Properties

Label 5.49
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 13.64739
Fricke sign +1+1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 13.6473942984543737641050917837±1010913.6473942984543737641050917837 \pm 10 \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=+1.11088028±1.2105a_{2}= +1.11088028 \pm 1.2 \cdot 10^{-5} a3=0.17425754±1.3105a_{3}= -0.17425754 \pm 1.3 \cdot 10^{-5}
a4=+0.23405500±1.0105a_{4}= +0.23405500 \pm 1.0 \cdot 10^{-5} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.19357926±1.2105a_{6}= -0.19357926 \pm 1.2 \cdot 10^{-5}
a7=+1.83541165±5.0106a_{7}= +1.83541165 \pm 5.0 \cdot 10^{-6} a8=0.85087320±1.1105a_{8}= -0.85087320 \pm 1.1 \cdot 10^{-5} a9=0.96963431±6.4106a_{9}= -0.96963431 \pm 6.4 \cdot 10^{-6}
a10=0.49680076±1.2105a_{10}= -0.49680076 \pm 1.2 \cdot 10^{-5} a11=0.75542845±6.8106a_{11}= -0.75542845 \pm 6.8 \cdot 10^{-6} a12=0.04078585±1.1105a_{12}= -0.04078585 \pm 1.1 \cdot 10^{-5}
a13=1.05671932±8.6106a_{13}= -1.05671932 \pm 8.6 \cdot 10^{-6} a14=+2.03892261±5.1106a_{14}= +2.03892261 \pm 5.1 \cdot 10^{-6} a15=+0.07793034±1.3105a_{15}= +0.07793034 \pm 1.3 \cdot 10^{-5}
a16=1.17927326±5.4106a_{16}= -1.17927326 \pm 5.4 \cdot 10^{-6} a17=0.33370103±1.3105a_{17}= -0.33370103 \pm 1.3 \cdot 10^{-5} a18=1.07714764±5.7106a_{18}= -1.07714764 \pm 5.7 \cdot 10^{-6}
a19=0.19896072±1.2105a_{19}= -0.19896072 \pm 1.2 \cdot 10^{-5} a20=0.10467258±1.0105a_{20}= -0.10467258 \pm 1.0 \cdot 10^{-5} a21=0.31983432±5.6106a_{21}= -0.31983432 \pm 5.6 \cdot 10^{-6}
a22=0.83919057±7.2106a_{22}= -0.83919057 \pm 7.2 \cdot 10^{-6} a23=1.52474887±5.2106a_{23}= -1.52474887 \pm 5.2 \cdot 10^{-6} a24=+0.14827107±1.1105a_{24}= +0.14827107 \pm 1.1 \cdot 10^{-5}
a25=+0.2a_{25}= +0.2 a26=1.17388866±1.0105a_{26}= -1.17388866 \pm 1.0 \cdot 10^{-5} a27=+0.34322363±1.0105a_{27}= +0.34322363 \pm 1.0 \cdot 10^{-5}
a28=+0.42958727±4.1106a_{28}= +0.42958727 \pm 4.1 \cdot 10^{-6} a29=0.92616787±6.1106a_{29}= -0.92616787 \pm 6.1 \cdot 10^{-6} a30=+0.08657128±2.5105a_{30}= +0.08657128 \pm 2.5 \cdot 10^{-5}
a31=+0.57848674±1.3105a_{31}= +0.57848674 \pm 1.3 \cdot 10^{-5} a32=0.45915821±1.3105a_{32}= -0.45915821 \pm 1.3 \cdot 10^{-5} a33=+0.13163910±4.9106a_{33}= +0.13163910 \pm 4.9 \cdot 10^{-6}
a34=0.37070189±1.2105a_{34}= -0.37070189 \pm 1.2 \cdot 10^{-5} a35=0.82082104±5.0106a_{35}= -0.82082104 \pm 5.0 \cdot 10^{-6} a36=0.22694776±3.0106a_{36}= -0.22694776 \pm 3.0 \cdot 10^{-6}
a37=+1.12637488±1.6105a_{37}= +1.12637488 \pm 1.6 \cdot 10^{-5} a38=0.22102154±8.8106a_{38}= -0.22102154 \pm 8.8 \cdot 10^{-6} a39=+0.18414131±6.8106a_{39}= +0.18414131 \pm 6.8 \cdot 10^{-6}
a40=+0.38052206±1.1105a_{40}= +0.38052206 \pm 1.1 \cdot 10^{-5} a41=+0.52233007±1.3105a_{41}= +0.52233007 \pm 1.3 \cdot 10^{-5} a42=0.35529764±5.2106a_{42}= -0.35529764 \pm 5.2 \cdot 10^{-6}
a43=0.57389719±1.3105a_{43}= -0.57389719 \pm 1.3 \cdot 10^{-5} a44=0.17681181±5.1106a_{44}= -0.17681181 \pm 5.1 \cdot 10^{-6} a45=+0.43363365±6.4106a_{45}= +0.43363365 \pm 6.4 \cdot 10^{-6}
a46=1.69381346±6.3106a_{46}= -1.69381346 \pm 6.3 \cdot 10^{-6} a47=0.46539521±8.1106a_{47}= -0.46539521 \pm 8.1 \cdot 10^{-6} a48=+0.20549726±5.5106a_{48}= +0.20549726 \pm 5.5 \cdot 10^{-6}
a49=+2.36873593±1.1105a_{49}= +2.36873593 \pm 1.1 \cdot 10^{-5} a50=+0.22217606±1.2105a_{50}= +0.22217606 \pm 1.2 \cdot 10^{-5} a51=+0.05814992±1.3105a_{51}= +0.05814992 \pm 1.3 \cdot 10^{-5}
a52=0.24733044±8.2106a_{52}= -0.24733044 \pm 8.2 \cdot 10^{-6} a53=0.48902105±1.2105a_{53}= -0.48902105 \pm 1.2 \cdot 10^{-5} a54=+0.38128036±1.0105a_{54}= +0.38128036 \pm 1.0 \cdot 10^{-5}
a55=+0.33783787±6.8106a_{55}= +0.33783787 \pm 6.8 \cdot 10^{-6} a56=1.56170258±4.4106a_{56}= -1.56170258 \pm 4.4 \cdot 10^{-6} a57=+0.03467041±1.4105a_{57}= +0.03467041 \pm 1.4 \cdot 10^{-5}
a58=1.02886162±4.8106a_{58}= -1.02886162 \pm 4.8 \cdot 10^{-6} a59=+0.27014848±1.0105a_{59}= +0.27014848 \pm 1.0 \cdot 10^{-5} a60=+0.01823999±2.3105a_{60}= +0.01823999 \pm 2.3 \cdot 10^{-5}

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