Properties

Label 5.31
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 11.15393
Fricke sign +1+1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 11.1539349347579065694605247753±2101011.1539349347579065694605247753 \pm 2 \cdot 10^{-10}

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=+1.48828655±2.3107a_{2}= +1.48828655 \pm 2.3 \cdot 10^{-7} a3=0.69640225±2.5107a_{3}= -0.69640225 \pm 2.5 \cdot 10^{-7}
a4=+1.21499686±2.0107a_{4}= +1.21499686 \pm 2.0 \cdot 10^{-7} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=1.03644610±2.3107a_{6}= -1.03644610 \pm 2.3 \cdot 10^{-7}
a7=0.71279555±9.6108a_{7}= -0.71279555 \pm 9.6 \cdot 10^{-8} a8=+0.31997694±2.1107a_{8}= +0.31997694 \pm 2.1 \cdot 10^{-7} a9=0.51502391±1.2107a_{9}= -0.51502391 \pm 1.2 \cdot 10^{-7}
a10=0.66558198±2.4107a_{10}= -0.66558198 \pm 2.4 \cdot 10^{-7} a11=+0.51774918±1.2107a_{11}= +0.51774918 \pm 1.2 \cdot 10^{-7} a12=0.84612655±2.1107a_{12}= -0.84612655 \pm 2.1 \cdot 10^{-7}
a13=1.48686381±1.6107a_{13}= -1.48686381 \pm 1.6 \cdot 10^{-7} a14=1.06084404±9.8108a_{14}= -1.06084404 \pm 9.8 \cdot 10^{-8} a15=+0.31144055±2.6107a_{15}= +0.31144055 \pm 2.6 \cdot 10^{-7}
a16=0.73877948±1.0107a_{16}= -0.73877948 \pm 1.0 \cdot 10^{-7} a17=+1.13353925±2.5107a_{17}= +1.13353925 \pm 2.5 \cdot 10^{-7} a18=0.76650316±1.0107a_{18}= -0.76650316 \pm 1.0 \cdot 10^{-7}
a19=1.63881495±2.3107a_{19}= -1.63881495 \pm 2.3 \cdot 10^{-7} a20=0.54336312±2.1107a_{20}= -0.54336312 \pm 2.1 \cdot 10^{-7} a21=+0.49639242±1.0107a_{21}= +0.49639242 \pm 1.0 \cdot 10^{-7}
a22=+0.77055915±1.3107a_{22}= +0.77055915 \pm 1.3 \cdot 10^{-7} a23=+0.60856473±1.0107a_{23}= +0.60856473 \pm 1.0 \cdot 10^{-7} a24=0.22283266±2.2107a_{24}= -0.22283266 \pm 2.2 \cdot 10^{-7}
a25=+0.2a_{25}= +0.2 a26=2.21287941±1.9107a_{26}= -2.21287941 \pm 1.9 \cdot 10^{-7} a27=+1.05506606±1.9107a_{27}= +1.05506606 \pm 1.9 \cdot 10^{-7}
a28=0.86604436±7.9108a_{28}= -0.86604436 \pm 7.9 \cdot 10^{-8} a29=+1.22542299±1.1107a_{29}= +1.22542299 \pm 1.1 \cdot 10^{-7} a30=+0.46351279±4.9107a_{30}= +0.46351279 \pm 4.9 \cdot 10^{-7}
a31=+0.05438510±2.4107a_{31}= +0.05438510 \pm 2.4 \cdot 10^{-7} a32=1.41949251±2.5107a_{32}= -1.41949251 \pm 2.5 \cdot 10^{-7} a33=0.36056169±9.3108a_{33}= -0.36056169 \pm 9.3 \cdot 10^{-8}
a34=+1.68703123±2.4107a_{34}= +1.68703123 \pm 2.4 \cdot 10^{-7} a35=+0.31877186±1.0107a_{35}= +0.31877186 \pm 1.0 \cdot 10^{-7} a36=0.62575244±5.7108a_{36}= -0.62575244 \pm 5.7 \cdot 10^{-8}
a37=+0.87246569±3.0107a_{37}= +0.87246569 \pm 3.0 \cdot 10^{-7} a38=2.43902625±1.6107a_{38}= -2.43902625 \pm 1.6 \cdot 10^{-7} a39=+1.03545530±1.3107a_{39}= +1.03545530 \pm 1.3 \cdot 10^{-7}
a40=0.14309804±2.2107a_{40}= -0.14309804 \pm 2.2 \cdot 10^{-7} a41=0.12814554±2.6107a_{41}= -0.12814554 \pm 2.6 \cdot 10^{-7} a42=+0.73877417±1.0107a_{42}= +0.73877417 \pm 1.0 \cdot 10^{-7}
a43=1.16468558±2.6107a_{43}= -1.16468558 \pm 2.6 \cdot 10^{-7} a44=+0.62906363±9.8108a_{44}= +0.62906363 \pm 9.8 \cdot 10^{-8} a45=+0.23032569±1.3107a_{45}= +0.23032569 \pm 1.3 \cdot 10^{-7}
a46=+0.90571871±1.2107a_{46}= +0.90571871 \pm 1.2 \cdot 10^{-7} a47=0.13919694±1.5107a_{47}= -0.13919694 \pm 1.5 \cdot 10^{-7} a48=+0.51448769±1.0107a_{48}= +0.51448769 \pm 1.0 \cdot 10^{-7}
a49=0.49192250±2.1107a_{49}= -0.49192250 \pm 2.1 \cdot 10^{-7} a50=+0.29765731±2.4107a_{50}= +0.29765731 \pm 2.4 \cdot 10^{-7} a51=0.78939928±2.5107a_{51}= -0.78939928 \pm 2.5 \cdot 10^{-7}
a52=1.80653486±1.5107a_{52}= -1.80653486 \pm 1.5 \cdot 10^{-7} a53=0.73622937±2.4107a_{53}= -0.73622937 \pm 2.4 \cdot 10^{-7} a54=+1.57024062±1.9107a_{54}= +1.57024062 \pm 1.9 \cdot 10^{-7}
a55=0.23154447±1.3107a_{55}= -0.23154447 \pm 1.3 \cdot 10^{-7} a56=0.22807814±8.4108a_{56}= -0.22807814 \pm 8.4 \cdot 10^{-8} a57=+1.14127441±2.7107a_{57}= +1.14127441 \pm 2.7 \cdot 10^{-7}
a58=+1.82378056±9.1108a_{58}= +1.82378056 \pm 9.1 \cdot 10^{-8} a59=0.06746689±1.9107a_{59}= -0.06746689 \pm 1.9 \cdot 10^{-7} a60=+0.37839930±4.6107a_{60}= +0.37839930 \pm 4.6 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000