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: \( 35.5023497714 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.123590292\) \(a_{3}=-0.508132825\) \(a_{4}=-0.984725440\) \(a_{5}=-0.590742097\)
\(a_{6}=-0.062800284\) \(a_{7}=-1.164954200\) \(a_{8}=-0.245292797\) \(a_{9}=-0.741801032\) \(a_{10}=-0.073009988\)
\(a_{11}=-0.894111099\) \(a_{12}=+0.500371320\) \(a_{13}=-0.338853896\) \(a_{14}=-0.143977030\) \(a_{15}=+0.300175451\)
\(a_{16}=+0.954409631\) \(a_{17}=-1.096099119\) \(a_{18}=-0.091679406\) \(a_{19}=+0.207405132\) \(a_{20}=+0.581718771\)
\(a_{21}=+0.591951469\) \(a_{22}=-0.110503452\) \(a_{23}=-1.541572058\) \(a_{24}=+0.124641322\) \(a_{25}=-0.651023775\)
\(a_{26}=-0.041879052\) \(a_{27}=+0.885066280\) \(a_{28}=+1.147160037\) \(a_{29}=+1.102470561\) \(a_{30}=+0.037098772\)
\(a_{31}=+1.944345335\) \(a_{32}=+0.363248562\) \(a_{33}=+0.454327199\) \(a_{34}=-0.135467210\) \(a_{35}=+0.688187487\)
\(a_{36}=+0.730470347\) \(a_{37}=-0.606662293\) \(a_{38}=+0.025633261\) \(a_{39}=+0.172182787\) \(a_{40}=+0.144904781\)
\(a_{41}=+0.313212463\) \(a_{42}=+0.073159455\) \(a_{43}=-1.265391511\) \(a_{44}=+0.880453945\) \(a_{45}=+0.438213097\)
\(a_{46}=-0.190523341\) \(a_{47}=-0.178862686\) \(a_{48}=-0.484966862\) \(a_{49}=+0.357118289\) \(a_{50}=-0.080460219\)
\(a_{51}=+0.556963942\) \(a_{52}=+0.333678051\) \(a_{53}=-1.348570002\) \(a_{54}=+0.109385600\) \(a_{55}=+0.528189065\)
\(a_{56}=+0.285754874\) \(a_{57}=-0.105389356\) \(a_{58}=+0.136254659\) \(a_{59}=-0.499610288\) \(a_{60}=-0.295590402\)
\(a_{61}=+0.185300905\) \(a_{62}=+0.240302208\) \(a_{63}=+0.864164225\) \(a_{64}=-0.909515633\) \(a_{65}=+0.200175265\)
\(a_{66}=+0.056150437\) \(a_{67}=-1.389242204\) \(a_{68}=+1.079356687\) \(a_{69}=+0.783323365\) \(a_{70}=+0.085053293\)
\(a_{71}=-0.923374426\) \(a_{72}=+0.181958450\) \(a_{73}=-0.315760242\) \(a_{74}=-0.074977570\) \(a_{75}=+0.330806550\)
\(a_{76}=-0.204237110\) \(a_{77}=+1.041598481\) \(a_{78}=+0.021280121\) \(a_{79}=-0.917344688\) \(a_{80}=-0.563809947\)
\(a_{81}=+0.292069803\) \(a_{82}=+0.038710020\) \(a_{83}=+0.852492766\) \(a_{84}=-0.582909671\) \(a_{85}=+0.647511892\)
\(a_{86}=-0.156390107\) \(a_{87}=-0.560201481\) \(a_{88}=+0.219319012\) \(a_{89}=-0.784048386\) \(a_{90}=+0.054158885\)
\(a_{91}=+0.394749269\) \(a_{92}=+1.518025222\) \(a_{93}=-0.987985689\) \(a_{94}=-0.022105692\) \(a_{95}=-0.122522943\)
\(a_{96}=-0.184578518\) \(a_{97}=-0.699561291\) \(a_{98}=+0.044136354\) \(a_{99}=+0.663252536\) \(a_{100}=+0.641079673\)

Showing 100 of 5000 available coefficients

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