Properties

Label 13.195
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 14.68678
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: 14.6867865799050458251438388791±210714.6867865799050458251438388791 \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=+1.94787247±1.1104a_{2}= +1.94787247 \pm 1.1 \cdot 10^{-4} a3=+1.55128076±1.0104a_{3}= +1.55128076 \pm 1.0 \cdot 10^{-4}
a4=+2.79420716±1.0104a_{4}= +2.79420716 \pm 1.0 \cdot 10^{-4} a5=+0.77122104±9.4105a_{5}= +0.77122104 \pm 9.4 \cdot 10^{-5} a6=+3.02169709±1.2104a_{6}= +3.02169709 \pm 1.2 \cdot 10^{-4}
a7=0.43375318±9.7105a_{7}= -0.43375318 \pm 9.7 \cdot 10^{-5} a8=+3.49488674±8.3105a_{8}= +3.49488674 \pm 8.3 \cdot 10^{-5} a9=+1.40647200±1.0104a_{9}= +1.40647200 \pm 1.0 \cdot 10^{-4}
a10=+1.50224024±1.0104a_{10}= +1.50224024 \pm 1.0 \cdot 10^{-4} a11=1.52707194±8.9105a_{11}= -1.52707194 \pm 8.9 \cdot 10^{-5} a12=+4.33459981±1.0104a_{12}= +4.33459981 \pm 1.0 \cdot 10^{-4}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=0.84489589±1.0104a_{14}= -0.84489589 \pm 1.0 \cdot 10^{-4} a15=+1.19638036±1.1104a_{15}= +1.19638036 \pm 1.1 \cdot 10^{-4}
a16=+4.01338651±8.6105a_{16}= +4.01338651 \pm 8.6 \cdot 10^{-5} a17=+0.24554588±9.7105a_{17}= +0.24554588 \pm 9.7 \cdot 10^{-5} a18=+2.73962808±1.1104a_{18}= +2.73962808 \pm 1.1 \cdot 10^{-4}
a19=0.91265373±7.9105a_{19}= -0.91265373 \pm 7.9 \cdot 10^{-5} a20=+2.15495136±9.8105a_{20}= +2.15495136 \pm 9.8 \cdot 10^{-5} a21=0.67287297±8.3105a_{21}= -0.67287297 \pm 8.3 \cdot 10^{-5}
a22=2.97454139±9.8105a_{22}= -2.97454139 \pm 9.8 \cdot 10^{-5} a23=0.04233970±8.1105a_{23}= -0.04233970 \pm 8.1 \cdot 10^{-5} a24=+5.42155056±8.1105a_{24}= +5.42155056 \pm 8.1 \cdot 10^{-5}
a25=0.40521811±7.3105a_{25}= -0.40521811 \pm 7.3 \cdot 10^{-5} a26=+0.54024262±1.1104a_{26}= +0.54024262 \pm 1.1 \cdot 10^{-4} a27=+0.63055219±8.6105a_{27}= +0.63055219 \pm 8.6 \cdot 10^{-5}
a28=1.21199625±9.1105a_{28}= -1.21199625 \pm 9.1 \cdot 10^{-5} a29=+0.98052051±7.2105a_{29}= +0.98052051 \pm 7.2 \cdot 10^{-5} a30=+2.33039637±1.3104a_{30}= +2.33039637 \pm 1.3 \cdot 10^{-4}
a31=+0.70762566±1.0104a_{31}= +0.70762566 \pm 1.0 \cdot 10^{-4} a32=+4.32267836±1.1104a_{32}= +4.32267836 \pm 1.1 \cdot 10^{-4} a33=2.36891732±7.7105a_{33}= -2.36891732 \pm 7.7 \cdot 10^{-5}
a34=+0.47829207±1.0104a_{34}= +0.47829207 \pm 1.0 \cdot 10^{-4} a35=0.33451958±7.8105a_{35}= -0.33451958 \pm 7.8 \cdot 10^{-5} a36=+3.92997412±9.7105a_{36}= +3.92997412 \pm 9.7 \cdot 10^{-5}
a37=1.45487692±1.2104a_{37}= -1.45487692 \pm 1.2 \cdot 10^{-4} a38=1.77773308±7.6105a_{38}= -1.77773308 \pm 7.6 \cdot 10^{-5} a39=+0.43024787±1.0104a_{39}= +0.43024787 \pm 1.0 \cdot 10^{-4}
a40=+2.69533019±8.3105a_{40}= +2.69533019 \pm 8.3 \cdot 10^{-5} a41=+0.15920503±8.7105a_{41}= +0.15920503 \pm 8.7 \cdot 10^{-5} a42=1.31067073±6.9105a_{42}= -1.31067073 \pm 6.9 \cdot 10^{-5}
a43=+0.15553059±9.7105a_{43}= +0.15553059 \pm 9.7 \cdot 10^{-5} a44=4.26695535±9.3105a_{44}= -4.26695535 \pm 9.3 \cdot 10^{-5} a45=+1.08470080±1.0104a_{45}= +1.08470080 \pm 1.0 \cdot 10^{-4}
a46=0.08247233±1.0104a_{46}= -0.08247233 \pm 1.0 \cdot 10^{-4} a47=1.18094594±1.0104a_{47}= -1.18094594 \pm 1.0 \cdot 10^{-4} a48=+6.22588927±9.8105a_{48}= +6.22588927 \pm 9.8 \cdot 10^{-5}
a49=0.81185818±8.8105a_{49}= -0.81185818 \pm 8.8 \cdot 10^{-5} a50=0.78931319±8.7105a_{50}= -0.78931319 \pm 8.7 \cdot 10^{-5} a51=+0.38091060±1.1104a_{51}= +0.38091060 \pm 1.1 \cdot 10^{-4}
a52=+0.77497363±1.0104a_{52}= +0.77497363 \pm 1.0 \cdot 10^{-4} a53=0.33552997±7.4105a_{53}= -0.33552997 \pm 7.4 \cdot 10^{-5} a54=+1.22823524±1.0104a_{54}= +1.22823524 \pm 1.0 \cdot 10^{-4}
a55=1.17771001±6.4105a_{55}= -1.17771001 \pm 6.4 \cdot 10^{-5} a56=1.51591825±7.3105a_{56}= -1.51591825 \pm 7.3 \cdot 10^{-5} a57=1.41578218±7.7105a_{57}= -1.41578218 \pm 7.7 \cdot 10^{-5}
a58=+1.90992891±7.0105a_{58}= +1.90992891 \pm 7.0 \cdot 10^{-5} a59=+0.59839164±8.9105a_{59}= +0.59839164 \pm 8.9 \cdot 10^{-5} a60=+3.34293458±1.1104a_{60}= +3.34293458 \pm 1.1 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000