Properties

Label 3.39
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 17.28832
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: 17.2883277696958706487727893028±610617.2883277696958706487727893028 \pm 6 \cdot 10^{-6}

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=+0.15268036±5.8104a_{2}= +0.15268036 \pm 5.8 \cdot 10^{-4} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.97668871±1.0103a_{4}= -0.97668871 \pm 1.0 \cdot 10^{-3} a5=1.63487950±8.0104a_{5}= -1.63487950 \pm 8.0 \cdot 10^{-4} a6=+0.08815005±5.8104a_{6}= +0.08815005 \pm 5.8 \cdot 10^{-4}
a7=+0.43448281±6.6104a_{7}= +0.43448281 \pm 6.6 \cdot 10^{-4} a8=0.30180154±7.1104a_{8}= -0.30180154 \pm 7.1 \cdot 10^{-4} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.24961399±4.6104a_{10}= -0.24961399 \pm 4.6 \cdot 10^{-4} a11=+1.63699990±7.3104a_{11}= +1.63699990 \pm 7.3 \cdot 10^{-4} a12=0.56389149±1.0103a_{12}= -0.56389149 \pm 1.0 \cdot 10^{-3}
a13=0.82216821±7.1104a_{13}= -0.82216821 \pm 7.1 \cdot 10^{-4} a14=+0.06633699±4.5104a_{14}= +0.06633699 \pm 4.5 \cdot 10^{-4} a15=0.94389812±8.0104a_{15}= -0.94389812 \pm 8.0 \cdot 10^{-4}
a16=+0.93060954±8.6104a_{16}= +0.93060954 \pm 8.6 \cdot 10^{-4} a17=0.04830386±5.3104a_{17}= -0.04830386 \pm 5.3 \cdot 10^{-4} a18=+0.05089345±5.8104a_{18}= +0.05089345 \pm 5.8 \cdot 10^{-4}
a19=+1.12670635±4.3104a_{19}= +1.12670635 \pm 4.3 \cdot 10^{-4} a20=+1.59676834±7.5104a_{20}= +1.59676834 \pm 7.5 \cdot 10^{-4} a21=+0.25084877±6.6104a_{21}= +0.25084877 \pm 6.6 \cdot 10^{-4}
a22=+0.24993773±3.7104a_{22}= +0.24993773 \pm 3.7 \cdot 10^{-4} a23=+0.32871172±1.6103a_{23}= +0.32871172 \pm 1.6 \cdot 10^{-3} a24=0.17424520±7.1104a_{24}= -0.17424520 \pm 7.1 \cdot 10^{-4}
a25=+1.67283097±6.6104a_{25}= +1.67283097 \pm 6.6 \cdot 10^{-4} a26=0.12552894±2.5104a_{26}= -0.12552894 \pm 2.5 \cdot 10^{-4} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.42435445±4.3104a_{28}= -0.42435445 \pm 4.3 \cdot 10^{-4} a29=+0.27864256±1.5103a_{29}= +0.27864256 \pm 1.5 \cdot 10^{-3} a30=0.14411470±1.3103a_{30}= -0.14411470 \pm 1.3 \cdot 10^{-3}
a31=0.35895031±6.8104a_{31}= -0.35895031 \pm 6.8 \cdot 10^{-4} a32=+0.44388734±9.5104a_{32}= +0.44388734 \pm 9.5 \cdot 10^{-4} a33=+0.94512233±7.3104a_{33}= +0.94512233 \pm 7.3 \cdot 10^{-4}
a34=0.00737505±6.5104a_{34}= -0.00737505 \pm 6.5 \cdot 10^{-4} a35=0.71032703±2.9104a_{35}= -0.71032703 \pm 2.9 \cdot 10^{-4} a36=0.32556290±1.0103a_{36}= -0.32556290 \pm 1.0 \cdot 10^{-3}
a37=+0.05009193±8.1104a_{37}= +0.05009193 \pm 8.1 \cdot 10^{-4} a38=+0.17202593±1.9104a_{38}= +0.17202593 \pm 1.9 \cdot 10^{-4} a39=0.47467904±7.1104a_{39}= -0.47467904 \pm 7.1 \cdot 10^{-4}
a40=+0.49340915±4.4104a_{40}= +0.49340915 \pm 4.4 \cdot 10^{-4} a41=+0.36101357±1.5103a_{41}= +0.36101357 \pm 1.5 \cdot 10^{-3} a42=+0.03829968±1.2103a_{42}= +0.03829968 \pm 1.2 \cdot 10^{-3}
a43=+1.16288445±1.0103a_{43}= +1.16288445 \pm 1.0 \cdot 10^{-3} a44=1.59883931±6.4104a_{44}= -1.59883931 \pm 6.4 \cdot 10^{-4} a45=0.54495983±8.0104a_{45}= -0.54495983 \pm 8.0 \cdot 10^{-4}
a46=+0.05018782±4.6104a_{46}= +0.05018782 \pm 4.6 \cdot 10^{-4} a47=+0.42383768±1.2103a_{47}= +0.42383768 \pm 1.2 \cdot 10^{-3} a48=+0.53728767±8.6104a_{48}= +0.53728767 \pm 8.6 \cdot 10^{-4}
a49=0.81122469±1.1103a_{49}= -0.81122469 \pm 1.1 \cdot 10^{-3} a50=+0.25540843±3.2104a_{50}= +0.25540843 \pm 3.2 \cdot 10^{-4} a51=0.02788825±5.3104a_{51}= -0.02788825 \pm 5.3 \cdot 10^{-4}
a52=+0.80300240±6.5104a_{52}= +0.80300240 \pm 6.5 \cdot 10^{-4} a53=+0.96210845±6.4104a_{53}= +0.96210845 \pm 6.4 \cdot 10^{-4} a54=+0.02938335±5.8104a_{54}= +0.02938335 \pm 5.8 \cdot 10^{-4}
a55=2.67629757±5.1104a_{55}= -2.67629757 \pm 5.1 \cdot 10^{-4} a56=0.13112758±6.3104a_{56}= -0.13112758 \pm 6.3 \cdot 10^{-4} a57=+0.65050421±4.3104a_{57}= +0.65050421 \pm 4.3 \cdot 10^{-4}
a58=+0.04254325±6.3104a_{58}= +0.04254325 \pm 6.3 \cdot 10^{-4} a59=+0.27465322±1.0103a_{59}= +0.27465322 \pm 1.0 \cdot 10^{-3} a60=+0.92189463±1.8103a_{60}= +0.92189463 \pm 1.8 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000