Properties

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

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.98941333027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.303359155\) \(a_{3}=+0.365412874\) \(a_{4}=-0.907973223\) \(a_{5}=-0.005126980\)
\(a_{6}=-0.110851341\) \(a_{7}=-0.670339997\) \(a_{8}=+0.578801144\) \(a_{9}=-0.866473431\) \(a_{10}=+0.001555316\)
\(a_{11}=+1.607855647\) \(a_{12}=-0.331785105\) \(a_{13}=+0.348029194\) \(a_{14}=+0.203353775\) \(a_{15}=-0.001873465\)
\(a_{16}=+0.732388597\) \(a_{17}=+1.696042436\) \(a_{18}=+0.262852648\) \(a_{19}=-0.229415734\) \(a_{20}=+0.004655161\)
\(a_{21}=-0.244950865\) \(a_{22}=-0.487757730\) \(a_{23}=+0.773056660\) \(a_{24}=+0.211501390\) \(a_{25}=-0.999973714\)
\(a_{26}=-0.105577842\) \(a_{27}=-0.682033421\) \(a_{28}=+0.608650767\) \(a_{29}=+1.808832023\) \(a_{30}=+0.000568333\)
\(a_{31}=+0.360114038\) \(a_{32}=-0.800977930\) \(a_{33}=+0.587531153\) \(a_{34}=-0.514510000\) \(a_{35}=+0.003436820\)
\(a_{36}=+0.786734674\) \(a_{37}=-0.322202127\) \(a_{38}=+0.069595363\) \(a_{39}=+0.127174348\) \(a_{40}=-0.002967502\)
\(a_{41}=-0.240775793\) \(a_{42}=+0.074308087\) \(a_{43}=-0.196756675\) \(a_{44}=-1.459889874\) \(a_{45}=+0.004442392\)
\(a_{46}=-0.234513815\) \(a_{47}=-0.022022291\) \(a_{48}=+0.267624222\) \(a_{49}=-0.550644289\) \(a_{50}=+0.303351181\)
\(a_{51}=+0.619755741\) \(a_{52}=-0.316001189\) \(a_{53}=+1.656437288\) \(a_{54}=+0.206901082\) \(a_{55}=-0.008243444\)
\(a_{56}=-0.387993557\) \(a_{57}=-0.083831463\) \(a_{58}=-0.548725754\) \(a_{59}=+1.552862548\) \(a_{60}=+0.001701056\)
\(a_{61}=-0.139049741\) \(a_{62}=-0.109243890\) \(a_{63}=+0.580831797\) \(a_{64}=-0.489404609\) \(a_{65}=-0.001784339\)
\(a_{66}=-0.178232954\) \(a_{67}=-0.531214045\) \(a_{68}=-1.539961117\) \(a_{69}=+0.282484856\) \(a_{70}=-0.001042591\)
\(a_{71}=+0.056795017\) \(a_{72}=-0.501515814\) \(a_{73}=+1.194902540\) \(a_{74}=+0.097742965\) \(a_{75}=-0.365403269\)
\(a_{76}=+0.208303343\) \(a_{77}=-1.077809949\) \(a_{78}=-0.038579503\) \(a_{79}=-0.934489795\) \(a_{80}=-0.003754942\)
\(a_{81}=+0.617249639\) \(a_{82}=+0.073041541\) \(a_{83}=+0.954197030\) \(a_{84}=+0.222408826\) \(a_{85}=-0.008695576\)
\(a_{86}=+0.059687939\) \(a_{87}=+0.660970508\) \(a_{88}=+0.930628689\) \(a_{89}=+0.146340230\) \(a_{90}=-0.001347640\)
\(a_{91}=-0.233297889\) \(a_{92}=-0.701914747\) \(a_{93}=+0.131590306\) \(a_{94}=+0.006680664\) \(a_{95}=+0.001176210\)
\(a_{96}=-0.292687648\) \(a_{97}=+1.195010689\) \(a_{98}=+0.167042986\) \(a_{99}=-1.393164200\) \(a_{100}=+0.907949356\)

Showing 100 of 546 available coefficients

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