Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.17455185368 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.709991130\) \(a_{3}=+0.577350269\) \(a_{4}=-0.495912595\) \(a_{5}=+0.650509130\)
\(a_{6}=+0.409913570\) \(a_{7}=+0.581748748\) \(a_{8}=-1.062084674\) \(a_{9}=+0.333333333\) \(a_{10}=+0.461855712\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.286315270\) \(a_{13}=+1.008991779\) \(a_{14}=+0.413036451\) \(a_{15}=+0.375571621\)
\(a_{16}=-0.258158102\) \(a_{17}=-1.865125864\) \(a_{18}=+0.236663710\) \(a_{19}=-0.006886468\) \(a_{20}=-0.322595671\)
\(a_{21}=+0.335872796\) \(a_{22}=+0.214070380\) \(a_{23}=-0.517362956\) \(a_{24}=-0.613194872\) \(a_{25}=-0.576837872\)
\(a_{26}=+0.716375213\) \(a_{27}=+0.192450090\) \(a_{28}=-0.288496532\) \(a_{29}=+0.548697066\) \(a_{30}=+0.266652520\)
\(a_{31}=-0.221006123\) \(a_{32}=+0.878794711\) \(a_{33}=+0.174077656\) \(a_{34}=-1.324222820\) \(a_{35}=+0.378432872\)
\(a_{36}=-0.165304198\) \(a_{37}=+1.515886966\) \(a_{38}=-0.004889331\) \(a_{39}=+0.582541675\) \(a_{40}=-0.690895777\)
\(a_{41}=+0.498269387\) \(a_{42}=+0.238466706\) \(a_{43}=+1.319377625\) \(a_{44}=-0.149523273\) \(a_{45}=+0.216836377\)
\(a_{46}=-0.367323109\) \(a_{47}=-1.660384499\) \(a_{48}=-0.149047650\) \(a_{49}=-0.661568394\) \(a_{50}=-0.409549772\)
\(a_{51}=-1.076830920\) \(a_{52}=-0.500371732\) \(a_{53}=-0.062775331\) \(a_{54}=+0.136637857\) \(a_{55}=+0.196135882\)
\(a_{56}=-0.617866429\) \(a_{57}=-0.003975904\) \(a_{58}=+0.389570050\) \(a_{59}=-0.774793082\) \(a_{60}=-0.186250697\)
\(a_{61}=+1.575279810\) \(a_{62}=-0.156912387\) \(a_{63}=+0.193916249\) \(a_{64}=+0.882094552\) \(a_{65}=+0.656358364\)
\(a_{66}=+0.123593592\) \(a_{67}=-1.469206255\) \(a_{68}=+0.924939408\) \(a_{69}=-0.298699642\) \(a_{70}=+0.268683982\)
\(a_{71}=-0.152555364\) \(a_{72}=-0.354028225\) \(a_{73}=+1.746065558\) \(a_{74}=+1.076266300\) \(a_{75}=-0.333037501\)
\(a_{76}=+0.003415086\) \(a_{77}=+0.175403847\) \(a_{78}=+0.413599422\) \(a_{79}=-0.914466443\) \(a_{80}=-0.167934202\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.353766845\) \(a_{83}=-1.377128522\) \(a_{84}=-0.166563550\) \(a_{85}=-1.213281403\)
\(a_{86}=+0.936746411\) \(a_{87}=+0.316790399\) \(a_{88}=-0.320230578\) \(a_{89}=+0.391554227\) \(a_{90}=+0.153951904\)
\(a_{91}=+0.586979704\) \(a_{92}=+0.256566806\) \(a_{93}=-0.127597944\) \(a_{94}=-1.178858267\) \(a_{95}=-0.004479711\)
\(a_{96}=+0.507372363\) \(a_{97}=-1.144526787\) \(a_{98}=-0.469707692\) \(a_{99}=+0.100503782\) \(a_{100}=+0.286061166\)

Showing 100 of 270 available coefficients

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