Properties

Label 14.96
Level 1414
Weight 00
Character 14.1
Symmetry even
RR 13.72298
Fricke sign +1+1

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Maass form invariants

Level: 14=27 14 = 2 \cdot 7
Weight: 0 0
Character: 14.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 13.7229827041542024618797899614±510813.7229827041542024618797899614 \pm 5 \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=+0.70710678±1.0108a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} a3=+1.97406954±5.7107a_{3}= +1.97406954 \pm 5.7 \cdot 10^{-7}
a4=+0.5a_{4}= +0.5 a5=+0.99642243±8.6107a_{5}= +0.99642243 \pm 8.6 \cdot 10^{-7} a6=+1.39587796±5.8107a_{6}= +1.39587796 \pm 5.8 \cdot 10^{-7}
a7=+0.37796447±1.0108a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=+2.89695054±7.9107a_{9}= +2.89695054 \pm 7.9 \cdot 10^{-7}
a10=+0.70457706±8.7107a_{10}= +0.70457706 \pm 8.7 \cdot 10^{-7} a11=0.81746955±1.0106a_{11}= -0.81746955 \pm 1.0 \cdot 10^{-6} a12=+0.98703477±5.8107a_{12}= +0.98703477 \pm 5.8 \cdot 10^{-7}
a13=+0.08680522±7.3107a_{13}= +0.08680522 \pm 7.3 \cdot 10^{-7} a14=+0.26726124±1.0108a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} a15=+1.96700717±5.8107a_{15}= +1.96700717 \pm 5.8 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=1.26373710±9.4107a_{17}= -1.26373710 \pm 9.4 \cdot 10^{-7} a18=+2.04845337±8.0107a_{18}= +2.04845337 \pm 8.0 \cdot 10^{-7}
a19=+1.14289288±6.2107a_{19}= +1.14289288 \pm 6.2 \cdot 10^{-7} a20=+0.49821122±8.7107a_{20}= +0.49821122 \pm 8.7 \cdot 10^{-7} a21=+0.74612815±5.8107a_{21}= +0.74612815 \pm 5.8 \cdot 10^{-7}
a22=0.57803826±1.0106a_{22}= -0.57803826 \pm 1.0 \cdot 10^{-6} a23=+0.08959890±5.1107a_{23}= +0.08959890 \pm 5.1 \cdot 10^{-7} a24=+0.69793898±5.8107a_{24}= +0.69793898 \pm 5.8 \cdot 10^{-7}
a25=0.00714234±1.0106a_{25}= -0.00714234 \pm 1.0 \cdot 10^{-6} a26=+0.06138056±7.4107a_{26}= +0.06138056 \pm 7.4 \cdot 10^{-7} a27=+3.74471228±6.2107a_{27}= +3.74471228 \pm 6.2 \cdot 10^{-7}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=0.32649023±7.8107a_{29}= -0.32649023 \pm 7.8 \cdot 10^{-7} a30=+1.39088411±1.4106a_{30}= +1.39088411 \pm 1.4 \cdot 10^{-6}
a31=+0.07066552±9.1107a_{31}= +0.07066552 \pm 9.1 \cdot 10^{-7} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.61374173±5.3107a_{33}= -1.61374173 \pm 5.3 \cdot 10^{-7}
a34=0.89359707±9.5107a_{34}= -0.89359707 \pm 9.5 \cdot 10^{-7} a35=+0.37661228±8.7107a_{35}= +0.37661228 \pm 8.7 \cdot 10^{-7} a36=+1.44847527±8.0107a_{36}= +1.44847527 \pm 8.0 \cdot 10^{-7}
a37=1.16605999±3.9107a_{37}= -1.16605999 \pm 3.9 \cdot 10^{-7} a38=+0.80814731±6.3107a_{38}= +0.80814731 \pm 6.3 \cdot 10^{-7} a39=+0.17135954±8.1107a_{39}= +0.17135954 \pm 8.1 \cdot 10^{-7}
a40=+0.35228853±8.7107a_{40}= +0.35228853 \pm 8.7 \cdot 10^{-7} a41=1.71470670±8.2107a_{41}= -1.71470670 \pm 8.2 \cdot 10^{-7} a42=+0.52759228±5.8107a_{42}= +0.52759228 \pm 5.8 \cdot 10^{-7}
a43=1.60534037±5.8107a_{43}= -1.60534037 \pm 5.8 \cdot 10^{-7} a44=0.40873477±1.0106a_{44}= -0.40873477 \pm 1.0 \cdot 10^{-6} a45=+2.88658651±8.7107a_{45}= +2.88658651 \pm 8.7 \cdot 10^{-7}
a46=+0.06335599±5.2107a_{46}= +0.06335599 \pm 5.2 \cdot 10^{-7} a47=+0.26777542±6.9107a_{47}= +0.26777542 \pm 6.9 \cdot 10^{-7} a48=+0.49351738±5.8107a_{48}= +0.49351738 \pm 5.8 \cdot 10^{-7}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.00505039±1.0106a_{50}= -0.00505039 \pm 1.0 \cdot 10^{-6} a51=2.49470491±4.7107a_{51}= -2.49470491 \pm 4.7 \cdot 10^{-7}
a52=+0.04340261±7.4107a_{52}= +0.04340261 \pm 7.4 \cdot 10^{-7} a53=+0.91881566±9.2107a_{53}= +0.91881566 \pm 9.2 \cdot 10^{-7} a54=+2.64791145±6.3107a_{54}= +2.64791145 \pm 6.3 \cdot 10^{-7}
a55=0.81454499±9.1107a_{55}= -0.81454499 \pm 9.1 \cdot 10^{-7} a56=+0.13363062±1.6107a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} a57=+2.25615002±5.3107a_{57}= +2.25615002 \pm 5.3 \cdot 10^{-7}
a58=0.23086346±7.9107a_{58}= -0.23086346 \pm 7.9 \cdot 10^{-7} a59=+0.95545462±7.3107a_{59}= +0.95545462 \pm 7.3 \cdot 10^{-7} a60=+0.98350359±1.4106a_{60}= +0.98350359 \pm 1.4 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000