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: \( 18.1809178345 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.374063347\) \(a_{3}=+0.101958698\) \(a_{4}=-0.860076613\) \(a_{5}=+0.637330829\)
\(a_{6}=+0.038139012\) \(a_{7}=-1.542099223\) \(a_{8}=-0.695786483\) \(a_{9}=-0.989604424\) \(a_{10}=+0.238402103\)
\(a_{11}=-0.411715707\) \(a_{12}=-0.087692292\) \(a_{13}=+0.478703730\) \(a_{14}=-0.576842796\) \(a_{15}=+0.064981421\)
\(a_{16}=+0.599808392\) \(a_{17}=-0.548557415\) \(a_{18}=-0.370174743\) \(a_{19}=+1.030984158\) \(a_{20}=-0.548153341\)
\(a_{21}=-0.157230428\) \(a_{22}=-0.154007755\) \(a_{23}=+0.663425771\) \(a_{24}=-0.070941484\) \(a_{25}=-0.593809414\)
\(a_{26}=+0.179065519\) \(a_{27}=-0.202857476\) \(a_{28}=+1.326323476\) \(a_{29}=-1.270822496\) \(a_{30}=+0.024307168\)
\(a_{31}=-0.223968760\) \(a_{32}=+0.920152817\) \(a_{33}=-0.041977997\) \(a_{34}=-0.205195223\) \(a_{35}=-0.982827377\)
\(a_{36}=+0.851135621\) \(a_{37}=-0.108741557\) \(a_{38}=+0.385653385\) \(a_{39}=+0.048808009\) \(a_{40}=-0.443446176\)
\(a_{41}=-0.419097540\) \(a_{42}=-0.058814140\) \(a_{43}=+0.848150865\) \(a_{44}=+0.354107050\) \(a_{45}=-0.630705408\)
\(a_{46}=+0.248163264\) \(a_{47}=-1.086301666\) \(a_{48}=+0.061155682\) \(a_{49}=+1.378070014\) \(a_{50}=-0.222122337\)
\(a_{51}=-0.055930200\) \(a_{52}=-0.411721882\) \(a_{53}=-0.220437332\) \(a_{54}=-0.075881546\) \(a_{55}=-0.262399112\)
\(a_{56}=+1.072971793\) \(a_{57}=+0.105117803\) \(a_{58}=-0.475368120\) \(a_{59}=+0.113545005\) \(a_{60}=-0.055889001\)
\(a_{61}=-0.989820518\) \(a_{62}=-0.083778504\) \(a_{63}=+1.526068214\) \(a_{64}=-0.255612950\) \(a_{65}=+0.305092645\)
\(a_{66}=-0.015702430\) \(a_{67}=-1.452568060\) \(a_{68}=+0.471801403\) \(a_{69}=+0.067642028\) \(a_{70}=-0.367639698\)
\(a_{71}=+0.970402832\) \(a_{72}=+0.688553382\) \(a_{73}=-0.848806889\) \(a_{74}=-0.040676231\) \(a_{75}=-0.060544034\)
\(a_{76}=-0.886725362\) \(a_{77}=+0.634906472\) \(a_{78}=+0.018257287\) \(a_{79}=-0.126310868\) \(a_{80}=+0.382276380\)
\(a_{81}=+0.968921340\) \(a_{82}=-0.156769028\) \(a_{83}=-1.345371665\) \(a_{84}=+0.135230214\) \(a_{85}=-0.349612552\)
\(a_{86}=+0.317262151\) \(a_{87}=-0.129571407\) \(a_{88}=+0.286466224\) \(a_{89}=+1.369206135\) \(a_{90}=-0.235923776\)
\(a_{91}=-0.738208650\) \(a_{92}=-0.570596990\) \(a_{93}=-0.022835563\) \(a_{94}=-0.406345637\) \(a_{95}=+0.657077988\)
\(a_{96}=+0.093817582\) \(a_{97}=-0.200862068\) \(a_{98}=+0.515485482\) \(a_{99}=+0.407435686\) \(a_{100}=+0.510721592\)

Showing 100 of 5000 available coefficients

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