Properties

Label 14.10
Level 1414
Weight 00
Character 14.1
Symmetry even
RR 4.522084
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: 4.52208412028612686745489020782±1010124.52208412028612686745489020782 \pm 10 \cdot 10^{-12}

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=+1.32467011±1108a_{3}= +1.32467011 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.13167540±1108a_{5}= +0.13167540 \pm 1 \cdot 10^{-8} a6=+0.93668322±1.0108a_{6}= +0.93668322 \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=+0.75475091±1108a_{9}= +0.75475091 \pm 1 \cdot 10^{-8}
a10=+0.09310857±1.0108a_{10}= +0.09310857 \pm 1.0 \cdot 10^{-8} a11=+0.10577529±1108a_{11}= +0.10577529 \pm 1 \cdot 10^{-8} a12=+0.66233506±1.0108a_{12}= +0.66233506 \pm 1.0 \cdot 10^{-8}
a13=1.84479213±1108a_{13}= -1.84479213 \pm 1 \cdot 10^{-8} a14=+0.26726124±1.0108a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} a15=+0.17442647±1108a_{15}= +0.17442647 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.97938942±1108a_{17}= -0.97938942 \pm 1 \cdot 10^{-8} a18=+0.53368949±1.0108a_{18}= +0.53368949 \pm 1.0 \cdot 10^{-8}
a19=+1.65887722±1108a_{19}= +1.65887722 \pm 1 \cdot 10^{-8} a20=+0.06583770±1.0108a_{20}= +0.06583770 \pm 1.0 \cdot 10^{-8} a21=+0.50067824±1.0108a_{21}= +0.50067824 \pm 1.0 \cdot 10^{-8}
a22=+0.07479443±1.0108a_{22}= +0.07479443 \pm 1.0 \cdot 10^{-8} a23=0.93516861±1108a_{23}= -0.93516861 \pm 1 \cdot 10^{-8} a24=+0.46834161±1.0108a_{24}= +0.46834161 \pm 1.0 \cdot 10^{-8}
a25=0.98266159±1108a_{25}= -0.98266159 \pm 1 \cdot 10^{-8} a26=1.30446502±1.0108a_{26}= -1.30446502 \pm 1.0 \cdot 10^{-8} a27=0.32487414±1108a_{27}= -0.32487414 \pm 1 \cdot 10^{-8}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=+0.35132938±1108a_{29}= +0.35132938 \pm 1 \cdot 10^{-8} a30=+0.12333814±1.0108a_{30}= +0.12333814 \pm 1.0 \cdot 10^{-8}
a31=+1.24279344±1108a_{31}= +1.24279344 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.14011737±1108a_{33}= +0.14011737 \pm 1 \cdot 10^{-8}
a34=0.69253290±1.0108a_{34}= -0.69253290 \pm 1.0 \cdot 10^{-8} a35=+0.04976862±1.0108a_{35}= +0.04976862 \pm 1.0 \cdot 10^{-8} a36=+0.37737545±1.0108a_{36}= +0.37737545 \pm 1.0 \cdot 10^{-8}
a37=0.23292103±1108a_{37}= -0.23292103 \pm 1 \cdot 10^{-8} a38=+1.17300333±1.0108a_{38}= +1.17300333 \pm 1.0 \cdot 10^{-8} a39=2.44374100±1108a_{39}= -2.44374100 \pm 1 \cdot 10^{-8}
a40=+0.04655428±1.0108a_{40}= +0.04655428 \pm 1.0 \cdot 10^{-8} a41=+1.75198818±1108a_{41}= +1.75198818 \pm 1 \cdot 10^{-8} a42=+0.35403298±1.0108a_{42}= +0.35403298 \pm 1.0 \cdot 10^{-8}
a43=0.19939104±1108a_{43}= -0.19939104 \pm 1 \cdot 10^{-8} a44=+0.05288765±1.0108a_{44}= +0.05288765 \pm 1.0 \cdot 10^{-8} a45=+0.09938213±1108a_{45}= +0.09938213 \pm 1 \cdot 10^{-8}
a46=0.66126407±1.0108a_{46}= -0.66126407 \pm 1.0 \cdot 10^{-8} a47=+0.01862931±1108a_{47}= +0.01862931 \pm 1 \cdot 10^{-8} a48=+0.33116753±1.0108a_{48}= +0.33116753 \pm 1.0 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.69484667±1.0108a_{50}= -0.69484667 \pm 1.0 \cdot 10^{-8} a51=1.29736789±1108a_{51}= -1.29736789 \pm 1 \cdot 10^{-8}
a52=0.92239606±1.0108a_{52}= -0.92239606 \pm 1.0 \cdot 10^{-8} a53=+0.08272793±1108a_{53}= +0.08272793 \pm 1 \cdot 10^{-8} a54=0.22972071±1.0108a_{54}= -0.22972071 \pm 1.0 \cdot 10^{-8}
a55=+0.01392800±1108a_{55}= +0.01392800 \pm 1 \cdot 10^{-8} a56=+0.13363062±1.6107a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} a57=+2.19746508±1108a_{57}= +2.19746508 \pm 1 \cdot 10^{-8}
a58=+0.24842739±1.0108a_{58}= +0.24842739 \pm 1.0 \cdot 10^{-8} a59=+0.52927526±1108a_{59}= +0.52927526 \pm 1 \cdot 10^{-8} a60=+0.08721323±1.0108a_{60}= +0.08721323 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000