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: \( 4.43217458695 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.070625725\) \(a_{3}=-0.456312487\) \(a_{4}=+0.146239443\) \(a_{5}=-0.925084407\)
\(a_{6}=-0.488539888\) \(a_{7}=-0.600512133\) \(a_{8}=-0.914058015\) \(a_{9}=-0.791778913\) \(a_{10}=-0.990419163\)
\(a_{11}=+1.629095908\) \(a_{12}=-0.066730885\) \(a_{13}=+0.609987297\) \(a_{14}=-0.642923735\) \(a_{15}=+0.422127566\)
\(a_{16}=-1.124853468\) \(a_{17}=-0.692149317\) \(a_{18}=-0.847698874\) \(a_{19}=-0.229415734\) \(a_{20}=-0.135283828\)
\(a_{21}=+0.274021185\) \(a_{22}=+1.744151988\) \(a_{23}=-0.857610847\) \(a_{24}=+0.417096087\) \(a_{25}=-0.144218839\)
\(a_{26}=+0.653068090\) \(a_{27}=+0.817611088\) \(a_{28}=-0.087818558\) \(a_{29}=-0.520439086\) \(a_{30}=+0.451940632\)
\(a_{31}=-0.344655296\) \(a_{32}=-0.290239048\) \(a_{33}=-0.743376802\) \(a_{34}=-0.741032860\) \(a_{35}=+0.555524406\)
\(a_{36}=-0.115789310\) \(a_{37}=-0.466784219\) \(a_{38}=-0.245618382\) \(a_{39}=-0.278344775\) \(a_{40}=+0.845580807\)
\(a_{41}=-1.213343492\) \(a_{42}=+0.293374125\) \(a_{43}=+1.733229936\) \(a_{44}=+0.238238097\) \(a_{45}=+0.732462320\)
\(a_{46}=-0.918180271\) \(a_{47}=-0.380263174\) \(a_{48}=+0.513284678\) \(a_{49}=-0.639385151\) \(a_{50}=-0.154404362\)
\(a_{51}=+0.315836279\) \(a_{52}=+0.089204184\) \(a_{53}=+1.031616399\) \(a_{54}=+0.875355581\) \(a_{55}=-1.507051277\)
\(a_{56}=+0.548902945\) \(a_{57}=+0.104685347\) \(a_{58}=-0.557195456\) \(a_{59}=-1.550911029\) \(a_{60}=+0.061731672\)
\(a_{61}=+1.415071828\) \(a_{62}=-0.368996815\) \(a_{63}=+0.475472721\) \(a_{64}=+0.814116009\) \(a_{65}=-0.564289648\)
\(a_{66}=-0.795878243\) \(a_{67}=-1.681085743\) \(a_{68}=-0.101219605\) \(a_{69}=+0.391338485\) \(a_{70}=+0.594758768\)
\(a_{71}=+0.598660802\) \(a_{72}=+0.723731889\) \(a_{73}=-0.770297172\) \(a_{74}=-0.499751168\) \(a_{75}=+0.065808890\)
\(a_{76}=-0.033549634\) \(a_{77}=-0.978291866\) \(a_{78}=-0.298003157\) \(a_{79}=-0.053346166\) \(a_{80}=+1.040584436\)
\(a_{81}=+0.418692752\) \(a_{82}=-1.299036688\) \(a_{83}=+1.486487004\) \(a_{84}=+0.040072720\) \(a_{85}=+0.640296565\)
\(a_{86}=+1.855640527\) \(a_{87}=+0.237482834\) \(a_{88}=-1.489088106\) \(a_{89}=+1.006917178\) \(a_{90}=+0.784192937\)
\(a_{91}=-0.366304711\) \(a_{92}=-0.125416575\) \(a_{93}=+0.157270503\) \(a_{94}=-0.407119570\) \(a_{95}=+0.212228914\)
\(a_{96}=+0.132439723\) \(a_{97}=-0.869238941\) \(a_{98}=-0.684542330\) \(a_{99}=-1.289883733\) \(a_{100}=-0.021090464\)

Showing 100 of 1500 available coefficients

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