Properties

Label 11.160
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 14.81037
Fricke sign 1-1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 14.8103795352232879036592441547±210714.8103795352232879036592441547 \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=+0.09443521±1.7103a_{2}= +0.09443521 \pm 1.7 \cdot 10^{-3} a3=+1.79041375±1.4103a_{3}= +1.79041375 \pm 1.4 \cdot 10^{-3}
a4=0.99108199±2.0103a_{4}= -0.99108199 \pm 2.0 \cdot 10^{-3} a5=+0.77363586±1.5103a_{5}= +0.77363586 \pm 1.5 \cdot 10^{-3} a6=+0.16907809±1.7103a_{6}= +0.16907809 \pm 1.7 \cdot 10^{-3}
a7=+0.37351923±1.5103a_{7}= +0.37351923 \pm 1.5 \cdot 10^{-3} a8=0.18802824±1.7103a_{8}= -0.18802824 \pm 1.7 \cdot 10^{-3} a9=+2.20558139±1.6103a_{9}= +2.20558139 \pm 1.6 \cdot 10^{-3}
a10=+0.07305846±1.8103a_{10}= +0.07305846 \pm 1.8 \cdot 10^{-3} a11=+0.30151134±1.0108a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} a12=1.77444682±1.8103a_{12}= -1.77444682 \pm 1.8 \cdot 10^{-3}
a13=0.66755367±1.1103a_{13}= -0.66755367 \pm 1.1 \cdot 10^{-3} a14=+0.03527337±1.2103a_{14}= +0.03527337 \pm 1.2 \cdot 10^{-3} a15=+1.38512828±1.1103a_{15}= +1.38512828 \pm 1.1 \cdot 10^{-3}
a16=+0.97332551±1.5103a_{16}= +0.97332551 \pm 1.5 \cdot 10^{-3} a17=0.69440097±1.4103a_{17}= -0.69440097 \pm 1.4 \cdot 10^{-3} a18=+0.20828453±1.6103a_{18}= +0.20828453 \pm 1.6 \cdot 10^{-3}
a19=+1.68472998±1.0103a_{19}= +1.68472998 \pm 1.0 \cdot 10^{-3} a20=0.76673657±1.9103a_{20}= -0.76673657 \pm 1.9 \cdot 10^{-3} a21=+0.66875397±1.1103a_{21}= +0.66875397 \pm 1.1 \cdot 10^{-3}
a22=+0.02847329±1.7103a_{22}= +0.02847329 \pm 1.7 \cdot 10^{-3} a23=+1.52025048±1.3103a_{23}= +1.52025048 \pm 1.3 \cdot 10^{-3} a24=0.33664834±2.0103a_{24}= -0.33664834 \pm 2.0 \cdot 10^{-3}
a25=0.40148755±1.2103a_{25}= -0.40148755 \pm 1.2 \cdot 10^{-3} a26=0.06304057±9.2104a_{26}= -0.06304057 \pm 9.2 \cdot 10^{-4} a27=+2.15848949±1.3103a_{27}= +2.15848949 \pm 1.3 \cdot 10^{-3}
a28=0.37018818±1.5103a_{28}= -0.37018818 \pm 1.5 \cdot 10^{-3} a29=+0.36185300±1.3103a_{29}= +0.36185300 \pm 1.3 \cdot 10^{-3} a30=+0.13080487±1.0103a_{30}= +0.13080487 \pm 1.0 \cdot 10^{-3}
a31=1.40355306±1.4103a_{31}= -1.40355306 \pm 1.4 \cdot 10^{-3} a32=+0.27994443±1.2103a_{32}= +0.27994443 \pm 1.2 \cdot 10^{-3} a33=+0.53983006±1.4103a_{33}= +0.53983006 \pm 1.4 \cdot 10^{-3}
a34=0.06557590±1.7103a_{34}= -0.06557590 \pm 1.7 \cdot 10^{-3} a35=+0.28896787±1.4103a_{35}= +0.28896787 \pm 1.4 \cdot 10^{-3} a36=2.18591200±1.7103a_{36}= -2.18591200 \pm 1.7 \cdot 10^{-3}
a37=+0.28504196±1.4103a_{37}= +0.28504196 \pm 1.4 \cdot 10^{-3} a38=+0.15909782±1.4103a_{38}= +0.15909782 \pm 1.4 \cdot 10^{-3} a39=1.19519726±8.6104a_{39}= -1.19519726 \pm 8.6 \cdot 10^{-4}
a40=0.14546539±1.4103a_{40}= -0.14546539 \pm 1.4 \cdot 10^{-3} a41=+0.18037046±9.8104a_{41}= +0.18037046 \pm 9.8 \cdot 10^{-4} a42=+0.06315392±1.2103a_{42}= +0.06315392 \pm 1.2 \cdot 10^{-3}
a43=+1.25014492±1.4103a_{43}= +1.25014492 \pm 1.4 \cdot 10^{-3} a44=0.29882246±2.0103a_{44}= -0.29882246 \pm 2.0 \cdot 10^{-3} a45=+1.70631686±1.5103a_{45}= +1.70631686 \pm 1.5 \cdot 10^{-3}
a46=+0.14356517±2.0103a_{46}= +0.14356517 \pm 2.0 \cdot 10^{-3} a47=0.45293810±1.1103a_{47}= -0.45293810 \pm 1.1 \cdot 10^{-3} a48=+1.74265537±1.5103a_{48}= +1.74265537 \pm 1.5 \cdot 10^{-3}
a49=0.86048338±1.3103a_{49}= -0.86048338 \pm 1.3 \cdot 10^{-3} a50=0.03791456±1.8103a_{50}= -0.03791456 \pm 1.8 \cdot 10^{-3} a51=1.24326504±1.4103a_{51}= -1.24326504 \pm 1.4 \cdot 10^{-3}
a52=+0.66160042±1.2103a_{52}= +0.66160042 \pm 1.2 \cdot 10^{-3} a53=+1.39335227±1.1103a_{53}= +1.39335227 \pm 1.1 \cdot 10^{-3} a54=+0.20383740±1.1103a_{54}= +0.20383740 \pm 1.1 \cdot 10^{-3}
a55=+0.23325999±1.5103a_{55}= +0.23325999 \pm 1.5 \cdot 10^{-3} a56=0.07023216±1.0103a_{56}= -0.07023216 \pm 1.0 \cdot 10^{-3} a57=+3.01636372±9.6104a_{57}= +3.01636372 \pm 9.6 \cdot 10^{-4}
a58=+0.03417166±1.3103a_{58}= +0.03417166 \pm 1.3 \cdot 10^{-3} a59=+0.49375585±1.6103a_{59}= +0.49375585 \pm 1.6 \cdot 10^{-3} a60=1.37277570±9.1104a_{60}= -1.37277570 \pm 9.1 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000