Properties

Level $853$
Weight $0$
Character 853.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 853 \)
Weight: \( 0 \)
Character: 853.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.3818974926 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.255237571\) \(a_{3}=-1.623675385\) \(a_{4}=+0.575621527\) \(a_{5}=+1.467711267\)
\(a_{6}=-2.038098255\) \(a_{7}=+1.271586027\) \(a_{8}=-0.532695783\) \(a_{9}=+1.636321758\) \(a_{10}=+1.842326482\)
\(a_{11}=-1.082637791\) \(a_{12}=-0.934622482\) \(a_{13}=+1.067526589\) \(a_{14}=+1.596142810\) \(a_{15}=-2.383086697\)
\(a_{16}=-1.244281286\) \(a_{17}=-0.555140881\) \(a_{18}=+2.053972543\) \(a_{19}=+1.349729819\) \(a_{20}=+0.844846180\)
\(a_{21}=-2.064642993\) \(a_{22}=-1.358967507\) \(a_{23}=+0.426090348\) \(a_{24}=+0.864924936\) \(a_{25}=+1.154176465\)
\(a_{26}=+1.339999582\) \(a_{27}=-1.033180037\) \(a_{28}=+0.731952354\) \(a_{29}=+0.566962094\) \(a_{30}=-2.991340043\)
\(a_{31}=+0.635113046\) \(a_{32}=-1.029172993\) \(a_{33}=+1.757852346\) \(a_{34}=-0.696833598\) \(a_{35}=+1.866321312\)
\(a_{36}=+0.941901957\) \(a_{37}=+0.179961874\) \(a_{38}=+1.694231796\) \(a_{39}=-1.733316621\) \(a_{40}=-0.781843641\)
\(a_{41}=-0.169537457\) \(a_{42}=-2.591617609\) \(a_{43}=+0.959441390\) \(a_{44}=-0.623189621\) \(a_{45}=+2.401647872\)
\(a_{46}=+0.534844746\) \(a_{47}=+1.689710038\) \(a_{48}=+2.020309093\) \(a_{49}=+0.616931174\) \(a_{50}=+1.448765941\)
\(a_{51}=+0.901368488\) \(a_{52}=+0.614491270\) \(a_{53}=-1.208489475\) \(a_{54}=-1.296886358\) \(a_{55}=-1.588999505\)
\(a_{56}=-0.677368691\) \(a_{57}=-2.191523072\) \(a_{58}=+0.711672167\) \(a_{59}=+1.665818605\) \(a_{60}=-1.371756019\)
\(a_{61}=+0.561029658\) \(a_{62}=+0.797217634\) \(a_{63}=+2.080723987\) \(a_{64}=-0.047575333\) \(a_{65}=+1.566820783\)
\(a_{66}=+2.206522062\) \(a_{67}=-1.672665185\) \(a_{68}=-0.319551040\) \(a_{69}=-0.691832270\) \(a_{70}=+2.342676781\)
\(a_{71}=+0.289798893\) \(a_{72}=-0.871661642\) \(a_{73}=+0.588491953\) \(a_{74}=+0.225894929\) \(a_{75}=-1.874008049\)
\(a_{76}=+0.776933609\) \(a_{77}=-1.376666997\) \(a_{78}=-2.175724218\) \(a_{79}=-1.364754024\) \(a_{80}=-1.826245769\)
\(a_{81}=+0.041227186\) \(a_{82}=-0.212809867\) \(a_{83}=-1.187973098\) \(a_{84}=-1.188453112\) \(a_{85}=-0.814786518\)
\(a_{86}=+1.204326922\) \(a_{87}=-0.920562231\) \(a_{88}=+0.576716423\) \(a_{89}=+0.006012603\) \(a_{90}=+3.014638985\)
\(a_{91}=+1.357451952\) \(a_{92}=+0.245266897\) \(a_{93}=-1.031217394\) \(a_{94}=+2.120987888\) \(a_{95}=+1.981013811\)
\(a_{96}=+1.671042890\) \(a_{97}=-0.286953660\) \(a_{98}=+0.774395534\) \(a_{99}=-1.771543687\) \(a_{100}=+0.664368825\)

Showing 100 of 2160 available coefficients

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