Properties

Label 2.34
Level 22
Weight 00
Character 2.1
Symmetry even
RR 22.75821
Fricke sign not computed rigorously

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Maass form invariants

Level: 2 2
Weight: 0 0
Character: 2.1
Symmetry: even
Fricke sign: not computed rigorously
Spectral parameter: 22.7582184886991529054041038537±610322.7582184886991529054041038537 \pm 6 \cdot 10^{-3}

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=±0.70710678±1.0108a_{2}= \pm0.70710678 \pm 1.0 \cdot 10^{-8} a3=+0.69564349±1.4104a_{3}= +0.69564349 \pm 1.4 \cdot 10^{-4}
a4=±0.5a_{4}= \pm0.5 a5=0.25510796±1.1104a_{5}= -0.25510796 \pm 1.1 \cdot 10^{-4} a6=±0.49189423±1.0104a_{6}= \pm0.49189423 \pm 1.0 \cdot 10^{-4}
a7=1.48407981±1.0104a_{7}= -1.48407981 \pm 1.0 \cdot 10^{-4} a8=±0.35355339±1.0108a_{8}= \pm0.35355339 \pm 1.0 \cdot 10^{-8} a9=0.51608013±3.2105a_{9}= -0.51608013 \pm 3.2 \cdot 10^{-5}
a10=±0.18038857±8.4105a_{10}= \pm0.18038857 \pm 8.4 \cdot 10^{-5} a11=0.77208940±7.4105a_{11}= -0.77208940 \pm 7.4 \cdot 10^{-5} a12=±0.34782175±7.3105a_{12}= \pm0.34782175 \pm 7.3 \cdot 10^{-5}
a13=0.90792109±1.1104a_{13}= -0.90792109 \pm 1.1 \cdot 10^{-4} a14=±1.04940289±7.7105a_{14}= \pm1.04940289 \pm 7.7 \cdot 10^{-5} a15=0.17746419±1.3104a_{15}= -0.17746419 \pm 1.3 \cdot 10^{-4}
a16=±0.25a_{16}= \pm0.25 a17=+1.01066209±4.5105a_{17}= +1.01066209 \pm 4.5 \cdot 10^{-5} a18=±0.36492376±2.2105a_{18}= \pm0.36492376 \pm 2.2 \cdot 10^{-5}
a19=+0.94531266±9.6105a_{19}= +0.94531266 \pm 9.6 \cdot 10^{-5} a20=±0.12755398±5.9105a_{20}= \pm0.12755398 \pm 5.9 \cdot 10^{-5} a21=1.03239046±1.2104a_{21}= -1.03239046 \pm 1.2 \cdot 10^{-4}
a22=±0.54594965±5.2105a_{22}= \pm0.54594965 \pm 5.2 \cdot 10^{-5} a23=1.54522778±1.3105a_{23}= -1.54522778 \pm 1.3 \cdot 10^{-5} a24=±0.24594712±5.1105a_{24}= \pm0.24594712 \pm 5.1 \cdot 10^{-5}
a25=0.93491993±2.4105a_{25}= -0.93491993 \pm 2.4 \cdot 10^{-5} a26=±0.64199716±7.8105a_{26}= \pm0.64199716 \pm 7.8 \cdot 10^{-5} a27=1.05465128±1.1104a_{27}= -1.05465128 \pm 1.1 \cdot 10^{-4}
a28=±0.74203990±5.4105a_{28}= \pm0.74203990 \pm 5.4 \cdot 10^{-5} a29=+1.26706849±2.2104a_{29}= +1.26706849 \pm 2.2 \cdot 10^{-4} a30=±0.12548614±9.3105a_{30}= \pm0.12548614 \pm 9.3 \cdot 10^{-5}
a31=1.34507150±2.0104a_{31}= -1.34507150 \pm 2.0 \cdot 10^{-4} a32=±0.17677670±1.0108a_{32}= \pm0.17677670 \pm 1.0 \cdot 10^{-8} a33=0.53709897±8.2105a_{33}= -0.53709897 \pm 8.2 \cdot 10^{-5}
a34=±0.71464602±3.2105a_{34}= \pm0.71464602 \pm 3.2 \cdot 10^{-5} a35=+0.37860058±9.8105a_{35}= +0.37860058 \pm 9.8 \cdot 10^{-5} a36=±0.25804007±1.6105a_{36}= \pm0.25804007 \pm 1.6 \cdot 10^{-5}
a37=0.68704600±1.0104a_{37}= -0.68704600 \pm 1.0 \cdot 10^{-4} a38=±0.66843699±6.8105a_{38}= \pm0.66843699 \pm 6.8 \cdot 10^{-5} a39=0.63158940±1.2104a_{39}= -0.63158940 \pm 1.2 \cdot 10^{-4}
a40=±0.09019429±4.2105a_{40}= \pm0.09019429 \pm 4.2 \cdot 10^{-5} a41=+0.70790335±9.8105a_{41}= +0.70790335 \pm 9.8 \cdot 10^{-5} a42=±0.73001030±8.5105a_{42}= \pm0.73001030 \pm 8.5 \cdot 10^{-5}
a43=+1.12779579±1.0104a_{43}= +1.12779579 \pm 1.0 \cdot 10^{-4} a44=±0.38604470±3.7105a_{44}= \pm0.38604470 \pm 3.7 \cdot 10^{-5} a45=+0.13165615±2.8105a_{45}= +0.13165615 \pm 2.8 \cdot 10^{-5}
a46=±1.09264104±9.2106a_{46}= \pm1.09264104 \pm 9.2 \cdot 10^{-6} a47=0.04620758±1.3104a_{47}= -0.04620758 \pm 1.3 \cdot 10^{-4} a48=±0.17391087±3.6105a_{48}= \pm0.17391087 \pm 3.6 \cdot 10^{-5}
a49=+1.20249287±4.3105a_{49}= +1.20249287 \pm 4.3 \cdot 10^{-5} a50=±0.66108822±1.7105a_{50}= \pm0.66108822 \pm 1.7 \cdot 10^{-5} a51=+0.70306051±5.3105a_{51}= +0.70306051 \pm 5.3 \cdot 10^{-5}
a52=±0.45396055±5.5105a_{52}= \pm0.45396055 \pm 5.5 \cdot 10^{-5} a53=0.10428699±1.5104a_{53}= -0.10428699 \pm 1.5 \cdot 10^{-4} a54=±0.74575107±8.0105a_{54}= \pm0.74575107 \pm 8.0 \cdot 10^{-5}
a55=+0.19696615±6.7105a_{55}= +0.19696615 \pm 6.7 \cdot 10^{-5} a56=±0.52470145±3.8105a_{56}= \pm0.52470145 \pm 3.8 \cdot 10^{-5} a57=+0.65760060±1.0104a_{57}= +0.65760060 \pm 1.0 \cdot 10^{-4}
a58=±0.89595272±1.6104a_{58}= \pm0.89595272 \pm 1.6 \cdot 10^{-4} a59=+0.38767502±2.1105a_{59}= +0.38767502 \pm 2.1 \cdot 10^{-5} a60=±0.08873210±6.6105a_{60}= \pm0.08873210 \pm 6.6 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000