Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 48.0393309051 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.800654182\) \(a_{3}=-0.222801079\) \(a_{4}=+2.242355482\) \(a_{5}=+0.560195645\)
\(a_{6}=-0.401187695\) \(a_{7}=+1.381612562\) \(a_{8}=+2.237052594\) \(a_{9}=-0.950359679\) \(a_{10}=+1.008718631\)
\(a_{11}=-0.395396532\) \(a_{12}=-0.499599221\) \(a_{13}=+1.737456914\) \(a_{14}=+2.487806438\) \(a_{15}=-0.124812194\)
\(a_{16}=+1.785802625\) \(a_{17}=+0.066153796\) \(a_{18}=-1.711269130\) \(a_{19}=+0.391253877\) \(a_{20}=+1.256157786\)
\(a_{21}=-0.307824839\) \(a_{22}=-0.711972419\) \(a_{23}=-0.880028022\) \(a_{24}=-0.498417732\) \(a_{25}=-0.686180839\)
\(a_{26}=+3.128559057\) \(a_{27}=+0.434542241\) \(a_{28}=+3.098066503\) \(a_{29}=+0.215390215\) \(a_{30}=-0.224743599\)
\(a_{31}=+1.312771574\) \(a_{32}=+0.978560371\) \(a_{33}=+0.088094774\) \(a_{34}=+0.119120109\) \(a_{35}=+0.773973341\)
\(a_{36}=-2.131044236\) \(a_{37}=+0.160205984\) \(a_{38}=+0.704512932\) \(a_{39}=-0.387107275\) \(a_{40}=+1.253187121\)
\(a_{41}=+0.590681808\) \(a_{42}=-0.554285959\) \(a_{43}=+0.714006405\) \(a_{44}=-0.886619581\) \(a_{45}=-0.532387353\)
\(a_{46}=-1.584626139\) \(a_{47}=+0.279089527\) \(a_{48}=-0.397878752\) \(a_{49}=+0.908853272\) \(a_{50}=-1.235574397\)
\(a_{51}=-0.014739137\) \(a_{52}=+3.895996035\) \(a_{53}=-0.857011883\) \(a_{54}=+0.782460303\) \(a_{55}=-0.221499415\)
\(a_{56}=+3.090739966\) \(a_{57}=-0.087171788\) \(a_{58}=+0.387843293\) \(a_{59}=+1.063435482\) \(a_{60}=-0.279873312\)
\(a_{61}=-0.035474015\) \(a_{62}=+2.363847599\) \(a_{63}=-1.313028855\) \(a_{64}=-0.023753756\) \(a_{65}=+0.973315604\)
\(a_{66}=+0.158628223\) \(a_{67}=-0.834354355\) \(a_{68}=+0.148340327\) \(a_{69}=+0.196071193\) \(a_{70}=+1.393658332\)
\(a_{71}=-0.302204863\) \(a_{72}=-2.126004585\) \(a_{73}=+1.030697053\) \(a_{74}=+0.288475574\) \(a_{75}=+0.152881831\)
\(a_{76}=+0.877330279\) \(a_{77}=-0.546284816\) \(a_{78}=-0.697046334\) \(a_{79}=-1.066552801\) \(a_{80}=+1.000398854\)
\(a_{81}=+0.853543199\) \(a_{82}=+1.063613667\) \(a_{83}=-1.683858754\) \(a_{84}=-0.690252560\) \(a_{85}=+0.037059069\)
\(a_{86}=+1.285678618\) \(a_{87}=-0.047989172\) \(a_{88}=-0.884522837\) \(a_{89}=+0.606619984\) \(a_{90}=-0.958645514\)
\(a_{91}=+2.400492299\) \(a_{92}=-1.973335660\) \(a_{93}=-0.292486922\) \(a_{94}=+0.502543723\) \(a_{95}=+0.219178718\)
\(a_{96}=-0.218024303\) \(a_{97}=-0.543192393\) \(a_{98}=+1.636530444\) \(a_{99}=+0.375768929\) \(a_{100}=-1.538661374\)

Showing 100 of 5000 available coefficients

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