Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 19.1254224082 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.764797899\) \(a_{4}=+0.500000000\) \(a_{5}=-0.759710449\)
\(a_{6}=+0.540793781\) \(a_{7}=-1.236306935\) \(a_{8}=-0.353553391\) \(a_{9}=-0.415084173\) \(a_{10}=+0.537196410\)
\(a_{11}=-1.302354948\) \(a_{12}=-0.382398950\) \(a_{13}=-0.417392355\) \(a_{14}=+0.874201017\) \(a_{15}=+0.581024955\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.919045763\) \(a_{18}=+0.293508833\) \(a_{19}=+0.491150904\) \(a_{20}=-0.379855224\)
\(a_{21}=+0.945524947\) \(a_{22}=+0.920904015\) \(a_{23}=-0.931973605\) \(a_{24}=+0.270396890\) \(a_{25}=-0.422840034\)
\(a_{26}=+0.295140964\) \(a_{27}=+1.082253403\) \(a_{28}=-0.618153468\) \(a_{29}=-0.378070479\) \(a_{30}=-0.410846686\)
\(a_{31}=+0.601448886\) \(a_{32}=-0.176776695\) \(a_{33}=+0.996038329\) \(a_{34}=-1.356970272\) \(a_{35}=+0.939235296\)
\(a_{36}=-0.207542086\) \(a_{37}=-0.482646598\) \(a_{38}=-0.347296135\) \(a_{39}=+0.319220796\) \(a_{40}=+0.268598205\)
\(a_{41}=+1.314729768\) \(a_{42}=-0.668587102\) \(a_{43}=-0.898523209\) \(a_{44}=-0.651177474\) \(a_{45}=+0.315343783\)
\(a_{46}=+0.659004856\) \(a_{47}=+0.265907428\) \(a_{48}=-0.191199475\) \(a_{49}=+0.528454838\) \(a_{50}=+0.298993056\)
\(a_{51}=-1.467682168\) \(a_{52}=-0.208696177\) \(a_{53}=+0.656527121\) \(a_{54}=-0.765268720\) \(a_{55}=+0.989412662\)
\(a_{56}=+0.437100509\) \(a_{57}=-0.375631180\) \(a_{58}=+0.267336199\) \(a_{59}=-0.366982782\) \(a_{60}=+0.290512478\)
\(a_{61}=-0.721600989\) \(a_{62}=-0.425288586\) \(a_{63}=+0.513171442\) \(a_{64}=+0.125000000\) \(a_{65}=+0.317097333\)
\(a_{66}=-0.704305457\) \(a_{67}=+0.320119418\) \(a_{68}=+0.959522881\) \(a_{69}=+0.712771455\) \(a_{70}=-0.664139647\)
\(a_{71}=-1.666126646\) \(a_{72}=+0.146754417\) \(a_{73}=-0.370313650\) \(a_{74}=+0.341282682\) \(a_{75}=+0.323387170\)
\(a_{76}=+0.245575452\) \(a_{77}=+1.610110455\) \(a_{78}=-0.225723190\) \(a_{79}=-0.847786299\) \(a_{80}=-0.189927612\)
\(a_{81}=-0.412620956\) \(a_{82}=-0.929654335\) \(a_{83}=+1.069815710\) \(a_{84}=+0.472762474\) \(a_{85}=-1.457919117\)
\(a_{86}=+0.635351854\) \(a_{87}=+0.289147508\) \(a_{88}=+0.460452008\) \(a_{89}=+0.276320863\) \(a_{90}=-0.222981728\)
\(a_{91}=+0.516025063\) \(a_{92}=-0.465986802\) \(a_{93}=-0.459986845\) \(a_{94}=-0.188024946\) \(a_{95}=-0.373132473\)
\(a_{96}=+0.135198445\) \(a_{97}=+0.252550882\) \(a_{98}=-0.373673999\) \(a_{99}=+0.540586927\) \(a_{100}=-0.211420017\)

Showing 100 of 1228 available coefficients

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