Properties

Label 13.106
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 11.15411
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: 11.1541136158394570484299428908±210911.1541136158394570484299428908 \pm 2 \cdot 10^{-9}

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=0.77908793±8.2105a_{2}= -0.77908793 \pm 8.2 \cdot 10^{-5} a3=0.84954762±7.9105a_{3}= -0.84954762 \pm 7.9 \cdot 10^{-5}
a4=0.39302199±7.4105a_{4}= -0.39302199 \pm 7.4 \cdot 10^{-5} a5=+0.29000761±7.0105a_{5}= +0.29000761 \pm 7.0 \cdot 10^{-5} a6=+0.66187230±9.0105a_{6}= +0.66187230 \pm 9.0 \cdot 10^{-5}
a7=0.40364812±7.2105a_{7}= -0.40364812 \pm 7.2 \cdot 10^{-5} a8=+1.08528662±6.2105a_{8}= +1.08528662 \pm 6.2 \cdot 10^{-5} a9=0.27826883±7.7105a_{9}= -0.27826883 \pm 7.7 \cdot 10^{-5}
a10=0.22594143±8.0105a_{10}= -0.22594143 \pm 8.0 \cdot 10^{-5} a11=1.71813494±6.6105a_{11}= -1.71813494 \pm 6.6 \cdot 10^{-5} a12=+0.33389090±8.0105a_{12}= +0.33389090 \pm 8.0 \cdot 10^{-5}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.31447738±7.8105a_{14}= +0.31447738 \pm 7.8 \cdot 10^{-5} a15=0.24637528±8.6105a_{15}= -0.24637528 \pm 8.6 \cdot 10^{-5}
a16=0.45251172±6.4105a_{16}= -0.45251172 \pm 6.4 \cdot 10^{-5} a17=1.52813884±7.2105a_{17}= -1.52813884 \pm 7.2 \cdot 10^{-5} a18=+0.21679589±8.8105a_{18}= +0.21679589 \pm 8.8 \cdot 10^{-5}
a19=1.73224163±5.9105a_{19}= -1.73224163 \pm 5.9 \cdot 10^{-5} a20=0.11397937±7.2105a_{20}= -0.11397937 \pm 7.2 \cdot 10^{-5} a21=+0.34291830±6.2105a_{21}= +0.34291830 \pm 6.2 \cdot 10^{-5}
a22=+1.33857820±7.3105a_{22}= +1.33857820 \pm 7.3 \cdot 10^{-5} a23=1.64203854±6.0105a_{23}= -1.64203854 \pm 6.0 \cdot 10^{-5} a24=0.92200267±6.0105a_{24}= -0.92200267 \pm 6.0 \cdot 10^{-5}
a25=0.91589558±5.4105a_{25}= -0.91589558 \pm 5.4 \cdot 10^{-5} a26=0.21608011±8.2105a_{26}= -0.21608011 \pm 8.2 \cdot 10^{-5} a27=+1.08595025±6.4105a_{27}= +1.08595025 \pm 6.4 \cdot 10^{-5}
a28=+0.15864259±6.8105a_{28}= +0.15864259 \pm 6.8 \cdot 10^{-5} a29=+0.49981393±5.3105a_{29}= +0.49981393 \pm 5.3 \cdot 10^{-5} a30=+0.19194801±1.0104a_{30}= +0.19194801 \pm 1.0 \cdot 10^{-4}
a31=+0.72295661±7.7105a_{31}= +0.72295661 \pm 7.7 \cdot 10^{-5} a32=0.73274020±8.3105a_{32}= -0.73274020 \pm 8.3 \cdot 10^{-5} a33=+1.45963746±5.7105a_{33}= +1.45963746 \pm 5.7 \cdot 10^{-5}
a34=+1.19055453±7.9105a_{34}= +1.19055453 \pm 7.9 \cdot 10^{-5} a35=0.11706103±5.8105a_{35}= -0.11706103 \pm 5.8 \cdot 10^{-5} a36=+0.10936577±7.2105a_{36}= +0.10936577 \pm 7.2 \cdot 10^{-5}
a37=0.10367080±8.9105a_{37}= -0.10367080 \pm 8.9 \cdot 10^{-5} a38=+1.34956855±5.6105a_{38}= +1.34956855 \pm 5.6 \cdot 10^{-5} a39=0.23562212±7.9105a_{39}= -0.23562212 \pm 7.9 \cdot 10^{-5}
a40=+0.31474139±6.1105a_{40}= +0.31474139 \pm 6.1 \cdot 10^{-5} a41=+0.71053435±6.5105a_{41}= +0.71053435 \pm 6.5 \cdot 10^{-5} a42=0.26716351±5.1105a_{42}= -0.26716351 \pm 5.1 \cdot 10^{-5}
a43=0.86355996±7.2105a_{43}= -0.86355996 \pm 7.2 \cdot 10^{-5} a44=+0.67526482±6.9105a_{44}= +0.67526482 \pm 6.9 \cdot 10^{-5} a45=0.08070008±7.7105a_{45}= -0.08070008 \pm 7.7 \cdot 10^{-5}
a46=+1.27929241±7.8105a_{46}= +1.27929241 \pm 7.8 \cdot 10^{-5} a47=0.38237666±7.5105a_{47}= -0.38237666 \pm 7.5 \cdot 10^{-5} a48=+0.38443026±7.3105a_{48}= +0.38443026 \pm 7.3 \cdot 10^{-5}
a49=0.83706820±6.5105a_{49}= -0.83706820 \pm 6.5 \cdot 10^{-5} a50=+0.71356320±6.5105a_{50}= +0.71356320 \pm 6.5 \cdot 10^{-5} a51=+1.29822672±8.4105a_{51}= +1.29822672 \pm 8.4 \cdot 10^{-5}
a52=0.10900469±7.4105a_{52}= -0.10900469 \pm 7.4 \cdot 10^{-5} a53=+0.99122803±5.5105a_{53}= +0.99122803 \pm 5.5 \cdot 10^{-5} a54=0.84605074±7.4105a_{54}= -0.84605074 \pm 7.4 \cdot 10^{-5}
a55=0.49827222±4.7105a_{55}= -0.49827222 \pm 4.7 \cdot 10^{-5} a56=0.43807391±5.4105a_{56}= -0.43807391 \pm 5.4 \cdot 10^{-5} a57=+1.47162177±5.7105a_{57}= +1.47162177 \pm 5.7 \cdot 10^{-5}
a58=0.38939900±5.2105a_{58}= -0.38939900 \pm 5.2 \cdot 10^{-5} a59=0.80597950±6.6105a_{59}= -0.80597950 \pm 6.6 \cdot 10^{-5} a60=+0.09683090±8.6105a_{60}= +0.09683090 \pm 8.6 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000