Properties

Level $66$
Weight $0$
Character 66.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( 0 \)
Character: 66.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.6107635037 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.117093768\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.520525051\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.789904579\)
\(a_{11}=-0.301511345\) \(a_{12}=-0.288675135\) \(a_{13}=+0.837420225\) \(a_{14}=+0.368066793\) \(a_{15}=+0.644954388\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.512067759\) \(a_{18}=-0.235702260\) \(a_{19}=-0.260974953\) \(a_{20}=-0.558546884\)
\(a_{21}=+0.300525278\) \(a_{22}=+0.213200716\) \(a_{23}=-0.790102795\) \(a_{24}=+0.204124145\) \(a_{25}=+0.247898488\)
\(a_{26}=-0.592145520\) \(a_{27}=-0.192450090\) \(a_{28}=-0.260262525\) \(a_{29}=+0.026115770\) \(a_{30}=-0.456051621\)
\(a_{31}=-1.199459037\) \(a_{32}=-0.176776695\) \(a_{33}=+0.174077656\) \(a_{34}=-1.069193366\) \(a_{35}=+0.581475291\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.373011302\) \(a_{38}=+0.184537159\) \(a_{39}=-0.483484793\) \(a_{40}=+0.394952289\)
\(a_{41}=+1.169370230\) \(a_{42}=-0.212503462\) \(a_{43}=-0.154862791\) \(a_{44}=-0.150755672\) \(a_{45}=-0.372364589\)
\(a_{46}=+0.558687044\) \(a_{47}=+0.907692892\) \(a_{48}=-0.144337567\) \(a_{49}=-0.729053671\) \(a_{50}=-0.175290702\)
\(a_{51}=-0.872992728\) \(a_{52}=+0.418710113\) \(a_{53}=-0.841839551\) \(a_{54}=+0.136082763\) \(a_{55}=+0.336816444\)
\(a_{56}=+0.184033397\) \(a_{57}=+0.150673959\) \(a_{58}=-0.018466638\) \(a_{59}=+1.174167284\) \(a_{60}=+0.322477194\)
\(a_{61}=+1.718020869\) \(a_{62}=+0.848145619\) \(a_{63}=-0.173508350\) \(a_{64}=+0.125000000\) \(a_{65}=-0.935476916\)
\(a_{66}=-0.123091491\) \(a_{67}=+1.477955620\) \(a_{68}=+0.756033879\) \(a_{69}=+0.456166061\) \(a_{70}=-0.411165121\)
\(a_{71}=-1.312576816\) \(a_{72}=-0.117851130\) \(a_{73}=-1.032925473\) \(a_{74}=+0.263758821\) \(a_{75}=-0.143124259\)
\(a_{76}=-0.130487476\) \(a_{77}=+0.156944208\) \(a_{78}=+0.341875375\) \(a_{79}=+0.227926452\) \(a_{80}=-0.279273442\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.826869619\) \(a_{83}=-1.234571465\) \(a_{84}=+0.150262639\) \(a_{85}=-1.689121471\)
\(a_{86}=+0.109504530\) \(a_{87}=-0.015077947\) \(a_{88}=+0.106600358\) \(a_{89}=+0.193585528\) \(a_{90}=+0.263301526\)
\(a_{91}=-0.435898205\) \(a_{92}=-0.395051397\) \(a_{93}=+0.692507998\) \(a_{94}=-0.641835799\) \(a_{95}=+0.291533493\)
\(a_{96}=+0.102062073\) \(a_{97}=+1.778703769\) \(a_{98}=+0.515518795\) \(a_{99}=-0.100503782\) \(a_{100}=+0.123949244\)

Showing 100 of 822 available coefficients

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