Properties

Level $98$
Weight $0$
Character 98.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 98 = 2 \cdot 7^{2} \)
Weight: \( 0 \)
Character: 98.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.44920935339 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.429343192\) \(a_{4}=+0.500000000\) \(a_{5}=-1.443755440\)
\(a_{6}=-1.010698264\) \(a_{7}=+0.000000000\) \(a_{8}=-0.353553391\) \(a_{9}=+1.043021960\) \(a_{10}=+1.020889262\)
\(a_{11}=-0.665168394\) \(a_{12}=+0.714671596\) \(a_{13}=-0.702467926\) \(a_{14}=+0.000000000\) \(a_{15}=-2.063622009\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.871295174\) \(a_{18}=-0.737527901\) \(a_{19}=-1.412678873\) \(a_{20}=-0.721877720\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.470345082\) \(a_{23}=-0.332773231\) \(a_{24}=-0.505349132\) \(a_{25}=+1.084429772\)
\(a_{26}=+0.496719834\) \(a_{27}=+0.061493145\) \(a_{28}=+0.000000000\) \(a_{29}=+0.225773312\) \(a_{30}=+1.459201117\)
\(a_{31}=+1.425871178\) \(a_{32}=-0.176776695\) \(a_{33}=-0.950753915\) \(a_{34}=+0.616098726\) \(a_{35}=+0.000000000\)
\(a_{36}=+0.521510980\) \(a_{37}=+0.751966342\) \(a_{38}=+0.998914811\) \(a_{39}=-1.004067748\) \(a_{40}=+0.510444631\)
\(a_{41}=-0.957230265\) \(a_{42}=+0.000000000\) \(a_{43}=+0.865056067\) \(a_{44}=-0.332584197\) \(a_{45}=-1.505868629\)
\(a_{46}=+0.235306209\) \(a_{47}=-1.050988973\) \(a_{48}=+0.357335798\) \(a_{49}=+0.000000000\) \(a_{50}=-0.766807645\)
\(a_{51}=-1.245379826\) \(a_{52}=-0.351233963\) \(a_{53}=+1.071649455\) \(a_{54}=-0.043482220\) \(a_{55}=+0.960340487\)
\(a_{56}=+0.000000000\) \(a_{57}=-2.019202930\) \(a_{58}=-0.159645840\) \(a_{59}=-0.675392149\) \(a_{60}=-1.031811005\)
\(a_{61}=+1.565237056\) \(a_{62}=-1.008243179\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+1.014191890\)
\(a_{66}=+0.672284541\) \(a_{67}=+0.428940706\) \(a_{68}=-0.435647587\) \(a_{69}=-0.475647152\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.174289851\) \(a_{72}=-0.368763950\) \(a_{73}=+0.333557253\) \(a_{74}=-0.531720500\) \(a_{75}=+1.550022311\)
\(a_{76}=-0.706339437\) \(a_{77}=+0.000000000\) \(a_{78}=+0.709983113\) \(a_{79}=-0.673491657\) \(a_{80}=-0.360938860\)
\(a_{81}=-0.955127152\) \(a_{82}=+0.676864011\) \(a_{83}=-0.095824394\) \(a_{84}=+0.000000000\) \(a_{85}=+1.257937149\)
\(a_{86}=-0.611687011\) \(a_{87}=+0.322707544\) \(a_{88}=+0.235172541\) \(a_{89}=-1.666144749\) \(a_{90}=+1.064809919\)
\(a_{91}=+0.000000000\) \(a_{92}=-0.166386616\) \(a_{93}=+2.038059259\) \(a_{94}=+0.743161430\) \(a_{95}=+2.039562809\)
\(a_{96}=-0.252674566\) \(a_{97}=-0.247314778\) \(a_{98}=+0.000000000\) \(a_{99}=-0.693785243\) \(a_{100}=+0.542214886\)

Showing 100 of 562 available coefficients

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