Properties

Label 14.39
Level 1414
Weight 00
Character 14.1
Symmetry even
RR 8.962464
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: 8.96246431384067503947859676439±210108.96246431384067503947859676439 \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=+0.70710678±1.0108a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} a3=+1.82356591±1108a_{3}= +1.82356591 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=1.35541637±1108a_{5}= -1.35541637 \pm 1 \cdot 10^{-8} a6=+1.28945582±1.0108a_{6}= +1.28945582 \pm 1.0 \cdot 10^{-8}
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=+2.32539263±1108a_{9}= +2.32539263 \pm 1 \cdot 10^{-8}
a10=0.95842411±1.1108a_{10}= -0.95842411 \pm 1.1 \cdot 10^{-8} a11=+1.26202172±1108a_{11}= +1.26202172 \pm 1 \cdot 10^{-8} a12=+0.91178296±1.0108a_{12}= +0.91178296 \pm 1.0 \cdot 10^{-8}
a13=+0.24183677±1108a_{13}= +0.24183677 \pm 1 \cdot 10^{-8} a14=+0.26726124±1.0108a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} a15=2.47169109±1108a_{15}= -2.47169109 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.96456120±1108a_{17}= +0.96456120 \pm 1 \cdot 10^{-8} a18=+1.64430090±1.1108a_{18}= +1.64430090 \pm 1.1 \cdot 10^{-8}
a19=+0.83672995±1108a_{19}= +0.83672995 \pm 1 \cdot 10^{-8} a20=0.67770819±1.1108a_{20}= -0.67770819 \pm 1.1 \cdot 10^{-8} a21=+0.68924313±1.0108a_{21}= +0.68924313 \pm 1.0 \cdot 10^{-8}
a22=+0.89238412±1.1108a_{22}= +0.89238412 \pm 1.1 \cdot 10^{-8} a23=1.17867796±1108a_{23}= -1.17867796 \pm 1 \cdot 10^{-8} a24=+0.64472791±1.0108a_{24}= +0.64472791 \pm 1.0 \cdot 10^{-8}
a25=+0.83715354±1108a_{25}= +0.83715354 \pm 1 \cdot 10^{-8} a26=+0.17100442±1.1108a_{26}= +0.17100442 \pm 1.1 \cdot 10^{-8} a27=+2.41694083±1108a_{27}= +2.41694083 \pm 1 \cdot 10^{-8}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=0.18256218±1108a_{29}= -0.18256218 \pm 1 \cdot 10^{-8} a30=1.74774953±1.1108a_{30}= -1.74774953 \pm 1.1 \cdot 10^{-8}
a31=0.95866357±1108a_{31}= -0.95866357 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+2.30137979±1108a_{33}= +2.30137979 \pm 1 \cdot 10^{-8}
a34=+0.68204777±1.1108a_{34}= +0.68204777 \pm 1.1 \cdot 10^{-8} a35=0.51229923±1.1108a_{35}= -0.51229923 \pm 1.1 \cdot 10^{-8} a36=+1.16269632±1.1108a_{36}= +1.16269632 \pm 1.1 \cdot 10^{-8}
a37=0.42418212±1108a_{37}= -0.42418212 \pm 1 \cdot 10^{-8} a38=+0.59165742±1.0108a_{38}= +0.59165742 \pm 1.0 \cdot 10^{-8} a39=+0.44100529±1108a_{39}= +0.44100529 \pm 1 \cdot 10^{-8}
a40=0.47921205±1.1108a_{40}= -0.47921205 \pm 1.1 \cdot 10^{-8} a41=0.48278922±1108a_{41}= -0.48278922 \pm 1 \cdot 10^{-8} a42=+0.48736849±1.0108a_{42}= +0.48736849 \pm 1.0 \cdot 10^{-8}
a43=0.20323361±1108a_{43}= -0.20323361 \pm 1 \cdot 10^{-8} a44=+0.63101086±1.1108a_{44}= +0.63101086 \pm 1.1 \cdot 10^{-8} a45=3.15187525±1108a_{45}= -3.15187525 \pm 1 \cdot 10^{-8}
a46=0.83345118±1.0108a_{46}= -0.83345118 \pm 1.0 \cdot 10^{-8} a47=+1.27766073±1108a_{47}= +1.27766073 \pm 1 \cdot 10^{-8} a48=+0.45589148±1.0108a_{48}= +0.45589148 \pm 1.0 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.59195694±1.1108a_{50}= +0.59195694 \pm 1.1 \cdot 10^{-8} a51=+1.75894092±1108a_{51}= +1.75894092 \pm 1 \cdot 10^{-8}
a52=+0.12091838±1.1108a_{52}= +0.12091838 \pm 1.1 \cdot 10^{-8} a53=1.43645387±1108a_{53}= -1.43645387 \pm 1 \cdot 10^{-8} a54=+1.70903525±1.0108a_{54}= +1.70903525 \pm 1.0 \cdot 10^{-8}
a55=1.71056490±1108a_{55}= -1.71056490 \pm 1 \cdot 10^{-8} a56=+0.13363062±1.6107a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} a57=+1.52583222±1108a_{57}= +1.52583222 \pm 1 \cdot 10^{-8}
a58=0.12909096±1.1108a_{58}= -0.12909096 \pm 1.1 \cdot 10^{-8} a59=+0.32723311±1108a_{59}= +0.32723311 \pm 1 \cdot 10^{-8} a60=1.23584555±1.1108a_{60}= -1.23584555 \pm 1.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000