}= +0.93023012 \pm 2.7 \cdot 10^{-8} a29=1.69047324±1.6108a_{29}= -1.69047324 \pm 1.6 \cdot 10^{-8} a30=+1.19291665±1.2108a_{30}= +1.19291665 \pm 1.2 \cdot 10^{-8}
a31=+1.61060473±1.3108a_{31}= +1.61060473 \pm 1.3 \cdot 10^{-8} a32=+0.25339792±1.7108a_{32}= +0.25339792 \pm 1.7 \cdot 10^{-8} a33=0.60044191±1.5108a_{33}= -0.60044191 \pm 1.5 \cdot 10^{-8}
a34=1.65502898±2.2108a_{34}= -1.65502898 \pm 2.2 \cdot 10^{-8} a35=+0.66022242±1.6108a_{35}= +0.66022242 \pm 1.6 \cdot 10^{-8} a36=1.42029930±1.5108a_{36}= -1.42029930 \pm 1.5 \cdot 10^{-8}
a37=+1.07027123±1.5108a_{37}= +1.07027123 \pm 1.5 \cdot 10^{-8} a38=0.00003766±2.5108a_{38}= -0.00003766 \pm 2.5 \cdot 10^{-8} a39=+0.14179744±2.8108a_{39}= +0.14179744 \pm 2.8 \cdot 10^{-8}
a40=2.15345011±2.0108a_{40}= -2.15345011 \pm 2.0 \cdot 10^{-8} a41=+0.52270619±2.5108a_{41}= +0.52270619 \pm 2.5 \cdot 10^{-8} a42=+0.42284138±2.0108a_{42}= +0.42284138 \pm 2.0 \cdot 10^{-8}
a43=+0.43744289±1.4108a_{43}= +0.43744289 \pm 1.4 \cdot 10^{-8} a44=+2.25835644±1.0108a_{44}= +2.25835644 \pm 1.0 \cdot 10^{-8} a45=1.00804458±1.3108a_{45}= -1.00804458 \pm 1.3 \cdot 10^{-8}
a46=+2.18434227±1.5108a_{46}= +2.18434227 \pm 1.5 \cdot 10^{-8} a47=0.44286120±1.3108a_{47}= -0.44286120 \pm 1.3 \cdot 10^{-8} a48=0.39607449±1.4108a_{48}= -0.39607449 \pm 1.4 \cdot 10^{-8}
a49=0.76597748±1.3108a_{49}= -0.76597748 \pm 1.3 \cdot 10^{-8} a50=1.47477279±1.7108a_{50}= -1.47477279 \pm 1.7 \cdot 10^{-8} a51=0.49492239±1.8108a_{51}= -0.49492239 \pm 1.8 \cdot 10^{-8}
a52=0.53332248±3.5108a_{52}= -0.53332248 \pm 3.5 \cdot 10^{-8} a53=+1.62729118±1.8108a_{53}= +1.62729118 \pm 1.8 \cdot 10^{-8} a54=1.51968003±2.0108a_{54}= -1.51968003 \pm 2.0 \cdot 10^{-8}
a55=+1.60284807±1.2108a_{55}= +1.60284807 \pm 1.2 \cdot 10^{-8} a56=0.76331220±2.1108a_{56}= -0.76331220 \pm 2.1 \cdot 10^{-8} a57=0.00001126±1.0108a_{57}= -0.00001126 \pm 1.0 \cdot 10^{-8}
a58=+2.89012670±2.7108a_{58}= +2.89012670 \pm 2.7 \cdot 10^{-8} a59=0.00812788±1.5108a_{59}= -0.00812788 \pm 1.5 \cdot 10^{-8} a60=1.34172369±1.4108a_{60}= -1.34172369 \pm 1.4 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000