Properties

Label 2.19
Level 22
Weight 00
Character 2.1
Symmetry odd
RR 17.49311
Fricke sign +1+1

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Maass form invariants

Level: 2 2
Weight: 0 0
Character: 2.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 17.4931127226685992093991119089±510617.4931127226685992093991119089 \pm 5 \cdot 10^{-6}

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}= -0.70710678 \pm 1.0 \cdot 10^{-8} a3=1.68121955±6.5104a_{3}= -1.68121955 \pm 6.5 \cdot 10^{-4}
a4=+0.5a_{4}= +0.5 a5=+0.81602816±4.7104a_{5}= +0.81602816 \pm 4.7 \cdot 10^{-4} a6=+1.18880175±6.5104a_{6}= +1.18880175 \pm 6.5 \cdot 10^{-4}
a7=+0.33076893±5.4104a_{7}= +0.33076893 \pm 5.4 \cdot 10^{-4} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=+1.82649919±1.1103a_{9}= +1.82649919 \pm 1.1 \cdot 10^{-3}
a10=0.57701904±4.7104a_{10}= -0.57701904 \pm 4.7 \cdot 10^{-4} a11=+0.79862660±1.5103a_{11}= +0.79862660 \pm 1.5 \cdot 10^{-3} a12=0.84060978±6.5104a_{12}= -0.84060978 \pm 6.5 \cdot 10^{-4}
a13=1.41850327±1.2103a_{13}= -1.41850327 \pm 1.2 \cdot 10^{-3} a14=0.23388895±5.4104a_{14}= -0.23388895 \pm 5.4 \cdot 10^{-4} a15=1.37192250±3.5104a_{15}= -1.37192250 \pm 3.5 \cdot 10^{-4}
a16=+0.25a_{16}= +0.25 a17=0.48398811±9.0104a_{17}= -0.48398811 \pm 9.0 \cdot 10^{-4} a18=1.29152996±1.1103a_{18}= -1.29152996 \pm 1.1 \cdot 10^{-3}
a19=+0.79258632±6.4104a_{19}= +0.79258632 \pm 6.4 \cdot 10^{-4} a20=+0.40801408±4.7104a_{20}= +0.40801408 \pm 4.7 \cdot 10^{-4} a21=0.55609520±2.7104a_{21}= -0.55609520 \pm 2.7 \cdot 10^{-4}
a22=0.56471428±1.5103a_{22}= -0.56471428 \pm 1.5 \cdot 10^{-3} a23=+0.07303840±6.5104a_{23}= +0.07303840 \pm 6.5 \cdot 10^{-4} a24=+0.59440087±6.5104a_{24}= +0.59440087 \pm 6.5 \cdot 10^{-4}
a25=0.33409804±1.2103a_{25}= -0.33409804 \pm 1.2 \cdot 10^{-3} a26=+1.00303328±1.2103a_{26}= +1.00303328 \pm 1.2 \cdot 10^{-3} a27=1.38952659±1.0103a_{27}= -1.38952659 \pm 1.0 \cdot 10^{-3}
a28=+0.16538447±5.4104a_{28}= +0.16538447 \pm 5.4 \cdot 10^{-4} a29=0.41502370±1.1103a_{29}= -0.41502370 \pm 1.1 \cdot 10^{-3} a30=+0.97009570±1.1103a_{30}= +0.97009570 \pm 1.1 \cdot 10^{-3}
a31=+0.49763209±1.2103a_{31}= +0.49763209 \pm 1.2 \cdot 10^{-3} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.34266665±6.2104a_{33}= -1.34266665 \pm 6.2 \cdot 10^{-4}
a34=+0.34223128±9.0104a_{34}= +0.34223128 \pm 9.0 \cdot 10^{-4} a35=+0.26991676±1.3104a_{35}= +0.26991676 \pm 1.3 \cdot 10^{-4} a36=+0.91324959±1.1103a_{36}= +0.91324959 \pm 1.1 \cdot 10^{-3}
a37=1.21954370±1.6103a_{37}= -1.21954370 \pm 1.6 \cdot 10^{-3} a38=0.56044316±6.4104a_{38}= -0.56044316 \pm 6.4 \cdot 10^{-4} a39=+2.38481544±4.9104a_{39}= +2.38481544 \pm 4.9 \cdot 10^{-4}
a40=0.28850952±4.7104a_{40}= -0.28850952 \pm 4.7 \cdot 10^{-4} a41=1.86645137±1.6103a_{41}= -1.86645137 \pm 1.6 \cdot 10^{-3} a42=+0.39321868±1.1103a_{42}= +0.39321868 \pm 1.1 \cdot 10^{-3}
a43=0.58566433±3.7104a_{43}= -0.58566433 \pm 3.7 \cdot 10^{-4} a44=+0.39931330±1.5103a_{44}= +0.39931330 \pm 1.5 \cdot 10^{-3} a45=+1.49047477±2.8104a_{45}= +1.49047477 \pm 2.8 \cdot 10^{-4}
a46=0.05164594±6.5104a_{46}= -0.05164594 \pm 6.5 \cdot 10^{-4} a47=0.34943216±1.1103a_{47}= -0.34943216 \pm 1.1 \cdot 10^{-3} a48=0.42030489±6.5104a_{48}= -0.42030489 \pm 6.5 \cdot 10^{-4}
a49=0.89059191±1.1103a_{49}= -0.89059191 \pm 1.1 \cdot 10^{-3} a50=+0.23624299±1.2103a_{50}= +0.23624299 \pm 1.2 \cdot 10^{-3} a51=+0.81369028±6.7104a_{51}= +0.81369028 \pm 6.7 \cdot 10^{-4}
a52=0.70925164±1.2103a_{52}= -0.70925164 \pm 1.2 \cdot 10^{-3} a53=0.13143755±1.3103a_{53}= -0.13143755 \pm 1.3 \cdot 10^{-3} a54=+0.98254368±1.0103a_{54}= +0.98254368 \pm 1.0 \cdot 10^{-3}
a55=+0.65170179±3.9104a_{55}= +0.65170179 \pm 3.9 \cdot 10^{-4} a56=0.11694448±5.4104a_{56}= -0.11694448 \pm 5.4 \cdot 10^{-4} a57=1.33251162±5.5104a_{57}= -1.33251162 \pm 5.5 \cdot 10^{-4}
a58=+0.29346607±1.1103a_{58}= +0.29346607 \pm 1.1 \cdot 10^{-3} a59=0.38820915±1.1103a_{59}= -0.38820915 \pm 1.1 \cdot 10^{-3} a60=0.68596125±1.1103a_{60}= -0.68596125 \pm 1.1 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000