Properties

Label 14.23
Level 1414
Weight 00
Character 14.1
Symmetry even
RR 6.755298
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: 6.75529844582064249219773781201±410116.75529844582064249219773781201 \pm 4 \cdot 10^{-11}

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=0.82627355±1108a_{3}= -0.82627355 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.64804579±1108a_{5}= +0.64804579 \pm 1 \cdot 10^{-8} a6=0.58426363±1.2108a_{6}= -0.58426363 \pm 1.2 \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=0.31727203±1108a_{9}= -0.31727203 \pm 1 \cdot 10^{-8}
a10=+0.45823758±1.3108a_{10}= +0.45823758 \pm 1.3 \cdot 10^{-8} a11=1.05702564±1108a_{11}= -1.05702564 \pm 1 \cdot 10^{-8} a12=0.41313677±1.2108a_{12}= -0.41313677 \pm 1.2 \cdot 10^{-8}
a13=1.66353822±1108a_{13}= -1.66353822 \pm 1 \cdot 10^{-8} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=0.53546310±1108a_{15}= -0.53546310 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.00373705±1108a_{17}= -0.00373705 \pm 1 \cdot 10^{-8} a18=0.22434520±1.2108a_{18}= -0.22434520 \pm 1.2 \cdot 10^{-8}
a19=0.54407171±1108a_{19}= -0.54407171 \pm 1 \cdot 10^{-8} a20=+0.32402290±1.3108a_{20}= +0.32402290 \pm 1.3 \cdot 10^{-8} a21=+0.31230205±1.2108a_{21}= +0.31230205 \pm 1.2 \cdot 10^{-8}
a22=0.74743000±1.3108a_{22}= -0.74743000 \pm 1.3 \cdot 10^{-8} a23=+0.53665100±1108a_{23}= +0.53665100 \pm 1 \cdot 10^{-8} a24=0.29213181±1.2108a_{24}= -0.29213181 \pm 1.2 \cdot 10^{-8}
a25=0.58003665±1108a_{25}= -0.58003665 \pm 1 \cdot 10^{-8} a26=1.17629915±1.2108a_{26}= -1.17629915 \pm 1.2 \cdot 10^{-8} a27=+1.08842703±1108a_{27}= +1.08842703 \pm 1 \cdot 10^{-8}
a28=0.18898224±9.4108a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} a29=0.93854623±1108a_{29}= -0.93854623 \pm 1 \cdot 10^{-8} a30=0.37862959±1.4108a_{30}= -0.37862959 \pm 1.4 \cdot 10^{-8}
a31=+1.34296159±1108a_{31}= +1.34296159 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.87339233±1108a_{33}= +0.87339233 \pm 1 \cdot 10^{-8}
a34=0.00264249±1.3108a_{34}= -0.00264249 \pm 1.3 \cdot 10^{-8} a35=0.24493829±1.3108a_{35}= -0.24493829 \pm 1.3 \cdot 10^{-8} a36=0.15863601±1.2108a_{36}= -0.15863601 \pm 1.2 \cdot 10^{-8}
a37=0.94842185±1108a_{37}= -0.94842185 \pm 1 \cdot 10^{-8} a38=0.38471680±1.2108a_{38}= -0.38471680 \pm 1.2 \cdot 10^{-8} a39=+1.37453762±1108a_{39}= +1.37453762 \pm 1 \cdot 10^{-8}
a40=+0.22911879±1.3108a_{40}= +0.22911879 \pm 1.3 \cdot 10^{-8} a41=+0.01677296±1108a_{41}= +0.01677296 \pm 1 \cdot 10^{-8} a42=+0.22083089±1.2108a_{42}= +0.22083089 \pm 1.2 \cdot 10^{-8}
a43=1.03326708±1108a_{43}= -1.03326708 \pm 1 \cdot 10^{-8} a44=0.52851282±1.3108a_{44}= -0.52851282 \pm 1.3 \cdot 10^{-8} a45=0.20560680±1108a_{45}= -0.20560680 \pm 1 \cdot 10^{-8}
a46=+0.37946956±1.1108a_{46}= +0.37946956 \pm 1.1 \cdot 10^{-8} a47=0.11274862±1108a_{47}= -0.11274862 \pm 1 \cdot 10^{-8} a48=0.20656839±1.2108a_{48}= -0.20656839 \pm 1.2 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.41014785±1.3108a_{50}= -0.41014785 \pm 1.3 \cdot 10^{-8} a51=+0.00308782±1108a_{51}= +0.00308782 \pm 1 \cdot 10^{-8}
a52=0.83176911±1.2108a_{52}= -0.83176911 \pm 1.2 \cdot 10^{-8} a53=+1.56919839±1108a_{53}= +1.56919839 \pm 1 \cdot 10^{-8} a54=+0.76963413±1.2108a_{54}= +0.76963413 \pm 1.2 \cdot 10^{-8}
a55=0.68500102±1108a_{55}= -0.68500102 \pm 1 \cdot 10^{-8} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=+0.44955206±1108a_{57}= +0.44955206 \pm 1 \cdot 10^{-8}
a58=0.66365241±1.2108a_{58}= -0.66365241 \pm 1.2 \cdot 10^{-8} a59=+1.81293420±1108a_{59}= +1.81293420 \pm 1 \cdot 10^{-8} a60=0.26773155±1.4108a_{60}= -0.26773155 \pm 1.4 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000