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: \( 41.8830032854 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.363847097\) \(a_{3}=+1.178594167\) \(a_{4}=-0.867615290\) \(a_{5}=+0.633799595\)
\(a_{6}=-0.428828067\) \(a_{7}=-1.074119651\) \(a_{8}=+0.679526402\) \(a_{9}=+0.389084211\) \(a_{10}=-0.230606143\)
\(a_{11}=-1.109179352\) \(a_{12}=-1.022566320\) \(a_{13}=+1.721332473\) \(a_{14}=+0.390815317\) \(a_{15}=+0.746992506\)
\(a_{16}=+0.620371581\) \(a_{17}=+0.056943400\) \(a_{18}=-0.141567161\) \(a_{19}=+0.654385085\) \(a_{20}=-0.549894221\)
\(a_{21}=-1.265951149\) \(a_{22}=+0.403571687\) \(a_{23}=-0.270993965\) \(a_{24}=+0.800885854\) \(a_{25}=-0.598298073\)
\(a_{26}=-0.626301823\) \(a_{27}=-0.720021785\) \(a_{28}=+0.931922632\) \(a_{29}=+0.531176470\) \(a_{30}=-0.271791055\)
\(a_{31}=+1.493704677\) \(a_{32}=-0.905246801\) \(a_{33}=-1.307272315\) \(a_{34}=-0.020718691\) \(a_{35}=-0.680776600\)
\(a_{36}=-0.337575411\) \(a_{37}=+0.424107194\) \(a_{38}=-0.238096114\) \(a_{39}=+2.028752413\) \(a_{40}=+0.430683558\)
\(a_{41}=+0.919576413\) \(a_{42}=+0.460612653\) \(a_{43}=+1.412879809\) \(a_{44}=+0.962340965\) \(a_{45}=+0.246601416\)
\(a_{46}=+0.098600368\) \(a_{47}=+0.365900251\) \(a_{48}=+0.731166327\) \(a_{49}=+0.153733024\) \(a_{50}=+0.217689017\)
\(a_{51}=+0.067113159\) \(a_{52}=-1.493454372\) \(a_{53}=+1.945775890\) \(a_{54}=+0.261977836\) \(a_{55}=-0.702997424\)
\(a_{56}=-0.729892661\) \(a_{57}=+0.771254445\) \(a_{58}=-0.193267017\) \(a_{59}=+0.527411052\) \(a_{60}=-0.648102120\)
\(a_{61}=+0.815179148\) \(a_{62}=-0.543480111\) \(a_{63}=-0.417922998\) \(a_{64}=-0.291000161\) \(a_{65}=+1.090979825\)
\(a_{66}=+0.475647236\) \(a_{67}=-0.938830249\) \(a_{68}=-0.049404966\) \(a_{69}=-0.319391920\) \(a_{70}=+0.247698590\)
\(a_{71}=+0.172581951\) \(a_{72}=+0.264392994\) \(a_{73}=+0.279621375\) \(a_{74}=-0.154310171\) \(a_{75}=-0.705150619\)
\(a_{76}=-0.567754505\) \(a_{77}=+1.191391338\) \(a_{78}=-0.738155676\) \(a_{79}=+1.081422012\) \(a_{80}=+0.393191257\)
\(a_{81}=-1.237697688\) \(a_{82}=-0.334585209\) \(a_{83}=-0.238769537\) \(a_{84}=+1.098358579\) \(a_{85}=+0.036090704\)
\(a_{86}=-0.514072217\) \(a_{87}=+0.626041490\) \(a_{88}=-0.753716654\) \(a_{89}=+0.917971422\) \(a_{90}=-0.089725209\)
\(a_{91}=-1.848917035\) \(a_{92}=+0.235118508\) \(a_{93}=+1.760471620\) \(a_{94}=-0.133131744\) \(a_{95}=+0.414749002\)
\(a_{96}=-1.066918599\) \(a_{97}=-0.107724550\) \(a_{98}=-0.055935315\) \(a_{99}=-0.431564174\) \(a_{100}=+0.519092556\)

Showing 100 of 5000 available coefficients

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