Properties

Label 3.32
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 15.75323
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: 15.7532336884908289702674270888±510715.7532336884908289702674270888 \pm 5 \cdot 10^{-7}

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=0.12044299±5.1105a_{2}= -0.12044299 \pm 5.1 \cdot 10^{-5} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.98549349±9.3105a_{4}= -0.98549349 \pm 9.3 \cdot 10^{-5} a5=+0.47652764±7.1105a_{5}= +0.47652764 \pm 7.1 \cdot 10^{-5} a6=0.06953779±5.1105a_{6}= -0.06953779 \pm 5.1 \cdot 10^{-5}
a7=+0.03761873±5.8105a_{7}= +0.03761873 \pm 5.8 \cdot 10^{-5} a8=+0.23913876±6.3105a_{8}= +0.23913876 \pm 6.3 \cdot 10^{-5} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.05739441±4.0105a_{10}= -0.05739441 \pm 4.0 \cdot 10^{-5} a11=1.18366316±6.4105a_{11}= -1.18366316 \pm 6.4 \cdot 10^{-5} a12=0.56897493±9.3105a_{12}= -0.56897493 \pm 9.3 \cdot 10^{-5}
a13=+1.03533166±6.3105a_{13}= +1.03533166 \pm 6.3 \cdot 10^{-5} a14=0.00453091±4.0105a_{14}= -0.00453091 \pm 4.0 \cdot 10^{-5} a15=+0.27512336±7.1105a_{15}= +0.27512336 \pm 7.1 \cdot 10^{-5}
a16=+0.95669090±7.5105a_{16}= +0.95669090 \pm 7.5 \cdot 10^{-5} a17=+1.33804212±4.7105a_{17}= +1.33804212 \pm 4.7 \cdot 10^{-5} a18=0.04014766±5.1105a_{18}= -0.04014766 \pm 5.1 \cdot 10^{-5}
a19=+1.39631786±3.8105a_{19}= +1.39631786 \pm 3.8 \cdot 10^{-5} a20=0.46961489±6.6105a_{20}= -0.46961489 \pm 6.6 \cdot 10^{-5} a21=+0.02171919±5.8105a_{21}= +0.02171919 \pm 5.8 \cdot 10^{-5}
a22=+0.14256392±3.2105a_{22}= +0.14256392 \pm 3.2 \cdot 10^{-5} a23=+1.28561551±1.4104a_{23}= +1.28561551 \pm 1.4 \cdot 10^{-4} a24=+0.13806683±6.3105a_{24}= +0.13806683 \pm 6.3 \cdot 10^{-5}
a25=0.77292141±5.8105a_{25}= -0.77292141 \pm 5.8 \cdot 10^{-5} a26=0.12469844±2.2105a_{26}= -0.12469844 \pm 2.2 \cdot 10^{-5} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.03707302±3.8105a_{28}= -0.03707302 \pm 3.8 \cdot 10^{-5} a29=+0.13659671±1.3104a_{29}= +0.13659671 \pm 1.3 \cdot 10^{-4} a30=0.03313668±1.2104a_{30}= -0.03313668 \pm 1.2 \cdot 10^{-4}
a31=+0.98573108±6.0105a_{31}= +0.98573108 \pm 6.0 \cdot 10^{-5} a32=0.35436547±8.4105a_{32}= -0.35436547 \pm 8.4 \cdot 10^{-5} a33=0.68338824±6.4105a_{33}= -0.68338824 \pm 6.4 \cdot 10^{-5}
a34=0.16115779±5.7105a_{34}= -0.16115779 \pm 5.7 \cdot 10^{-5} a35=+0.01792637±2.5105a_{35}= +0.01792637 \pm 2.5 \cdot 10^{-5} a36=0.32849783±9.3105a_{36}= -0.32849783 \pm 9.3 \cdot 10^{-5}
a37=+0.86623114±7.2105a_{37}= +0.86623114 \pm 7.2 \cdot 10^{-5} a38=0.16817669±1.7105a_{38}= -0.16817669 \pm 1.7 \cdot 10^{-5} a39=+0.59774901±6.3105a_{39}= +0.59774901 \pm 6.3 \cdot 10^{-5}
a40=+0.11395623±3.9105a_{40}= +0.11395623 \pm 3.9 \cdot 10^{-5} a41=0.47592056±1.3104a_{41}= -0.47592056 \pm 1.3 \cdot 10^{-4} a42=0.00261592±1.1104a_{42}= -0.00261592 \pm 1.1 \cdot 10^{-4}
a43=1.74460158±9.1105a_{43}= -1.74460158 \pm 9.1 \cdot 10^{-5} a44=+1.16649233±5.7105a_{44}= +1.16649233 \pm 5.7 \cdot 10^{-5} a45=+0.15884255±7.1105a_{45}= +0.15884255 \pm 7.1 \cdot 10^{-5}
a46=0.15484337±4.1105a_{46}= -0.15484337 \pm 4.1 \cdot 10^{-5} a47=+0.71850691±1.1104a_{47}= +0.71850691 \pm 1.1 \cdot 10^{-4} a48=+0.55234575±7.6105a_{48}= +0.55234575 \pm 7.6 \cdot 10^{-5}
a49=0.99858483±9.8105a_{49}= -0.99858483 \pm 9.8 \cdot 10^{-5} a50=+0.09309296±2.8105a_{50}= +0.09309296 \pm 2.8 \cdot 10^{-5} a51=+0.77251898±4.7105a_{51}= +0.77251898 \pm 4.7 \cdot 10^{-5}
a52=1.02031261±5.7105a_{52}= -1.02031261 \pm 5.7 \cdot 10^{-5} a53=0.07034417±5.6105a_{53}= -0.07034417 \pm 5.6 \cdot 10^{-5} a54=0.02317926±5.1105a_{54}= -0.02317926 \pm 5.1 \cdot 10^{-5}
a55=0.56404821±4.5105a_{55}= -0.56404821 \pm 4.5 \cdot 10^{-5} a56=+0.00899610±5.6105a_{56}= +0.00899610 \pm 5.6 \cdot 10^{-5} a57=+0.80616449±3.8105a_{57}= +0.80616449 \pm 3.8 \cdot 10^{-5}
a58=0.01645212±5.5105a_{58}= -0.01645212 \pm 5.5 \cdot 10^{-5} a59=+1.42692944±9.1105a_{59}= +1.42692944 \pm 9.1 \cdot 10^{-5} a60=0.27113228±1.6104a_{60}= -0.27113228 \pm 1.6 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000