Properties

Level $93$
Weight $0$
Character 93.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 93 = 3 \cdot 31 \)
Weight: \( 0 \)
Character: 93.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.12005945984 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.245506655\) \(a_{3}=-0.577350269\) \(a_{4}=+0.551286828\) \(a_{5}=-0.398575919\)
\(a_{6}=+0.719093603\) \(a_{7}=+0.566841685\) \(a_{8}=+0.558875242\) \(a_{9}=+0.333333333\) \(a_{10}=+0.496428960\)
\(a_{11}=+0.613925986\) \(a_{12}=-0.318285598\) \(a_{13}=+0.061635589\) \(a_{14}=-0.706005091\) \(a_{15}=+0.230117914\)
\(a_{16}=-1.247369661\) \(a_{17}=+0.003120743\) \(a_{18}=-0.415168885\) \(a_{19}=-1.009770725\) \(a_{20}=-0.219729654\)
\(a_{21}=-0.327266200\) \(a_{22}=-0.764648901\) \(a_{23}=+0.783898293\) \(a_{24}=-0.322666772\) \(a_{25}=-0.841137237\)
\(a_{26}=-0.076767536\) \(a_{27}=-0.192450090\) \(a_{28}=+0.312492355\) \(a_{29}=+1.442933756\) \(a_{30}=-0.286613394\)
\(a_{31}=-0.179605302\) \(a_{32}=+0.994731972\) \(a_{33}=-0.354450333\) \(a_{34}=-0.003886907\) \(a_{35}=-0.225929446\)
\(a_{36}=+0.183762276\) \(a_{37}=+0.720585345\) \(a_{38}=+1.257676159\) \(a_{39}=-0.035585324\) \(a_{40}=-0.222754213\)
\(a_{41}=-0.733765454\) \(a_{42}=+0.407612230\) \(a_{43}=-0.928863316\) \(a_{44}=+0.338449309\) \(a_{45}=-0.132858640\)
\(a_{46}=-0.976350541\) \(a_{47}=-0.330517769\) \(a_{48}=+0.720169210\) \(a_{49}=-0.678690504\) \(a_{50}=+1.047642026\)
\(a_{51}=-0.001801762\) \(a_{52}=+0.033978888\) \(a_{53}=-0.774897536\) \(a_{54}=+0.239697868\) \(a_{55}=-0.244696114\)
\(a_{56}=+0.316793784\) \(a_{57}=+0.582991400\) \(a_{58}=-1.797183596\) \(a_{59}=-0.562189786\) \(a_{60}=+0.126860975\)
\(a_{61}=+0.470865003\) \(a_{62}=+0.223699599\) \(a_{63}=+0.188947228\) \(a_{64}=+0.008424370\) \(a_{65}=-0.024566461\)
\(a_{66}=+0.441470249\) \(a_{67}=-1.992221142\) \(a_{68}=+0.001720425\) \(a_{69}=-0.452583891\) \(a_{70}=+0.281396628\)
\(a_{71}=-0.305372502\) \(a_{72}=+0.186291747\) \(a_{73}=-0.204937169\) \(a_{74}=-0.897493843\) \(a_{75}=+0.485630810\)
\(a_{76}=-0.556673300\) \(a_{77}=+0.347998841\) \(a_{78}=+0.044321757\) \(a_{79}=-0.547562113\) \(a_{80}=+0.497171509\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.913909756\) \(a_{83}=-0.080060787\) \(a_{84}=-0.180417545\) \(a_{85}=-0.001243853\)
\(a_{86}=+1.156905441\) \(a_{87}=-0.833078192\) \(a_{88}=+0.343108034\) \(a_{89}=+0.128028528\) \(a_{90}=+0.165476320\)
\(a_{91}=+0.034937621\) \(a_{92}=+0.432152803\) \(a_{93}=+0.103695169\) \(a_{94}=+0.411662080\) \(a_{95}=+0.402470295\)
\(a_{96}=-0.574308772\) \(a_{97}=+0.187950738\) \(a_{98}=+0.845313539\) \(a_{99}=+0.204641995\) \(a_{100}=-0.463707879\)

Showing 100 of 742 available coefficients

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