Properties

Label 3.49
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 19.02677
Fricke sign +1+1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 19.0267767277159515990093036122±210419.0267767277159515990093036122 \pm 2 \cdot 10^{-4}

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=0.08613898±2.7102a_{2}= -0.08613898 \pm 2.7 \cdot 10^{-2} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.99258008±4.9102a_{4}= -0.99258008 \pm 4.9 \cdot 10^{-2} a5=+0.10078856±3.7102a_{5}= +0.10078856 \pm 3.7 \cdot 10^{-2} a6=+0.04973236±2.7102a_{6}= +0.04973236 \pm 2.7 \cdot 10^{-2}
a7=+1.22782462±3.0102a_{7}= +1.22782462 \pm 3.0 \cdot 10^{-2} a8=+0.17163881±3.3102a_{8}= +0.17163881 \pm 3.3 \cdot 10^{-2} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.00868182±2.1102a_{10}= -0.00868182 \pm 2.1 \cdot 10^{-2} a11=+0.68050424±3.4102a_{11}= +0.68050424 \pm 3.4 \cdot 10^{-2} a12=+0.57306637±4.9102a_{12}= +0.57306637 \pm 4.9 \cdot 10^{-2}
a13=1.18003931±3.3102a_{13}= -1.18003931 \pm 3.3 \cdot 10^{-2} a14=0.10576356±2.1102a_{14}= -0.10576356 \pm 2.1 \cdot 10^{-2} a15=0.05819030±3.7102a_{15}= -0.05819030 \pm 3.7 \cdot 10^{-2}
a16=+0.97779528±4.0102a_{16}= +0.97779528 \pm 4.0 \cdot 10^{-2} a17=+0.15753027±2.5102a_{17}= +0.15753027 \pm 2.5 \cdot 10^{-2} a18=0.02871299±2.7102a_{18}= -0.02871299 \pm 2.7 \cdot 10^{-2}
a19=+0.92577735±2.0102a_{19}= +0.92577735 \pm 2.0 \cdot 10^{-2} a20=0.10004072±3.5102a_{20}= -0.10004072 \pm 3.5 \cdot 10^{-2} a21=0.70888488±3.0102a_{21}= -0.70888488 \pm 3.0 \cdot 10^{-2}
a22=0.05861794±1.7102a_{22}= -0.05861794 \pm 1.7 \cdot 10^{-2} a23=1.85747795±7.5102a_{23}= -1.85747795 \pm 7.5 \cdot 10^{-2} a24=0.09909572±3.3102a_{24}= -0.09909572 \pm 3.3 \cdot 10^{-2}
a25=0.98984167±3.1102a_{25}= -0.98984167 \pm 3.1 \cdot 10^{-2} a26=+0.10164738±1.1102a_{26}= +0.10164738 \pm 1.1 \cdot 10^{-2} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=1.21871426±2.0102a_{28}= -1.21871426 \pm 2.0 \cdot 10^{-2} a29=1.13235323±7.1102a_{29}= -1.13235323 \pm 7.1 \cdot 10^{-2} a30=+0.00501245±6.4102a_{30}= +0.00501245 \pm 6.4 \cdot 10^{-2}
a31=+0.73662808±3.1102a_{31}= +0.73662808 \pm 3.1 \cdot 10^{-2} a32=0.25586510±4.4102a_{32}= -0.25586510 \pm 4.4 \cdot 10^{-2} a33=0.39288931±3.4102a_{33}= -0.39288931 \pm 3.4 \cdot 10^{-2}
a34=0.01356950±3.0102a_{34}= -0.01356950 \pm 3.0 \cdot 10^{-2} a35=+0.12375067±1.3102a_{35}= +0.12375067 \pm 1.3 \cdot 10^{-2} a36=0.33086003±4.9102a_{36}= -0.33086003 \pm 4.9 \cdot 10^{-2}
a37=0.69030342±3.8102a_{37}= -0.69030342 \pm 3.8 \cdot 10^{-2} a38=0.07974552±9.2103a_{38}= -0.07974552 \pm 9.2 \cdot 10^{-3} a39=+0.68129601±3.3102a_{39}= +0.68129601 \pm 3.3 \cdot 10^{-2}
a40=+0.01729923±2.0102a_{40}= +0.01729923 \pm 2.0 \cdot 10^{-2} a41=+0.73078552±7.2102a_{41}= +0.73078552 \pm 7.2 \cdot 10^{-2} a42=+0.06106262±5.8102a_{42}= +0.06106262 \pm 5.8 \cdot 10^{-2}
a43=0.83201477±4.8102a_{43}= -0.83201477 \pm 4.8 \cdot 10^{-2} a44=0.67545495±3.0102a_{44}= -0.67545495 \pm 3.0 \cdot 10^{-2} a45=+0.03359619±3.7102a_{45}= +0.03359619 \pm 3.7 \cdot 10^{-2}
a46=+0.16000125±2.1102a_{46}= +0.16000125 \pm 2.1 \cdot 10^{-2} a47=+0.70211362±5.9102a_{47}= +0.70211362 \pm 5.9 \cdot 10^{-2} a48=0.56453037±4.0102a_{48}= -0.56453037 \pm 4.0 \cdot 10^{-2}
a49=+0.50755330±5.2102a_{49}= +0.50755330 \pm 5.2 \cdot 10^{-2} a50=+0.08526395±1.5102a_{50}= +0.08526395 \pm 1.5 \cdot 10^{-2} a51=0.09095014±2.5102a_{51}= -0.09095014 \pm 2.5 \cdot 10^{-2}
a52=+1.17128351±3.0102a_{52}= +1.17128351 \pm 3.0 \cdot 10^{-2} a53=1.84333098±3.0102a_{53}= -1.84333098 \pm 3.0 \cdot 10^{-2} a54=+0.01657745±2.7102a_{54}= +0.01657745 \pm 2.7 \cdot 10^{-2}
a55=+0.06858704±2.4102a_{55}= +0.06858704 \pm 2.4 \cdot 10^{-2} a56=+0.21074236±2.9102a_{56}= +0.21074236 \pm 2.9 \cdot 10^{-2} a57=0.53449780±2.0102a_{57}= -0.53449780 \pm 2.0 \cdot 10^{-2}
a58=+0.09753975±2.9102a_{58}= +0.09753975 \pm 2.9 \cdot 10^{-2} a59=+1.07935213±4.8102a_{59}= +1.07935213 \pm 4.8 \cdot 10^{-2} a60=+0.05775853±8.7102a_{60}= +0.05775853 \pm 8.7 \cdot 10^{-2}

Displaying ana_n with nn up to: 60 180 1000