Properties

Level $47$
Weight $0$
Character 47.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 47 \)
Weight: \( 0 \)
Character: 47.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.585452143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.932839580\) \(a_{3}=-1.204621614\) \(a_{4}=-0.129810318\) \(a_{5}=-0.669840440\)
\(a_{6}=+1.123718720\) \(a_{7}=-0.764587451\) \(a_{8}=+1.053931782\) \(a_{9}=+0.451113232\) \(a_{10}=+0.624853675\)
\(a_{11}=+0.569742873\) \(a_{12}=+0.156372314\) \(a_{13}=-0.741853752\) \(a_{14}=+0.713237437\) \(a_{15}=+0.806904272\)
\(a_{16}=-0.853338964\) \(a_{17}=-0.953128820\) \(a_{18}=-0.420816278\) \(a_{19}=+0.359096952\) \(a_{20}=+0.086952200\)
\(a_{21}=+0.921038569\) \(a_{22}=-0.531478703\) \(a_{23}=-1.620622573\) \(a_{24}=-1.269589004\) \(a_{25}=-0.551313784\)
\(a_{26}=+0.692030542\) \(a_{27}=+0.661200864\) \(a_{28}=+0.099251340\) \(a_{29}=+0.955975347\) \(a_{30}=-0.752712242\)
\(a_{31}=-0.254740207\) \(a_{32}=-0.257903422\) \(a_{33}=-0.686324579\) \(a_{34}=+0.889116289\) \(a_{35}=+0.512151595\)
\(a_{36}=-0.058559152\) \(a_{37}=+0.419328810\) \(a_{38}=-0.334979850\) \(a_{39}=+0.893653064\) \(a_{40}=-0.705966129\)
\(a_{41}=+0.695719166\) \(a_{42}=-0.859181232\) \(a_{43}=+0.966399548\) \(a_{44}=-0.073958503\) \(a_{45}=-0.302173886\)
\(a_{46}=+1.511780880\) \(a_{47}=-0.145864992\) \(a_{48}=+1.027950559\) \(a_{49}=-0.415406030\) \(a_{50}=+0.514287319\)
\(a_{51}=+1.148159578\) \(a_{52}=+0.096300271\) \(a_{53}=-0.550046401\) \(a_{54}=-0.616794337\) \(a_{55}=-0.381636817\)
\(a_{56}=-0.805823015\) \(a_{57}=-0.432575950\) \(a_{58}=-0.891771641\) \(a_{59}=-0.830234554\) \(a_{60}=-0.104744500\)
\(a_{61}=-1.703430326\) \(a_{62}=+0.237631748\) \(a_{63}=-0.344915516\) \(a_{64}=+1.093921483\) \(a_{65}=+0.496923644\)
\(a_{66}=+0.640230733\) \(a_{67}=-0.366650533\) \(a_{68}=+0.123725955\) \(a_{69}=+1.952236978\) \(a_{70}=-0.477755279\)
\(a_{71}=-1.913214018\) \(a_{72}=+0.475442573\) \(a_{73}=+1.219239885\) \(a_{74}=-0.391166511\) \(a_{75}=+0.664124501\)
\(a_{76}=-0.046614489\) \(a_{77}=-0.435618251\) \(a_{78}=-0.833634949\) \(a_{79}=+1.009185086\) \(a_{80}=+0.571600947\)
\(a_{81}=-1.247610084\) \(a_{82}=-0.648994375\) \(a_{83}=-0.610446887\) \(a_{84}=-0.119560309\) \(a_{85}=+0.638444229\)
\(a_{86}=-0.901495749\) \(a_{87}=-1.151588565\) \(a_{88}=+0.600470122\) \(a_{89}=+0.284561416\) \(a_{90}=+0.281879761\)
\(a_{91}=+0.567212069\) \(a_{92}=+0.210373531\) \(a_{93}=+0.306865559\) \(a_{94}=+0.136068637\) \(a_{95}=-0.240537661\)
\(a_{96}=+0.310676036\) \(a_{97}=+0.124177393\) \(a_{98}=+0.387507187\) \(a_{99}=+0.257018549\) \(a_{100}=+0.071566217\)

Showing 100 of 546 available coefficients

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