Properties

Label 3.11
Level 33
Weight 00
Character 3.1
Symmetry even
RR 10.23107
Fricke sign 1-1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 10.231075689323657356434721872±4101110.231075689323657356434721872 \pm 4 \cdot 10^{-11}

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=1.78019237±1108a_{2}= -1.78019237 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+2.16908488±1108a_{4}= +2.16908488 \pm 1 \cdot 10^{-8} a5=0.27577101±1108a_{5}= -0.27577101 \pm 1 \cdot 10^{-8} a6=1.02779454±1.0108a_{6}= -1.02779454 \pm 1.0 \cdot 10^{-8}
a7=+0.31247325±1108a_{7}= +0.31247325 \pm 1 \cdot 10^{-8} a8=2.08119597±1108a_{8}= -2.08119597 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.49092545±1108a_{10}= +0.49092545 \pm 1 \cdot 10^{-8} a11=1.50280572±1108a_{11}= -1.50280572 \pm 1 \cdot 10^{-8} a12=+1.25232174±1.0108a_{12}= +1.25232174 \pm 1.0 \cdot 10^{-8}
a13=0.50831111±1108a_{13}= -0.50831111 \pm 1 \cdot 10^{-8} a14=0.55626250±1108a_{14}= -0.55626250 \pm 1 \cdot 10^{-8} a15=0.15921647±1.0108a_{15}= -0.15921647 \pm 1.0 \cdot 10^{-8}
a16=+1.53584432±1108a_{16}= +1.53584432 \pm 1 \cdot 10^{-8} a17=0.46120248±1108a_{17}= -0.46120248 \pm 1 \cdot 10^{-8} a18=0.59339746±1.0108a_{18}= -0.59339746 \pm 1.0 \cdot 10^{-8}
a19=0.20775181±1108a_{19}= -0.20775181 \pm 1 \cdot 10^{-8} a20=0.59817073±1108a_{20}= -0.59817073 \pm 1 \cdot 10^{-8} a21=+0.18040652±1.0108a_{21}= +0.18040652 \pm 1.0 \cdot 10^{-8}
a22=+2.67528328±1108a_{22}= +2.67528328 \pm 1 \cdot 10^{-8} a23=1.04015381±1108a_{23}= -1.04015381 \pm 1 \cdot 10^{-8} a24=1.20157906±1.0108a_{24}= -1.20157906 \pm 1.0 \cdot 10^{-8}
a25=0.92395035±1108a_{25}= -0.92395035 \pm 1 \cdot 10^{-8} a26=+0.90489157±1108a_{26}= +0.90489157 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.67778100±1108a_{28}= +0.67778100 \pm 1 \cdot 10^{-8} a29=0.55070740±1108a_{29}= -0.55070740 \pm 1 \cdot 10^{-8} a30=+0.28343594±1.0108a_{30}= +0.28343594 \pm 1.0 \cdot 10^{-8}
a31=+0.41310336±1108a_{31}= +0.41310336 \pm 1 \cdot 10^{-8} a32=0.65290237±1108a_{32}= -0.65290237 \pm 1 \cdot 10^{-8} a33=0.86764529±1.0108a_{33}= -0.86764529 \pm 1.0 \cdot 10^{-8}
a34=+0.82102914±1108a_{34}= +0.82102914 \pm 1 \cdot 10^{-8} a35=0.08617107±1108a_{35}= -0.08617107 \pm 1 \cdot 10^{-8} a36=+0.72302829±1.0108a_{36}= +0.72302829 \pm 1.0 \cdot 10^{-8}
a37=1.32853091±1108a_{37}= -1.32853091 \pm 1 \cdot 10^{-8} a38=+0.36983819±1108a_{38}= +0.36983819 \pm 1 \cdot 10^{-8} a39=0.29347356±1.0108a_{39}= -0.29347356 \pm 1.0 \cdot 10^{-8}
a40=+0.57393352±1108a_{40}= +0.57393352 \pm 1 \cdot 10^{-8} a41=+1.97630462±1108a_{41}= +1.97630462 \pm 1 \cdot 10^{-8} a42=0.32115830±1.0108a_{42}= -0.32115830 \pm 1.0 \cdot 10^{-8}
a43=0.59404577±1108a_{43}= -0.59404577 \pm 1 \cdot 10^{-8} a44=3.25971317±1108a_{44}= -3.25971317 \pm 1 \cdot 10^{-8} a45=0.09192367±1.0108a_{45}= -0.09192367 \pm 1.0 \cdot 10^{-8}
a46=+1.85167388±1108a_{46}= +1.85167388 \pm 1 \cdot 10^{-8} a47=+0.46068561±1108a_{47}= +0.46068561 \pm 1 \cdot 10^{-8} a48=+0.88672013±1.0108a_{48}= +0.88672013 \pm 1.0 \cdot 10^{-8}
a49=0.90236047±1108a_{49}= -0.90236047 \pm 1 \cdot 10^{-8} a50=+1.64480936±1108a_{50}= +1.64480936 \pm 1 \cdot 10^{-8} a51=0.26627538±1.0108a_{51}= -0.26627538 \pm 1.0 \cdot 10^{-8}
a52=1.10256995±1108a_{52}= -1.10256995 \pm 1 \cdot 10^{-8} a53=0.66822974±1108a_{53}= -0.66822974 \pm 1 \cdot 10^{-8} a54=0.34259818±1.0108a_{54}= -0.34259818 \pm 1.0 \cdot 10^{-8}
a55=+0.41443026±1108a_{55}= +0.41443026 \pm 1 \cdot 10^{-8} a56=0.65031807±1108a_{56}= -0.65031807 \pm 1 \cdot 10^{-8} a57=0.11994556±1.0108a_{57}= -0.11994556 \pm 1.0 \cdot 10^{-8}
a58=+0.98036511±1108a_{58}= +0.98036511 \pm 1 \cdot 10^{-8} a59=+1.34566844±1108a_{59}= +1.34566844 \pm 1 \cdot 10^{-8} a60=0.34535403±1.0108a_{60}= -0.34535403 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000