Properties

Label 14.46
Level 1414
Weight 00
Character 14.1
Symmetry odd
RR 9.615741
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: odd
Fricke sign: 1-1
Spectral parameter: 9.6157410480843738310823441407±310109.6157410480843738310823441407 \pm 3 \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=+0.70710678±1.0108a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} a3=+1.71232722±9.7107a_{3}= +1.71232722 \pm 9.7 \cdot 10^{-7}
a4=+0.5a_{4}= +0.5 a5=+1.15974547±7.4107a_{5}= +1.15974547 \pm 7.4 \cdot 10^{-7} a6=+1.21079819±9.8107a_{6}= +1.21079819 \pm 9.8 \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=+1.93206450±7.6107a_{9}= +1.93206450 \pm 7.6 \cdot 10^{-7}
a10=+0.82006389±7.6107a_{10}= +0.82006389 \pm 7.6 \cdot 10^{-7} a11=+1.49733547±7.6107a_{11}= +1.49733547 \pm 7.6 \cdot 10^{-7} a12=+0.85616361±9.8107a_{12}= +0.85616361 \pm 9.8 \cdot 10^{-7}
a13=1.23443747±7.2107a_{13}= -1.23443747 \pm 7.2 \cdot 10^{-7} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=+1.98586373±9.2107a_{15}= +1.98586373 \pm 9.2 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=1.57020896±4.9107a_{17}= -1.57020896 \pm 4.9 \cdot 10^{-7} a18=+1.36617591±7.7107a_{18}= +1.36617591 \pm 7.7 \cdot 10^{-7}
a19=0.80781892±7.4107a_{19}= -0.80781892 \pm 7.4 \cdot 10^{-7} a20=+0.57987273±7.6107a_{20}= +0.57987273 \pm 7.6 \cdot 10^{-7} a21=0.64719885±9.8107a_{21}= -0.64719885 \pm 9.8 \cdot 10^{-7}
a22=+1.05877607±7.8107a_{22}= +1.05877607 \pm 7.8 \cdot 10^{-7} a23=+0.78026450±6.8107a_{23}= +0.78026450 \pm 6.8 \cdot 10^{-7} a24=+0.60539909±9.8107a_{24}= +0.60539909 \pm 9.8 \cdot 10^{-7}
a25=+0.34500955±5.8107a_{25}= +0.34500955 \pm 5.8 \cdot 10^{-7} a26=0.87287911±7.3107a_{26}= -0.87287911 \pm 7.3 \cdot 10^{-7} a27=+1.59599941±7.1107a_{27}= +1.59599941 \pm 7.1 \cdot 10^{-7}
a28=0.18898224±9.4108a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} a29=0.34000398±8.3107a_{29}= -0.34000398 \pm 8.3 \cdot 10^{-7} a30=+1.40421771±1.7106a_{30}= +1.40421771 \pm 1.7 \cdot 10^{-6}
a31=+0.32143315±8.2107a_{31}= +0.32143315 \pm 8.2 \cdot 10^{-7} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+2.56392829±9.1107a_{33}= +2.56392829 \pm 9.1 \cdot 10^{-7}
a34=1.11030540±5.0107a_{34}= -1.11030540 \pm 5.0 \cdot 10^{-7} a35=0.43834259±7.6107a_{35}= -0.43834259 \pm 7.6 \cdot 10^{-7} a36=+0.96603225±7.7107a_{36}= +0.96603225 \pm 7.7 \cdot 10^{-7}
a37=+0.70479254±5.9107a_{37}= +0.70479254 \pm 5.9 \cdot 10^{-7} a38=0.57121424±7.5107a_{38}= -0.57121424 \pm 7.5 \cdot 10^{-7} a39=2.11376088±8.3107a_{39}= -2.11376088 \pm 8.3 \cdot 10^{-7}
a40=+0.41003194±7.6107a_{40}= +0.41003194 \pm 7.6 \cdot 10^{-7} a41=0.46993306±4.8107a_{41}= -0.46993306 \pm 4.8 \cdot 10^{-7} a42=0.45763870±9.8107a_{42}= -0.45763870 \pm 9.8 \cdot 10^{-7}
a43=+0.94981999±7.5107a_{43}= +0.94981999 \pm 7.5 \cdot 10^{-7} a44=+0.74866774±7.8107a_{44}= +0.74866774 \pm 7.8 \cdot 10^{-7} a45=+2.24070305±6.6107a_{45}= +2.24070305 \pm 6.6 \cdot 10^{-7}
a46=+0.55173032±6.9107a_{46}= +0.55173032 \pm 6.9 \cdot 10^{-7} a47=0.44431620±5.4107a_{47}= -0.44431620 \pm 5.4 \cdot 10^{-7} a48=+0.42808180±9.8107a_{48}= +0.42808180 \pm 9.8 \cdot 10^{-7}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.24395860±5.9107a_{50}= +0.24395860 \pm 5.9 \cdot 10^{-7} a51=2.68871153±5.8107a_{51}= -2.68871153 \pm 5.8 \cdot 10^{-7}
a52=0.61721873±7.3107a_{52}= -0.61721873 \pm 7.3 \cdot 10^{-7} a53=0.32805540±7.2107a_{53}= -0.32805540 \pm 7.2 \cdot 10^{-7} a54=+1.12854200±7.2107a_{54}= +1.12854200 \pm 7.2 \cdot 10^{-7}
a55=+1.73652803±7.1107a_{55}= +1.73652803 \pm 7.1 \cdot 10^{-7} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=1.38325033±1.0106a_{57}= -1.38325033 \pm 1.0 \cdot 10^{-6}
a58=0.24041912±8.4107a_{58}= -0.24041912 \pm 8.4 \cdot 10^{-7} a59=0.16073985±7.8107a_{59}= -0.16073985 \pm 7.8 \cdot 10^{-7} a60=+0.99293187±1.7106a_{60}= +0.99293187 \pm 1.7 \cdot 10^{-6}

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