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: \( 39.4075318615 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.463194574\) \(a_{3}=+0.304451325\) \(a_{4}=-0.785450786\) \(a_{5}=-1.514234084\)
\(a_{6}=+0.141020202\) \(a_{7}=-0.996900010\) \(a_{8}=-0.827011117\) \(a_{9}=-0.907309391\) \(a_{10}=-0.701385012\)
\(a_{11}=+0.133277901\) \(a_{12}=-0.239131533\) \(a_{13}=+1.126444139\) \(a_{14}=-0.461758676\) \(a_{15}=-0.461010574\)
\(a_{16}=+0.402383724\) \(a_{17}=+0.556215858\) \(a_{18}=-0.420260787\) \(a_{19}=+0.594242216\) \(a_{20}=+1.189356348\)
\(a_{21}=-0.303507529\) \(a_{22}=+0.061733601\) \(a_{23}=-0.734331304\) \(a_{24}=-0.251784631\) \(a_{25}=+1.292904862\)
\(a_{26}=+0.521762814\) \(a_{27}=-0.580682872\) \(a_{28}=+0.783015897\) \(a_{29}=-1.628595050\) \(a_{30}=-0.213537597\)
\(a_{31}=-1.237027185\) \(a_{32}=+1.013393075\) \(a_{33}=+0.040576634\) \(a_{34}=+0.257636168\) \(a_{35}=+1.509539974\)
\(a_{36}=+0.712646874\) \(a_{37}=+1.506485868\) \(a_{38}=+0.275249770\) \(a_{39}=+0.342947411\) \(a_{40}=+1.252288422\)
\(a_{41}=+0.675288990\) \(a_{42}=-0.140583041\) \(a_{43}=-0.012434204\) \(a_{44}=-0.104683232\) \(a_{45}=+1.373878804\)
\(a_{46}=-0.340138276\) \(a_{47}=-0.542248314\) \(a_{48}=+0.122506258\) \(a_{49}=-0.006190369\) \(a_{50}=+0.598866517\)
\(a_{51}=+0.169340655\) \(a_{52}=-0.884766435\) \(a_{53}=+0.483671694\) \(a_{54}=-0.268969156\) \(a_{55}=-0.201813941\)
\(a_{56}=+0.824447391\) \(a_{57}=+0.180917830\) \(a_{58}=-0.754356391\) \(a_{59}=-0.418023635\) \(a_{60}=+0.362101118\)
\(a_{61}=+0.518033380\) \(a_{62}=-0.572984280\) \(a_{63}=+0.904496741\) \(a_{64}=+0.067014451\) \(a_{65}=-1.705700109\)
\(a_{66}=+0.018794875\) \(a_{67}=+1.701676138\) \(a_{68}=-0.436880182\) \(a_{69}=-0.223568139\) \(a_{70}=+0.699210726\)
\(a_{71}=-1.614679001\) \(a_{72}=+0.750354953\) \(a_{73}=-0.409316862\) \(a_{74}=+0.697796080\) \(a_{75}=+0.393626599\)
\(a_{76}=-0.466748016\) \(a_{77}=-0.132864741\) \(a_{78}=+0.158851380\) \(a_{79}=-0.313536762\) \(a_{80}=-0.609303149\)
\(a_{81}=+0.730519721\) \(a_{82}=+0.312790196\) \(a_{83}=+0.171560297\) \(a_{84}=+0.238390228\) \(a_{85}=-0.842241011\)
\(a_{86}=-0.005759456\) \(a_{87}=-0.495827921\) \(a_{88}=-0.110222306\) \(a_{89}=+1.146023023\) \(a_{90}=+0.636373208\)
\(a_{91}=-1.122952174\) \(a_{92}=+0.576781100\) \(a_{93}=-0.376614566\) \(a_{94}=-0.251166477\) \(a_{95}=-0.899821818\)
\(a_{96}=+0.308528865\) \(a_{97}=+1.501356177\) \(a_{98}=-0.002867346\) \(a_{99}=-0.120924291\) \(a_{100}=-1.015513141\)

Showing 100 of 5000 available coefficients

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