Properties

Level $57$
Weight $0$
Character 57.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 57 = 3 \cdot 19 \)
Weight: \( 0 \)
Character: 57.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.8770038522 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.194072127\) \(a_{3}=-0.577350269\) \(a_{4}=-0.962336010\) \(a_{5}=-0.742828367\)
\(a_{6}=+0.112047595\) \(a_{7}=+1.644258576\) \(a_{8}=+0.380834723\) \(a_{9}=+0.333333333\) \(a_{10}=+0.144162281\)
\(a_{11}=-1.263721329\) \(a_{12}=+0.555604954\) \(a_{13}=+0.312874135\) \(a_{14}=-0.319104759\) \(a_{15}=+0.428872158\)
\(a_{16}=+0.888426605\) \(a_{17}=+0.502922254\) \(a_{18}=-0.064690709\) \(a_{19}=-0.229415734\) \(a_{20}=+0.714850487\)
\(a_{21}=-0.949313132\) \(a_{22}=+0.245253086\) \(a_{23}=-0.534495327\) \(a_{24}=-0.219875030\) \(a_{25}=-0.448206016\)
\(a_{26}=-0.060720149\) \(a_{27}=-0.192450090\) \(a_{28}=-1.582329237\) \(a_{29}=+1.619199481\) \(a_{30}=-0.083232132\)
\(a_{31}=-0.578881532\) \(a_{32}=-0.553253564\) \(a_{33}=+0.729609850\) \(a_{34}=-0.097603192\) \(a_{35}=-1.221401914\)
\(a_{36}=-0.320778670\) \(a_{37}=+1.046994175\) \(a_{38}=+0.044523199\) \(a_{39}=-0.180637966\) \(a_{40}=-0.282894836\)
\(a_{41}=+0.055132370\) \(a_{42}=+0.184235219\) \(a_{43}=-0.571936176\) \(a_{44}=+1.216124541\) \(a_{45}=-0.247609456\)
\(a_{46}=+0.103730645\) \(a_{47}=-0.337575246\) \(a_{48}=-0.512933339\) \(a_{49}=+1.703586265\) \(a_{50}=+0.086984295\)
\(a_{51}=-0.290362299\) \(a_{52}=-0.301090046\) \(a_{53}=+1.217745535\) \(a_{54}=+0.037349198\) \(a_{55}=+0.938728052\)
\(a_{56}=+0.626190760\) \(a_{57}=+0.132453236\) \(a_{58}=-0.314241487\) \(a_{59}=+0.312966198\) \(a_{60}=-0.412719121\)
\(a_{61}=-1.195653517\) \(a_{62}=+0.112344770\) \(a_{63}=+0.548086192\) \(a_{64}=-0.781055509\) \(a_{65}=-0.232411783\)
\(a_{66}=-0.141596935\) \(a_{67}=+0.547651550\) \(a_{68}=-0.483980195\) \(a_{69}=+0.308591021\) \(a_{70}=+0.237040067\)
\(a_{71}=+0.757571164\) \(a_{72}=+0.126944908\) \(a_{73}=+0.606221008\) \(a_{74}=-0.203192386\) \(a_{75}=+0.258771864\)
\(a_{76}=+0.220775022\) \(a_{77}=-2.077884633\) \(a_{78}=+0.035056794\) \(a_{79}=-0.692558845\) \(a_{80}=-0.659948484\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.010699656\) \(a_{83}=-1.117198015\) \(a_{84}=+0.913558211\) \(a_{85}=-0.373584917\)
\(a_{86}=+0.110996870\) \(a_{87}=-0.934845256\) \(a_{88}=-0.481268963\) \(a_{89}=-0.334359242\) \(a_{90}=+0.048054094\)
\(a_{91}=+0.514445979\) \(a_{92}=+0.514364100\) \(a_{93}=+0.334217408\) \(a_{94}=+0.065513946\) \(a_{95}=+0.170416515\)
\(a_{96}=+0.319421094\) \(a_{97}=+0.412609841\) \(a_{98}=-0.330618610\) \(a_{99}=-0.421240443\) \(a_{100}=+0.431324789\)

Showing 100 of 442 available coefficients

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