Properties

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

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 11.3176797015 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.843438657\) \(a_{4}=+0.500000000\) \(a_{5}=-1.378525686\)
\(a_{6}=-0.596401194\) \(a_{7}=-0.587419700\) \(a_{8}=-0.353553391\) \(a_{9}=-0.288611232\) \(a_{10}=+0.974764867\)
\(a_{11}=-1.365536696\) \(a_{12}=+0.421719329\) \(a_{13}=+0.365405945\) \(a_{14}=+0.415368454\) \(a_{15}=-1.162701854\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.352228335\) \(a_{18}=+0.204078959\) \(a_{19}=+0.211187315\) \(a_{20}=-0.689262843\)
\(a_{21}=-0.495452483\) \(a_{22}=+0.965580258\) \(a_{23}=-0.163003313\) \(a_{24}=-0.298200597\) \(a_{25}=+0.900333067\)
\(a_{26}=-0.258381021\) \(a_{27}=-1.086864527\) \(a_{28}=-0.293709850\) \(a_{29}=+0.810691114\) \(a_{30}=+0.822154365\)
\(a_{31}=+0.036510354\) \(a_{32}=-0.176776695\) \(a_{33}=-1.151746438\) \(a_{34}=-0.249063044\) \(a_{35}=+0.809773145\)
\(a_{36}=-0.144305616\) \(a_{37}=+0.491858362\) \(a_{38}=-0.149331982\) \(a_{39}=+0.308197499\) \(a_{40}=+0.487382430\)
\(a_{41}=-1.824341116\) \(a_{42}=+0.350337811\) \(a_{43}=+0.647189650\) \(a_{44}=-0.682768348\) \(a_{45}=+0.397857995\)
\(a_{46}=+0.115260748\) \(a_{47}=+0.736090241\) \(a_{48}=+0.210859664\) \(a_{49}=-0.654938094\) \(a_{50}=-0.636631619\)
\(a_{51}=+0.297082992\) \(a_{52}=+0.182702979\) \(a_{53}=-1.864705872\) \(a_{54}=+0.768529267\) \(a_{55}=+1.882427418\)
\(a_{56}=+0.207684224\) \(a_{57}=+0.178123545\) \(a_{58}=-0.573245184\) \(a_{59}=-1.211715111\) \(a_{60}=-0.581350927\)
\(a_{61}=+0.834987944\) \(a_{62}=-0.025816719\) \(a_{63}=+0.169535923\) \(a_{64}=+0.125000000\) \(a_{65}=-0.503721481\)
\(a_{66}=+0.814407716\) \(a_{67}=+0.209925954\) \(a_{68}=+0.176114167\) \(a_{69}=-0.137483295\) \(a_{70}=-0.572596082\)
\(a_{71}=+0.015703382\) \(a_{72}=+0.102039479\) \(a_{73}=-0.928791330\) \(a_{74}=-0.347796384\) \(a_{75}=+0.759375713\)
\(a_{76}=+0.105593657\) \(a_{77}=+0.802143157\) \(a_{78}=-0.217928542\) \(a_{79}=+0.721097479\) \(a_{80}=-0.344631422\)
\(a_{81}=-0.628092326\) \(a_{82}=+1.290003975\) \(a_{83}=-1.636079008\) \(a_{84}=-0.247726242\) \(a_{85}=-0.485555807\)
\(a_{86}=-0.457632191\) \(a_{87}=+0.683768225\) \(a_{88}=+0.482790131\) \(a_{89}=+1.522632806\) \(a_{90}=-0.281328088\)
\(a_{91}=-0.214646651\) \(a_{92}=-0.081501654\) \(a_{93}=+0.030794247\) \(a_{94}=-0.520494405\) \(a_{95}=-0.291127136\)
\(a_{96}=-0.149100305\) \(a_{97}=-0.729130550\) \(a_{98}=+0.463111208\) \(a_{99}=+0.394109207\) \(a_{100}=+0.450166533\)

Showing 100 of 5000 available coefficients

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