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: \( 44.4263481186 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.946357176\) \(a_{3}=-0.783806387\) \(a_{4}=-0.104408095\) \(a_{5}=-0.341412439\)
\(a_{6}=+0.741760799\) \(a_{7}=+0.923918989\) \(a_{8}=+1.045164526\) \(a_{9}=-0.385647548\) \(a_{10}=+0.323098111\)
\(a_{11}=-0.702868442\) \(a_{12}=+0.081835731\) \(a_{13}=+0.666129014\) \(a_{14}=-0.874357366\) \(a_{15}=+0.267601250\)
\(a_{16}=-0.884690855\) \(a_{17}=-1.462784134\) \(a_{18}=+0.364960325\) \(a_{19}=+0.769958903\) \(a_{20}=+0.035646222\)
\(a_{21}=-0.724173602\) \(a_{22}=+0.665164564\) \(a_{23}=-1.737227324\) \(a_{24}=-0.819206631\) \(a_{25}=-0.883437547\)
\(a_{26}=-0.630395973\) \(a_{27}=+1.086079398\) \(a_{28}=-0.096464621\) \(a_{29}=-1.022879971\) \(a_{30}=-0.253246363\)
\(a_{31}=-0.155541783\) \(a_{32}=-0.207930986\) \(a_{33}=+0.550912774\) \(a_{34}=+1.384316263\) \(a_{35}=-0.315437435\)
\(a_{36}=+0.040264726\) \(a_{37}=-0.606605225\) \(a_{38}=-0.728656134\) \(a_{39}=-0.522116176\) \(a_{40}=-0.356832170\)
\(a_{41}=-0.974997688\) \(a_{42}=+0.685326888\) \(a_{43}=+1.437167296\) \(a_{44}=+0.073385155\) \(a_{45}=+0.131664870\)
\(a_{46}=+1.644037545\) \(a_{47}=+1.510224065\) \(a_{48}=+0.693426343\) \(a_{49}=-0.146373702\) \(a_{50}=+0.836047462\)
\(a_{51}=+1.146539547\) \(a_{52}=-0.069549261\) \(a_{53}=+1.264121441\) \(a_{54}=-1.027819032\) \(a_{55}=+0.239968029\)
\(a_{56}=+0.965647352\) \(a_{57}=-0.603498706\) \(a_{58}=+0.968009801\) \(a_{59}=-0.606301484\) \(a_{60}=-0.027939737\)
\(a_{61}=+0.006562412\) \(a_{62}=+0.147198083\) \(a_{63}=-0.356307093\) \(a_{64}=+1.081467836\) \(a_{65}=-0.227424731\)
\(a_{66}=-0.521360258\) \(a_{67}=-0.735718165\) \(a_{68}=+0.152726506\) \(a_{69}=+1.361649868\) \(a_{70}=+0.298516482\)
\(a_{71}=-1.015230866\) \(a_{72}=-0.403065137\) \(a_{73}=-0.298859024\) \(a_{74}=+0.574065208\) \(a_{75}=+0.692443992\)
\(a_{76}=-0.080389942\) \(a_{77}=-0.649393501\) \(a_{78}=+0.494108390\) \(a_{79}=-0.685013216\) \(a_{80}=+0.302044462\)
\(a_{81}=-0.465628421\) \(a_{82}=+0.922696059\) \(a_{83}=-0.266649242\) \(a_{84}=+0.075609586\) \(a_{85}=+0.499412698\)
\(a_{86}=-1.360073584\) \(a_{87}=+0.801739854\) \(a_{88}=-0.734613162\) \(a_{89}=+0.571013546\) \(a_{90}=-0.124601994\)
\(a_{91}=+0.615449245\) \(a_{92}=+0.181380595\) \(a_{93}=+0.121914643\) \(a_{94}=-1.429211382\) \(a_{95}=-0.262873547\)
\(a_{96}=+0.162977635\) \(a_{97}=+1.131394450\) \(a_{98}=+0.138521803\) \(a_{99}=+0.271059491\) \(a_{100}=+0.092238031\)

Showing 100 of 5000 available coefficients

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