Properties

Label 14.61
Level 1414
Weight 00
Character 14.1
Symmetry odd
RR 11.11343
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: 11.1134306546693979915166355651±210911.1134306546693979915166355651 \pm 2 \cdot 10^{-9}

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=+1.66654851±1.2105a_{3}= +1.66654851 \pm 1.2 \cdot 10^{-5}
a4=+0.5a_{4}= +0.5 a5=+1.34901476±9.8106a_{5}= +1.34901476 \pm 9.8 \cdot 10^{-6} a6=1.17842775±1.2105a_{6}= -1.17842775 \pm 1.2 \cdot 10^{-5}
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=+1.77738393±9.9106a_{9}= +1.77738393 \pm 9.9 \cdot 10^{-6}
a10=0.95389749±9.8106a_{10}= -0.95389749 \pm 9.8 \cdot 10^{-6} a11=+1.67397663±1.0105a_{11}= +1.67397663 \pm 1.0 \cdot 10^{-5} a12=+0.83327425±1.2105a_{12}= +0.83327425 \pm 1.2 \cdot 10^{-5}
a13=+0.78093275±9.4106a_{13}= +0.78093275 \pm 9.4 \cdot 10^{-6} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=+2.24819854±1.2105a_{15}= +2.24819854 \pm 1.2 \cdot 10^{-5}
a16=+0.25a_{16}= +0.25 a17=+0.00113081±6.5106a_{17}= +0.00113081 \pm 6.5 \cdot 10^{-6} a18=1.25680023±9.9106a_{18}= -1.25680023 \pm 9.9 \cdot 10^{-6}
a19=1.07438278±9.7106a_{19}= -1.07438278 \pm 9.7 \cdot 10^{-6} a20=+0.67450738±9.8106a_{20}= +0.67450738 \pm 9.8 \cdot 10^{-6} a21=+0.62989613±1.2105a_{21}= +0.62989613 \pm 1.2 \cdot 10^{-5}
a22=1.18368023±1.0105a_{22}= -1.18368023 \pm 1.0 \cdot 10^{-5} a23=1.05654566±8.9106a_{23}= -1.05654566 \pm 8.9 \cdot 10^{-6} a24=0.58921388±1.2105a_{24}= -0.58921388 \pm 1.2 \cdot 10^{-5}
a25=+0.81984083±7.6106a_{25}= +0.81984083 \pm 7.6 \cdot 10^{-6} a26=0.55220284±9.4106a_{26}= -0.55220284 \pm 9.4 \cdot 10^{-6} a27=+1.29554802±9.3106a_{27}= +1.29554802 \pm 9.3 \cdot 10^{-6}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=1.30218890±1.0105a_{29}= -1.30218890 \pm 1.0 \cdot 10^{-5} a30=1.58971643±2.2105a_{30}= -1.58971643 \pm 2.2 \cdot 10^{-5}
a31=+0.62470357±1.0105a_{31}= +0.62470357 \pm 1.0 \cdot 10^{-5} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=+2.78976326±1.1105a_{33}= +2.78976326 \pm 1.1 \cdot 10^{-5}
a34=0.00079960±6.5106a_{34}= -0.00079960 \pm 6.5 \cdot 10^{-6} a35=+0.50987965±9.8106a_{35}= +0.50987965 \pm 9.8 \cdot 10^{-6} a36=+0.88869196±9.9106a_{36}= +0.88869196 \pm 9.9 \cdot 10^{-6}
a37=+0.48026224±7.7106a_{37}= +0.48026224 \pm 7.7 \cdot 10^{-6} a38=+0.75970335±9.7106a_{38}= +0.75970335 \pm 9.7 \cdot 10^{-6} a39=+1.30146231±1.0105a_{39}= +1.30146231 \pm 1.0 \cdot 10^{-5}
a40=0.47694874±9.8106a_{40}= -0.47694874 \pm 9.8 \cdot 10^{-6} a41=1.27324812±6.3106a_{41}= -1.27324812 \pm 6.3 \cdot 10^{-6} a42=0.44540382±1.2105a_{42}= -0.44540382 \pm 1.2 \cdot 10^{-5}
a43=1.25735185±9.9106a_{43}= -1.25735185 \pm 9.9 \cdot 10^{-6} a44=+0.83698832±1.0105a_{44}= +0.83698832 \pm 1.0 \cdot 10^{-5} a45=+2.39771716±8.7106a_{45}= +2.39771716 \pm 8.7 \cdot 10^{-6}
a46=+0.74709060±8.9106a_{46}= +0.74709060 \pm 8.9 \cdot 10^{-6} a47=+0.12459623±7.1106a_{47}= +0.12459623 \pm 7.1 \cdot 10^{-6} a48=+0.41663713±1.2105a_{48}= +0.41663713 \pm 1.2 \cdot 10^{-5}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.57971501±7.6106a_{50}= -0.57971501 \pm 7.6 \cdot 10^{-6} a51=+0.00188455±7.6106a_{51}= +0.00188455 \pm 7.6 \cdot 10^{-6}
a52=+0.39046637±9.4106a_{52}= +0.39046637 \pm 9.4 \cdot 10^{-6} a53=0.52923718±9.5106a_{53}= -0.52923718 \pm 9.5 \cdot 10^{-6} a54=0.91609079±9.3106a_{54}= -0.91609079 \pm 9.3 \cdot 10^{-6}
a55=+2.25821919±9.3106a_{55}= +2.25821919 \pm 9.3 \cdot 10^{-6} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=1.79051102±1.3105a_{57}= -1.79051102 \pm 1.3 \cdot 10^{-5}
a58=+0.92078660±1.0105a_{58}= +0.92078660 \pm 1.0 \cdot 10^{-5} a59=+1.35801779±1.0105a_{59}= +1.35801779 \pm 1.0 \cdot 10^{-5} a60=+1.12409927±2.2105a_{60}= +1.12409927 \pm 2.2 \cdot 10^{-5}

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