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: \( 41.5555776736 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.058964637\) \(a_{3}=-0.958982287\) \(a_{4}=+0.121406102\) \(a_{5}=-0.633474987\)
\(a_{6}=-1.015528330\) \(a_{7}=-0.813552790\) \(a_{8}=-0.930399868\) \(a_{9}=-0.080352972\) \(a_{10}=-0.670827610\)
\(a_{11}=+1.136070262\) \(a_{12}=-0.116426302\) \(a_{13}=-1.115945326\) \(a_{14}=-0.861523635\) \(a_{15}=+0.607491292\)
\(a_{16}=-1.106666661\) \(a_{17}=-0.946067245\) \(a_{18}=-0.085090956\) \(a_{19}=+1.841453326\) \(a_{20}=-0.076907728\)
\(a_{21}=+0.780182715\) \(a_{22}=+1.203058232\) \(a_{23}=+0.404143397\) \(a_{24}=+0.892236994\) \(a_{25}=-0.598709441\)
\(a_{26}=-1.181746637\) \(a_{27}=+1.036039365\) \(a_{28}=-0.098770273\) \(a_{29}=+0.759926212\) \(a_{30}=+0.643311796\)
\(a_{31}=-0.393536157\) \(a_{32}=-0.241520990\) \(a_{33}=-1.089471258\) \(a_{34}=-1.001851757\) \(a_{35}=+0.515365343\)
\(a_{36}=-0.009755341\) \(a_{37}=-0.876803906\) \(a_{38}=+1.950033952\) \(a_{39}=+1.070171802\) \(a_{40}=+0.589385044\)
\(a_{41}=+0.568329155\) \(a_{42}=+0.826185906\) \(a_{43}=+1.762203589\) \(a_{44}=+0.137925862\) \(a_{45}=+0.050901598\)
\(a_{46}=+0.427973565\) \(a_{47}=+0.282291451\) \(a_{48}=+1.061273726\) \(a_{49}=-0.338131858\) \(a_{50}=-0.634012125\)
\(a_{51}=+0.907261731\) \(a_{52}=-0.135482572\) \(a_{53}=-0.462943328\) \(a_{54}=+1.097129050\) \(a_{55}=-0.719672094\)
\(a_{56}=+0.756929408\) \(a_{57}=-1.765921123\) \(a_{58}=+0.804734985\) \(a_{59}=+1.083930845\) \(a_{60}=+0.073753150\)
\(a_{61}=-1.041082970\) \(a_{62}=-0.416740873\) \(a_{63}=+0.065371384\) \(a_{64}=+0.850904473\) \(a_{65}=+0.706923452\)
\(a_{66}=-1.153711535\) \(a_{67}=+0.146317590\) \(a_{68}=-0.114858335\) \(a_{69}=-0.387566359\) \(a_{70}=+0.545753673\)
\(a_{71}=+0.299147552\) \(a_{72}=+0.074760395\) \(a_{73}=-0.055307272\) \(a_{74}=-0.928504330\) \(a_{75}=+0.574151749\)
\(a_{76}=+0.223563671\) \(a_{77}=-0.924253131\) \(a_{78}=+1.133274094\) \(a_{79}=-0.373070383\) \(a_{80}=+0.701045649\)
\(a_{81}=-0.913190428\) \(a_{82}=+0.601840477\) \(a_{83}=-1.369560223\) \(a_{84}=+0.094718942\) \(a_{85}=+0.599309936\)
\(a_{86}=+1.866111284\) \(a_{87}=-0.728755777\) \(a_{88}=-1.056999621\) \(a_{89}=-0.721921092\) \(a_{90}=+0.053902992\)
\(a_{91}=+0.907880433\) \(a_{92}=+0.049065474\) \(a_{93}=+0.377394204\) \(a_{94}=+0.298936664\) \(a_{95}=-1.166514622\)
\(a_{96}=+0.231614352\) \(a_{97}=+0.261490068\) \(a_{98}=-0.358069681\) \(a_{99}=-0.091286622\) \(a_{100}=-0.072686980\)

Showing 100 of 5000 available coefficients

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