Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 19.4847138547 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.700188032\) \(a_{3}=-0.614565377\) \(a_{4}=+1.890639345\) \(a_{5}=+0.819825344\)
\(a_{6}=+1.044876698\) \(a_{7}=+0.063568994\) \(a_{8}=-1.514254356\) \(a_{9}=-0.622309398\) \(a_{10}=-1.393857239\)
\(a_{11}=+0.659736424\) \(a_{12}=-1.161921483\) \(a_{13}=+0.662330122\) \(a_{14}=-0.108079242\) \(a_{15}=-0.503836271\)
\(a_{16}=+0.683877789\) \(a_{17}=-0.677781120\) \(a_{18}=+1.058042991\) \(a_{19}=-1.734407485\) \(a_{20}=+1.549994052\)
\(a_{21}=-0.039067303\) \(a_{22}=-1.121675972\) \(a_{23}=+0.334160763\) \(a_{24}=+0.930608299\) \(a_{25}=-0.327886405\)
\(a_{26}=-1.126085748\) \(a_{27}=+0.997015186\) \(a_{28}=+0.120186041\) \(a_{29}=-0.585623951\) \(a_{30}=+0.856616399\)
\(a_{31}=-0.988659933\) \(a_{32}=+0.351533524\) \(a_{33}=-0.405451164\) \(a_{34}=+1.152355348\) \(a_{35}=+0.052115472\)
\(a_{36}=-1.176562633\) \(a_{37}=-1.280980808\) \(a_{38}=+2.948818849\) \(a_{39}=-0.407045161\) \(a_{40}=-1.241424099\)
\(a_{41}=+0.239150191\) \(a_{42}=+0.066421760\) \(a_{43}=-0.429138221\) \(a_{44}=+1.247323640\) \(a_{45}=-0.510185016\)
\(a_{46}=-0.568136130\) \(a_{47}=+0.907515236\) \(a_{48}=-0.420287611\) \(a_{49}=-0.995958983\) \(a_{50}=+0.557468542\)
\(a_{51}=+0.416540809\) \(a_{52}=+1.252227389\) \(a_{53}=-0.749574599\) \(a_{54}=-1.695113288\) \(a_{55}=+0.540868642\)
\(a_{56}=-0.096259623\) \(a_{57}=+1.065906782\) \(a_{58}=+0.995670822\) \(a_{59}=-1.068785754\) \(a_{60}=-0.952572678\)
\(a_{61}=-0.497746120\) \(a_{62}=+1.680907786\) \(a_{63}=-0.039559582\) \(a_{64}=-1.281550879\) \(a_{65}=+0.542995021\)
\(a_{66}=+0.689343216\) \(a_{67}=+0.624948584\) \(a_{68}=-1.281439652\) \(a_{69}=-0.205363635\) \(a_{70}=-0.088606102\)
\(a_{71}=-0.244700789\) \(a_{72}=+0.942334717\) \(a_{73}=-0.733739237\) \(a_{74}=+2.177908240\) \(a_{75}=+0.201507632\)
\(a_{76}=-3.279139031\) \(a_{77}=+0.041938781\) \(a_{78}=+0.692053312\) \(a_{79}=+0.795005193\) \(a_{80}=+0.560660344\)
\(a_{81}=+0.009578385\) \(a_{82}=-0.406600292\) \(a_{83}=-0.297517348\) \(a_{84}=-0.073862179\) \(a_{85}=-0.555662140\)
\(a_{86}=+0.729615668\) \(a_{87}=+0.359904204\) \(a_{88}=-0.999008753\) \(a_{89}=-0.113619520\) \(a_{90}=+0.867410458\)
\(a_{91}=+0.042103660\) \(a_{92}=+0.631777486\) \(a_{93}=+0.607596164\) \(a_{94}=-1.542946544\) \(a_{95}=-1.421911213\)
\(a_{96}=-0.216040331\) \(a_{97}=+1.173602618\) \(a_{98}=+1.693317540\) \(a_{99}=-0.410560174\) \(a_{100}=-0.619914942\)

Showing 100 of 5000 available coefficients

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