Properties

Label 13.178
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 14.21380
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: 14.2138017412218413679300317845±910814.2138017412218413679300317845 \pm 9 \cdot 10^{-8}

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=+1.24750239±1.2105a_{2}= +1.24750239 \pm 1.2 \cdot 10^{-5} a3=0.95454844±9.1106a_{3}= -0.95454844 \pm 9.1 \cdot 10^{-6}
a4=+0.55626221±1.3105a_{4}= +0.55626221 \pm 1.3 \cdot 10^{-5} a5=1.41742099±1.0105a_{5}= -1.41742099 \pm 1.0 \cdot 10^{-5} a6=1.19080146±1.1105a_{6}= -1.19080146 \pm 1.1 \cdot 10^{-5}
a7=+0.57765953±9.2106a_{7}= +0.57765953 \pm 9.2 \cdot 10^{-6} a8=0.55356396±1.1105a_{8}= -0.55356396 \pm 1.1 \cdot 10^{-5} a9=0.08883727±8.2106a_{9}= -0.08883727 \pm 8.2 \cdot 10^{-6}
a10=1.76823607±9.2106a_{10}= -1.76823607 \pm 9.2 \cdot 10^{-6} a11=0.71121320±6.8106a_{11}= -0.71121320 \pm 6.8 \cdot 10^{-6} a12=0.53097922±1.1105a_{12}= -0.53097922 \pm 1.1 \cdot 10^{-5}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.72063165±1.3105a_{14}= +0.72063165 \pm 1.3 \cdot 10^{-5} a15=+1.35299700±7.5106a_{15}= +1.35299700 \pm 7.5 \cdot 10^{-6}
a16=1.24683456±8.3106a_{16}= -1.24683456 \pm 8.3 \cdot 10^{-6} a17=1.18399962±9.0106a_{17}= -1.18399962 \pm 9.0 \cdot 10^{-6} a18=0.11082471±9.6106a_{18}= -0.11082471 \pm 9.6 \cdot 10^{-6}
a19=0.05551808±9.8106a_{19}= -0.05551808 \pm 9.8 \cdot 10^{-6} a20=0.78845773±1.1105a_{20}= -0.78845773 \pm 1.1 \cdot 10^{-5} a21=0.55140401±7.5106a_{21}= -0.55140401 \pm 7.5 \cdot 10^{-6}
a22=0.88724017±6.5106a_{22}= -0.88724017 \pm 6.5 \cdot 10^{-6} a23=0.92207407±6.6106a_{23}= -0.92207407 \pm 6.6 \cdot 10^{-6} a24=+0.52840361±1.0105a_{24}= +0.52840361 \pm 1.0 \cdot 10^{-5}
a25=+1.00908226±1.1105a_{25}= +1.00908226 \pm 1.1 \cdot 10^{-5} a26=0.34599491±1.2105a_{26}= -0.34599491 \pm 1.2 \cdot 10^{-5} a27=+1.03934792±9.9106a_{27}= +1.03934792 \pm 9.9 \cdot 10^{-6}
a28=+0.32133017±1.4105a_{28}= +0.32133017 \pm 1.4 \cdot 10^{-5} a29=+1.54562156±8.7106a_{29}= +1.54562156 \pm 8.7 \cdot 10^{-6} a30=+1.68786699±6.2106a_{30}= +1.68786699 \pm 6.2 \cdot 10^{-6}
a31=+0.70170323±6.8106a_{31}= +0.70170323 \pm 6.8 \cdot 10^{-6} a32=1.00186514±9.0106a_{32}= -1.00186514 \pm 9.0 \cdot 10^{-6} a33=+0.67888746±8.1106a_{33}= +0.67888746 \pm 8.1 \cdot 10^{-6}
a34=1.47704236±1.1105a_{34}= -1.47704236 \pm 1.1 \cdot 10^{-5} a35=0.81878675±8.3106a_{35}= -0.81878675 \pm 8.3 \cdot 10^{-6} a36=0.04941682±8.0106a_{36}= -0.04941682 \pm 8.0 \cdot 10^{-6}
a37=+0.78429404±8.0106a_{37}= +0.78429404 \pm 8.0 \cdot 10^{-6} a38=0.06925893±1.3105a_{38}= -0.06925893 \pm 1.3 \cdot 10^{-5} a39=+0.26474410±9.2106a_{39}= +0.26474410 \pm 9.2 \cdot 10^{-6}
a40=+0.78463317±1.0105a_{40}= +0.78463317 \pm 1.0 \cdot 10^{-5} a41=+1.41787188±1.3105a_{41}= +1.41787188 \pm 1.3 \cdot 10^{-5} a42=0.68787782±1.0105a_{42}= -0.68787782 \pm 1.0 \cdot 10^{-5}
a43=1.26754883±7.6106a_{43}= -1.26754883 \pm 7.6 \cdot 10^{-6} a44=0.39562103±5.3106a_{44}= -0.39562103 \pm 5.3 \cdot 10^{-6} a45=+0.12591981±7.0106a_{45}= +0.12591981 \pm 7.0 \cdot 10^{-6}
a46=1.15028961±7.8106a_{46}= -1.15028961 \pm 7.8 \cdot 10^{-6} a47=+0.37300103±7.0106a_{47}= +0.37300103 \pm 7.0 \cdot 10^{-6} a48=+1.19016399±7.4106a_{48}= +1.19016399 \pm 7.4 \cdot 10^{-6}
a49=0.66630946±7.0106a_{49}= -0.66630946 \pm 7.0 \cdot 10^{-6} a50=+1.25883253±9.0106a_{50}= +1.25883253 \pm 9.0 \cdot 10^{-6} a51=+1.13018499±9.8106a_{51}= +1.13018499 \pm 9.8 \cdot 10^{-6}
a52=0.15427938±1.3105a_{52}= -0.15427938 \pm 1.3 \cdot 10^{-5} a53=0.34469640±9.6106a_{53}= -0.34469640 \pm 9.6 \cdot 10^{-6} a54=+1.29658901±1.0105a_{54}= +1.29658901 \pm 1.0 \cdot 10^{-5}
a55=+1.00808852±6.5106a_{55}= +1.00808852 \pm 6.5 \cdot 10^{-6} a56=0.31977150±1.1105a_{56}= -0.31977150 \pm 1.1 \cdot 10^{-5} a57=+0.05299469±5.5106a_{57}= +0.05299469 \pm 5.5 \cdot 10^{-6}
a58=+1.92816658±1.4105a_{58}= +1.92816658 \pm 1.4 \cdot 10^{-5} a59=0.23659806±8.0106a_{59}= -0.23659806 \pm 8.0 \cdot 10^{-6} a60=+0.75262110±7.2106a_{60}= +0.75262110 \pm 7.2 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000