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: \( 34.456271533 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.235723928\) \(a_{3}=-0.553990013\) \(a_{4}=+0.527013627\) \(a_{5}=+0.900853242\)
\(a_{6}=+0.684578716\) \(a_{7}=+0.614671425\) \(a_{8}=+0.584480578\) \(a_{9}=-0.693095065\) \(a_{10}=-1.113205907\)
\(a_{11}=+1.477661146\) \(a_{12}=-0.291960287\) \(a_{13}=-1.480912148\) \(a_{14}=-0.759564188\) \(a_{15}=-0.499063700\)
\(a_{16}=-1.249270264\) \(a_{17}=-0.669521188\) \(a_{18}=+0.856474157\) \(a_{19}=+0.105432335\) \(a_{20}=+0.474761935\)
\(a_{21}=-0.340521831\) \(a_{22}=-1.825981236\) \(a_{23}=+0.570982564\) \(a_{24}=-0.323796404\) \(a_{25}=-0.188463436\)
\(a_{26}=+1.829998577\) \(a_{27}=+0.937957758\) \(a_{28}=+0.323940217\) \(a_{29}=+1.452798831\) \(a_{30}=+0.616704956\)
\(a_{31}=+0.337443828\) \(a_{32}=+0.959272580\) \(a_{33}=-0.818609518\) \(a_{34}=+0.827343352\) \(a_{35}=+0.553728746\)
\(a_{36}=-0.365270544\) \(a_{37}=-0.272768152\) \(a_{38}=-0.130285259\) \(a_{39}=+0.820410541\) \(a_{40}=+0.526531224\)
\(a_{41}=-1.642854327\) \(a_{42}=+0.420790975\) \(a_{43}=+0.332251281\) \(a_{44}=+0.778747561\) \(a_{45}=-0.624376936\)
\(a_{46}=-0.705576817\) \(a_{47}=+0.334719135\) \(a_{48}=+0.692083250\) \(a_{49}=-0.622179039\) \(a_{50}=+0.232888778\)
\(a_{51}=+0.370908052\) \(a_{52}=-0.780460883\) \(a_{53}=+0.548363388\) \(a_{54}=-1.159056845\) \(a_{55}=+1.331155834\)
\(a_{56}=+0.359263510\) \(a_{57}=-0.058408460\) \(a_{58}=-1.795258278\) \(a_{59}=+0.877987136\) \(a_{60}=-0.263013371\)
\(a_{61}=+1.392589974\) \(a_{62}=-0.416987414\) \(a_{63}=-0.426025729\) \(a_{64}=+0.063874180\) \(a_{65}=-1.334084510\)
\(a_{66}=+1.011575399\) \(a_{67}=+1.004185491\) \(a_{68}=-0.352846790\) \(a_{69}=-0.316318638\) \(a_{70}=-0.684255861\)
\(a_{71}=+0.875865666\) \(a_{72}=-0.405100604\) \(a_{73}=-0.306066797\) \(a_{74}=+0.337066132\) \(a_{75}=+0.104406862\)
\(a_{76}=+0.055564277\) \(a_{77}=+0.908276082\) \(a_{78}=-1.013800937\) \(a_{79}=-0.055712344\) \(a_{80}=-1.125409167\)
\(a_{81}=+0.173475834\) \(a_{82}=+2.030114403\) \(a_{83}=-0.189919853\) \(a_{84}=-0.179459645\) \(a_{85}=-0.603140332\)
\(a_{86}=-0.410570859\) \(a_{87}=-0.804836044\) \(a_{88}=+0.863664241\) \(a_{89}=+0.469629945\) \(a_{90}=+0.771557521\)
\(a_{91}=-0.910274380\) \(a_{92}=+0.300915592\) \(a_{93}=-0.186940511\) \(a_{94}=-0.413620444\) \(a_{95}=+0.094979060\)
\(a_{96}=-0.531427429\) \(a_{97}=+0.678437492\) \(a_{98}=+0.768841527\) \(a_{99}=-1.024159648\) \(a_{100}=-0.099322799\)

Showing 100 of 5000 available coefficients

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