Properties

Level $743$
Weight $0$
Character 743.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 743 \)
Weight: \( 0 \)
Character: 743.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.44914347334 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.436956263\) \(a_{3}=+0.940620155\) \(a_{4}=+1.064842932\) \(a_{5}=-0.639232395\)
\(a_{6}=-1.351629875\) \(a_{7}=+1.325900693\) \(a_{8}=-0.093176512\) \(a_{9}=-0.115233691\) \(a_{10}=+0.918548973\)
\(a_{11}=+0.591067352\) \(a_{12}=+1.001612885\) \(a_{13}=-1.711379798\) \(a_{14}=-1.905261205\) \(a_{15}=-0.601275007\)
\(a_{16}=-0.930952489\) \(a_{17}=+1.000022404\) \(a_{18}=+0.165585821\) \(a_{19}=+0.435606349\) \(a_{20}=-0.680682086\)
\(a_{21}=+1.247168993\) \(a_{22}=-0.849337759\) \(a_{23}=+1.564899384\) \(a_{24}=-0.087643767\) \(a_{25}=-0.591381772\)
\(a_{26}=+2.459177790\) \(a_{27}=-1.049011279\) \(a_{28}=+1.411875973\) \(a_{29}=-1.212777543\) \(a_{30}=+0.864005687\)
\(a_{31}=-0.292332989\) \(a_{32}=+1.430914352\) \(a_{33}=+0.555969948\) \(a_{34}=-1.436988387\) \(a_{35}=-0.847558713\)
\(a_{36}=-0.122705697\) \(a_{37}=+0.901029103\) \(a_{38}=-0.625947153\) \(a_{39}=-1.609758450\) \(a_{40}=+0.059561538\)
\(a_{41}=+0.993390859\) \(a_{42}=-1.792127123\) \(a_{43}=-1.379991681\) \(a_{44}=+0.629393797\) \(a_{45}=+0.073661010\)
\(a_{46}=-2.248691762\) \(a_{47}=-0.190338953\) \(a_{48}=-0.875672621\) \(a_{49}=+0.758012578\) \(a_{50}=+0.849789647\)
\(a_{51}=+0.940641197\) \(a_{52}=-1.822350687\) \(a_{53}=+1.461695709\) \(a_{54}=+1.507383210\) \(a_{55}=-0.377829353\)
\(a_{56}=-0.123542731\) \(a_{57}=+0.409739955\) \(a_{58}=+1.742707890\) \(a_{59}=-1.113335344\) \(a_{60}=-0.640263348\)
\(a_{61}=-0.984973673\) \(a_{62}=+0.420069674\) \(a_{63}=-0.152788387\) \(a_{64}=-1.125208645\) \(a_{65}=+1.093969531\)
\(a_{66}=-0.798904243\) \(a_{67}=-0.669116648\) \(a_{68}=+1.064866892\) \(a_{69}=+1.471975828\) \(a_{70}=+1.217904792\)
\(a_{71}=-0.724641919\) \(a_{72}=+0.010737023\) \(a_{73}=-0.405036178\) \(a_{74}=-1.294739293\) \(a_{75}=-0.556265660\)
\(a_{76}=+0.463852280\) \(a_{77}=+0.783696604\) \(a_{78}=+2.313152114\) \(a_{79}=-0.581434706\) \(a_{80}=+0.595094953\)
\(a_{81}=-0.871487436\) \(a_{82}=-1.427459069\) \(a_{83}=+0.793955857\) \(a_{84}=+1.328039063\) \(a_{85}=-0.639246875\)
\(a_{86}=+1.982987539\) \(a_{87}=-1.140762951\) \(a_{88}=-0.055073562\) \(a_{89}=-1.028115205\) \(a_{90}=-0.105847732\)
\(a_{91}=-2.269119684\) \(a_{92}=+1.666371985\) \(a_{93}=-0.274974155\) \(a_{94}=+0.273508776\) \(a_{95}=-0.278453671\)
\(a_{96}=+1.345946824\) \(a_{97}=+1.117727025\) \(a_{98}=-1.089230889\) \(a_{99}=-0.068110824\) \(a_{100}=-0.629728824\)

Showing 100 of 1998 available coefficients

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