Properties

Level $89$
Weight $0$
Character 89.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 89 \)
Weight: \( 0 \)
Character: 89.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.86033398099 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.139762923\) \(a_{3}=-0.690777982\) \(a_{4}=-0.980466325\) \(a_{5}=-1.572653092\)
\(a_{6}=-0.096545150\) \(a_{7}=+0.796591283\) \(a_{8}=-0.276795763\) \(a_{9}=-0.522825780\) \(a_{10}=-0.219798593\)
\(a_{11}=+0.759314360\) \(a_{12}=+0.677284550\) \(a_{13}=+0.235441282\) \(a_{14}=+0.111333926\) \(a_{15}=+1.086354129\)
\(a_{16}=+0.941780541\) \(a_{17}=-1.857496930\) \(a_{18}=-0.073071659\) \(a_{19}=-0.865229660\) \(a_{20}=+1.541933398\)
\(a_{21}=-0.550267719\) \(a_{22}=+0.106123994\) \(a_{23}=-1.127567496\) \(a_{24}=+0.191204418\) \(a_{25}=+1.473237748\)
\(a_{26}=+0.032905962\) \(a_{27}=+1.051934519\) \(a_{28}=-0.781030928\) \(a_{29}=+1.078095483\) \(a_{30}=+0.151832029\)
\(a_{31}=-0.330028430\) \(a_{32}=+0.408421764\) \(a_{33}=-0.524517641\) \(a_{34}=-0.259609200\) \(a_{35}=-1.252761744\)
\(a_{36}=+0.512613071\) \(a_{37}=+0.033802290\) \(a_{38}=-0.120927026\) \(a_{39}=-0.162637654\) \(a_{40}=+0.435303712\)
\(a_{41}=-1.625134630\) \(a_{42}=-0.076907025\) \(a_{43}=-0.630042980\) \(a_{44}=-0.744482160\) \(a_{45}=+0.822223579\)
\(a_{46}=-0.157592129\) \(a_{47}=+0.558483137\) \(a_{48}=-0.650561261\) \(a_{49}=-0.365442328\) \(a_{50}=+0.205904014\)
\(a_{51}=+1.283117981\) \(a_{52}=-0.230842249\) \(a_{53}=+1.165361488\) \(a_{54}=+0.147021443\) \(a_{55}=-1.194138076\)
\(a_{56}=-0.220493092\) \(a_{57}=+0.597681599\) \(a_{58}=+0.150677776\) \(a_{59}=-0.293947486\) \(a_{60}=-1.065133641\)
\(a_{61}=-1.077798746\) \(a_{62}=-0.046125738\) \(a_{63}=-0.416478459\) \(a_{64}=-0.884698321\) \(a_{65}=-0.370267460\)
\(a_{66}=-0.073308119\) \(a_{67}=-0.024013397\) \(a_{68}=+1.821213189\) \(a_{69}=+0.778898799\) \(a_{70}=-0.175089643\)
\(a_{71}=+0.961873534\) \(a_{72}=+0.144715960\) \(a_{73}=+0.568673971\) \(a_{74}=+0.004724307\) \(a_{75}=-1.017680198\)
\(a_{76}=+0.848328545\) \(a_{77}=+0.604863200\) \(a_{78}=-0.022730714\) \(a_{79}=-1.435129636\) \(a_{80}=-1.481094079\)
\(a_{81}=-0.203827425\) \(a_{82}=-0.227133566\) \(a_{83}=+1.968073729\) \(a_{84}=+0.539518968\) \(a_{85}=+2.921198290\)
\(a_{86}=-0.088056649\) \(a_{87}=-0.744724622\) \(a_{88}=-0.210174997\) \(a_{89}=-0.105999788\) \(a_{90}=+0.114916371\)
\(a_{91}=+0.187550473\) \(a_{92}=+1.105541959\) \(a_{93}=+0.227976373\) \(a_{94}=+0.078055236\) \(a_{95}=+1.360706100\)
\(a_{96}=-0.282128762\) \(a_{97}=-0.287578866\) \(a_{98}=-0.051075288\) \(a_{99}=-0.396989122\) \(a_{100}=-1.444460001\)

Showing 100 of 546 available coefficients

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