Properties

Label 3.24
Level 33
Weight 00
Character 3.1
Symmetry even
RR 13.99317
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: 13.9931761915667650038932006134±210813.9931761915667650038932006134 \pm 2 \cdot 10^{-8}

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=0.64166864±1108a_{2}= -0.64166864 \pm 1 \cdot 10^{-8} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.58826136±1108a_{4}= -0.58826136 \pm 1 \cdot 10^{-8} a5=+0.23230069±1108a_{5}= +0.23230069 \pm 1 \cdot 10^{-8} a6=0.37046756±1.9108a_{6}= -0.37046756 \pm 1.9 \cdot 10^{-8}
a7=+0.49911333±1108a_{7}= +0.49911333 \pm 1 \cdot 10^{-8} a8=+1.01913750±1108a_{8}= +1.01913750 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.14906007±1108a_{10}= -0.14906007 \pm 1 \cdot 10^{-8} a11=0.34627569±1108a_{11}= -0.34627569 \pm 1 \cdot 10^{-8} a12=0.33963285±1.6108a_{12}= -0.33963285 \pm 1.6 \cdot 10^{-8}
a13=1.95599330±1108a_{13}= -1.95599330 \pm 1 \cdot 10^{-8} a14=0.32026537±1108a_{14}= -0.32026537 \pm 1 \cdot 10^{-8} a15=+0.13411886±1.1108a_{15}= +0.13411886 \pm 1.1 \cdot 10^{-8}
a16=0.06568722±1108a_{16}= -0.06568722 \pm 1 \cdot 10^{-8} a17=1.39631315±1108a_{17}= -1.39631315 \pm 1 \cdot 10^{-8} a18=0.21388955±1.9108a_{18}= -0.21388955 \pm 1.9 \cdot 10^{-8}
a19=+0.47163237±1.0108a_{19}= +0.47163237 \pm 1.0 \cdot 10^{-8} a20=0.13665352±1108a_{20}= -0.13665352 \pm 1 \cdot 10^{-8} a21=+0.28816322±1.5108a_{21}= +0.28816322 \pm 1.5 \cdot 10^{-8}
a22=+0.22219425±1108a_{22}= +0.22219425 \pm 1 \cdot 10^{-8} a23=1.19833433±1108a_{23}= -1.19833433 \pm 1 \cdot 10^{-8} a24=+0.58839931±1.2108a_{24}= +0.58839931 \pm 1.2 \cdot 10^{-8}
a25=0.94603639±1108a_{25}= -0.94603639 \pm 1 \cdot 10^{-8} a26=+1.25509956±1108a_{26}= +1.25509956 \pm 1 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.29360908±1108a_{28}= -0.29360908 \pm 1 \cdot 10^{-8} a29=0.27586335±1108a_{29}= -0.27586335 \pm 1 \cdot 10^{-8} a30=0.08605987±2.0108a_{30}= -0.08605987 \pm 2.0 \cdot 10^{-8}
a31=+0.52058242±1108a_{31}= +0.52058242 \pm 1 \cdot 10^{-8} a32=0.97698808±1108a_{32}= -0.97698808 \pm 1 \cdot 10^{-8} a33=0.19992236±1.3108a_{33}= -0.19992236 \pm 1.3 \cdot 10^{-8}
a34=+0.89597036±1108a_{34}= +0.89597036 \pm 1 \cdot 10^{-8} a35=+0.11594437±1108a_{35}= +0.11594437 \pm 1 \cdot 10^{-8} a36=0.19608712±1.6108a_{36}= -0.19608712 \pm 1.6 \cdot 10^{-8}
a37=+0.93320094±1108a_{37}= +0.93320094 \pm 1 \cdot 10^{-8} a38=0.30263170±1.3108a_{38}= -0.30263170 \pm 1.3 \cdot 10^{-8} a39=1.12929326±1.4108a_{39}= -1.12929326 \pm 1.4 \cdot 10^{-8}
a40=+0.23674634±1108a_{40}= +0.23674634 \pm 1 \cdot 10^{-8} a41=0.78294135±1108a_{41}= -0.78294135 \pm 1 \cdot 10^{-8} a42=0.18490530±2.4108a_{42}= -0.18490530 \pm 2.4 \cdot 10^{-8}
a43=+1.51636211±1108a_{43}= +1.51636211 \pm 1 \cdot 10^{-8} a44=+0.20370061±1108a_{44}= +0.20370061 \pm 1 \cdot 10^{-8} a45=+0.07743356±1.1108a_{45}= +0.07743356 \pm 1.1 \cdot 10^{-8}
a46=+0.76893356±1108a_{46}= +0.76893356 \pm 1 \cdot 10^{-8} a47=1.40858951±1108a_{47}= -1.40858951 \pm 1 \cdot 10^{-8} a48=0.03792453±1.8108a_{48}= -0.03792453 \pm 1.8 \cdot 10^{-8}
a49=0.75088588±1108a_{49}= -0.75088588 \pm 1 \cdot 10^{-8} a50=+0.60704188±1108a_{50}= +0.60704188 \pm 1 \cdot 10^{-8} a51=0.80616177±1.6108a_{51}= -0.80616177 \pm 1.6 \cdot 10^{-8}
a52=+1.15063527±1108a_{52}= +1.15063527 \pm 1 \cdot 10^{-8} a53=0.02788536±1108a_{53}= -0.02788536 \pm 1 \cdot 10^{-8} a54=0.12348919±1.9108a_{54}= -0.12348919 \pm 1.9 \cdot 10^{-8}
a55=0.08044008±1108a_{55}= -0.08044008 \pm 1 \cdot 10^{-8} a56=+0.50866511±1108a_{56}= +0.50866511 \pm 1 \cdot 10^{-8} a57=+0.27229707±2.0108a_{57}= +0.27229707 \pm 2.0 \cdot 10^{-8}
a58=+0.17701286±1108a_{58}= +0.17701286 \pm 1 \cdot 10^{-8} a59=0.78692022±1108a_{59}= -0.78692022 \pm 1 \cdot 10^{-8} a60=0.07889694±1.6108a_{60}= -0.07889694 \pm 1.6 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000