Properties

Label 2.32
Level 22
Weight 00
Character 2.1
Symmetry even
RR 22.08904
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: 22.0890454668192578773032661018±310322.0890454668192578773032661018 \pm 3 \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=1.16040571±1.2104a_{3}= -1.16040571 \pm 1.2 \cdot 10^{-4}
a4=±0.5a_{4}= \pm0.5 a5=+1.62780155±9.9105a_{5}= +1.62780155 \pm 9.9 \cdot 10^{-5} a6=±0.82053075±8.6105a_{6}= \pm0.82053075 \pm 8.6 \cdot 10^{-5}
a7=1.26807218±9.1105a_{7}= -1.26807218 \pm 9.1 \cdot 10^{-5} a8=±0.35355339±1.0108a_{8}= \pm0.35355339 \pm 1.0 \cdot 10^{-8} a9=+0.34654142±2.6105a_{9}= +0.34654142 \pm 2.6 \cdot 10^{-5}
a10=±1.15102951±7.0105a_{10}= \pm1.15102951 \pm 7.0 \cdot 10^{-5} a11=0.74934386±6.2105a_{11}= -0.74934386 \pm 6.2 \cdot 10^{-5} a12=±0.58020286±6.1105a_{12}= \pm0.58020286 \pm 6.1 \cdot 10^{-5}
a13=+0.32035835±9.2105a_{13}= +0.32035835 \pm 9.2 \cdot 10^{-5} a14=±0.89666244±6.4105a_{14}= \pm0.89666244 \pm 6.4 \cdot 10^{-5} a15=1.88891021±1.1104a_{15}= -1.88891021 \pm 1.1 \cdot 10^{-4}
a16=±0.25a_{16}= \pm0.25 a17=0.57721923±3.8105a_{17}= -0.57721923 \pm 3.8 \cdot 10^{-5} a18=±0.24504179±1.9105a_{18}= \pm0.24504179 \pm 1.9 \cdot 10^{-5}
a19=0.00850153±8.1105a_{19}= -0.00850153 \pm 8.1 \cdot 10^{-5} a20=±0.81390077±4.9105a_{20}= \pm0.81390077 \pm 4.9 \cdot 10^{-5} a21=+1.47147820±1.0104a_{21}= +1.47147820 \pm 1.0 \cdot 10^{-4}
a22=±0.52986612±4.4105a_{22}= \pm0.52986612 \pm 4.4 \cdot 10^{-5} a23=+0.33903249±1.0105a_{23}= +0.33903249 \pm 1.0 \cdot 10^{-5} a24=±0.41026537±4.3105a_{24}= \pm0.41026537 \pm 4.3 \cdot 10^{-5}
a25=+1.64973787±2.0105a_{25}= +1.64973787 \pm 2.0 \cdot 10^{-5} a26=±0.22652756±6.5105a_{26}= \pm0.22652756 \pm 6.5 \cdot 10^{-5} a27=+0.75827707±9.4105a_{27}= +0.75827707 \pm 9.4 \cdot 10^{-5}
a28=±0.63403609±4.5105a_{28}= \pm0.63403609 \pm 4.5 \cdot 10^{-5} a29=+0.01999078±1.9104a_{29}= +0.01999078 \pm 1.9 \cdot 10^{-4} a30=±1.33566122±7.8105a_{30}= \pm1.33566122 \pm 7.8 \cdot 10^{-5}
a31=0.72455230±1.7104a_{31}= -0.72455230 \pm 1.7 \cdot 10^{-4} a32=±0.17677670±1.0108a_{32}= \pm0.17677670 \pm 1.0 \cdot 10^{-8} a33=+0.86954289±6.8105a_{33}= +0.86954289 \pm 6.8 \cdot 10^{-5}
a34=±0.40815563±2.6105a_{34}= \pm0.40815563 \pm 2.6 \cdot 10^{-5} a35=2.06416986±8.2105a_{35}= -2.06416986 \pm 8.2 \cdot 10^{-5} a36=±0.17327071±1.3105a_{36}= \pm0.17327071 \pm 1.3 \cdot 10^{-5}
a37=+1.78875846±8.4105a_{37}= +1.78875846 \pm 8.4 \cdot 10^{-5} a38=±0.00601149±5.7105a_{38}= \pm0.00601149 \pm 5.7 \cdot 10^{-5} a39=0.37174566±1.0104a_{39}= -0.37174566 \pm 1.0 \cdot 10^{-4}
a40=±0.57551476±3.5105a_{40}= \pm0.57551476 \pm 3.5 \cdot 10^{-5} a41=0.00732486±8.2105a_{41}= -0.00732486 \pm 8.2 \cdot 10^{-5} a42=±1.04049222±7.1105a_{42}= \pm1.04049222 \pm 7.1 \cdot 10^{-5}
a43=+1.68710967±8.8105a_{43}= +1.68710967 \pm 8.8 \cdot 10^{-5} a44=±0.37467193±3.1105a_{44}= \pm0.37467193 \pm 3.1 \cdot 10^{-5} a45=+0.56410065±2.4105a_{45}= +0.56410065 \pm 2.4 \cdot 10^{-5}
a46=±0.23973217±7.7106a_{46}= \pm0.23973217 \pm 7.7 \cdot 10^{-6} a47=0.47062990±1.1104a_{47}= -0.47062990 \pm 1.1 \cdot 10^{-4} a48=±0.29010143±3.0105a_{48}= \pm0.29010143 \pm 3.0 \cdot 10^{-5}
a49=+0.60800706±3.6105a_{49}= +0.60800706 \pm 3.6 \cdot 10^{-5} a50=±1.16654084±1.4105a_{50}= \pm1.16654084 \pm 1.4 \cdot 10^{-5} a51=+0.66980849±4.4105a_{51}= +0.66980849 \pm 4.4 \cdot 10^{-5}
a52=±0.16017918±4.6105a_{52}= \pm0.16017918 \pm 4.6 \cdot 10^{-5} a53=+1.29190537±1.2104a_{53}= +1.29190537 \pm 1.2 \cdot 10^{-4} a54=±0.53618286±6.7105a_{54}= \pm0.53618286 \pm 6.7 \cdot 10^{-5}
a55=1.21978309±5.6105a_{55}= -1.21978309 \pm 5.6 \cdot 10^{-5} a56=±0.44833122±3.2105a_{56}= \pm0.44833122 \pm 3.2 \cdot 10^{-5} a57=+0.00986522±8.9105a_{57}= +0.00986522 \pm 8.9 \cdot 10^{-5}
a58=±0.01413562±1.3104a_{58}= \pm0.01413562 \pm 1.3 \cdot 10^{-4} a59=+0.09414930±1.7105a_{59}= +0.09414930 \pm 1.7 \cdot 10^{-5} a60=±0.94445511±5.5105a_{60}= \pm0.94445511 \pm 5.5 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000