Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.19257888594 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.118982213\) \(a_{3}=-0.085712905\) \(a_{4}=-0.985843233\) \(a_{5}=-1.083297469\)
\(a_{6}=+0.010198311\) \(a_{7}=+1.073466554\) \(a_{8}=+0.236280023\) \(a_{9}=-0.992653298\) \(a_{10}=+0.128893131\)
\(a_{11}=+0.599197960\) \(a_{12}=+0.084499487\) \(a_{13}=-1.725732916\) \(a_{14}=-0.127723427\) \(a_{15}=+0.092852573\)
\(a_{16}=+0.957730113\) \(a_{17}=-0.956546361\) \(a_{18}=+0.118108087\) \(a_{19}=-0.229415734\) \(a_{20}=+1.067961479\)
\(a_{21}=-0.092009937\) \(a_{22}=-0.071293899\) \(a_{23}=+0.704508911\) \(a_{24}=-0.020252247\) \(a_{25}=+0.173533407\)
\(a_{26}=+0.205331521\) \(a_{27}=+0.170796103\) \(a_{28}=-1.058269739\) \(a_{29}=+0.378160126\) \(a_{30}=-0.011047800\)
\(a_{31}=-0.767366469\) \(a_{32}=-0.350232868\) \(a_{33}=-0.051358996\) \(a_{34}=+0.113811994\) \(a_{35}=-1.162883585\)
\(a_{36}=+0.978600516\) \(a_{37}=-0.341222455\) \(a_{38}=+0.027296405\) \(a_{39}=+0.147917535\) \(a_{40}=-0.255961553\)
\(a_{41}=+1.515546188\) \(a_{42}=+0.010947545\) \(a_{43}=-0.734358615\) \(a_{44}=-0.590715254\) \(a_{45}=+1.075338802\)
\(a_{46}=-0.083824026\) \(a_{47}=+0.664808717\) \(a_{48}=-0.082089827\) \(a_{49}=+0.152330444\) \(a_{50}=-0.020647395\)
\(a_{51}=+0.081988372\) \(a_{52}=+1.701302113\) \(a_{53}=-1.254157274\) \(a_{54}=-0.020321698\) \(a_{55}=-0.649109644\)
\(a_{56}=+0.253638703\) \(a_{57}=+0.019663883\) \(a_{58}=-0.044994307\) \(a_{59}=-0.780886905\) \(a_{60}=-0.091538085\)
\(a_{61}=-1.785886941\) \(a_{62}=+0.091302947\) \(a_{63}=-1.065580101\) \(a_{64}=-0.916058593\) \(a_{65}=+1.869482120\)
\(a_{66}=+0.006110760\) \(a_{67}=+1.032616637\) \(a_{68}=+0.943004753\) \(a_{69}=-0.060385432\) \(a_{70}=+0.138362560\)
\(a_{71}=+0.292497255\) \(a_{72}=-0.234544142\) \(a_{73}=-0.935431338\) \(a_{74}=+0.040599409\) \(a_{75}=-0.014874056\)
\(a_{76}=+0.226167941\) \(a_{77}=+0.643218972\) \(a_{78}=-0.017599594\) \(a_{79}=-0.349991795\) \(a_{80}=-1.037506603\)
\(a_{81}=+0.978013845\) \(a_{82}=-0.180323021\) \(a_{83}=+1.799308842\) \(a_{84}=+0.090707442\) \(a_{85}=+1.036224299\)
\(a_{86}=+0.087375659\) \(a_{87}=-0.032413196\) \(a_{88}=+0.141578499\) \(a_{89}=-0.716362862\) \(a_{90}=-0.127946196\)
\(a_{91}=-1.852516543\) \(a_{92}=-0.694535325\) \(a_{93}=+0.065773196\) \(a_{94}=-0.079100421\) \(a_{95}=+0.248525484\)
\(a_{96}=+0.030019460\) \(a_{97}=-0.190520905\) \(a_{98}=-0.018124608\) \(a_{99}=-0.594795827\) \(a_{100}=-0.171076709\)

Showing 100 of 1500 available coefficients

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