Properties

Level $66$
Weight $0$
Character 66.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( 0 \)
Character: 66.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.8925227298 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.600123655\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.896097970\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.131458287\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.288675135\) \(a_{13}=-1.160691150\) \(a_{14}=-0.633636951\) \(a_{15}=-0.923831823\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.131883507\) \(a_{18}=-0.235702260\) \(a_{19}=+0.521438682\) \(a_{20}=+0.800061827\)
\(a_{21}=-0.517362404\) \(a_{22}=-0.213200716\) \(a_{23}=-1.545378657\) \(a_{24}=+0.204124145\) \(a_{25}=+1.560395711\)
\(a_{26}=+0.820732583\) \(a_{27}=-0.192450090\) \(a_{28}=+0.448048985\) \(a_{29}=-0.857770359\) \(a_{30}=+0.653247747\)
\(a_{31}=+0.105870504\) \(a_{32}=-0.176776695\) \(a_{33}=-0.174077656\) \(a_{34}=-0.093255722\) \(a_{35}=+1.433867559\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.047915396\) \(a_{38}=-0.368712828\) \(a_{39}=+0.670125348\) \(a_{40}=-0.565729144\)
\(a_{41}=+0.797171768\) \(a_{42}=+0.365830464\) \(a_{43}=-0.578904318\) \(a_{44}=+0.150755672\) \(a_{45}=+0.533374552\)
\(a_{46}=+1.092747728\) \(a_{47}=-0.662817194\) \(a_{48}=-0.144337567\) \(a_{49}=-0.197008428\) \(a_{50}=-1.103366388\)
\(a_{51}=-0.076142978\) \(a_{52}=-0.580345575\) \(a_{53}=-1.539363268\) \(a_{54}=+0.136082763\) \(a_{55}=+0.482455435\)
\(a_{56}=-0.316818476\) \(a_{57}=-0.301052763\) \(a_{58}=+0.606535238\) \(a_{59}=+0.378623782\) \(a_{60}=-0.461915911\)
\(a_{61}=-0.276254073\) \(a_{62}=-0.074861751\) \(a_{63}=+0.298699323\) \(a_{64}=+0.125000000\) \(a_{65}=-1.857249365\)
\(a_{66}=+0.123091491\) \(a_{67}=-0.911002705\) \(a_{68}=+0.065941753\) \(a_{69}=+0.892224783\) \(a_{70}=-1.013897474\)
\(a_{71}=+1.651260828\) \(a_{72}=-0.117851130\) \(a_{73}=+1.348508061\) \(a_{74}=-0.033881301\) \(a_{75}=-0.900894884\)
\(a_{76}=+0.260719341\) \(a_{77}=+0.270183704\) \(a_{78}=-0.473850178\) \(a_{79}=-0.579731021\) \(a_{80}=+0.400030914\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.563685563\) \(a_{83}=+0.809300295\) \(a_{84}=-0.258681202\) \(a_{85}=+0.211029919\)
\(a_{86}=+0.409347169\) \(a_{87}=+0.495233948\) \(a_{88}=-0.106600358\) \(a_{89}=+1.034227270\) \(a_{90}=-0.377152762\)
\(a_{91}=-1.040092983\) \(a_{92}=-0.772689328\) \(a_{93}=-0.061124364\) \(a_{94}=+0.468682532\) \(a_{95}=+0.834366369\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.604016169\) \(a_{98}=+0.139305996\) \(a_{99}=+0.100503782\) \(a_{100}=+0.780197855\)

Showing 100 of 852 available coefficients

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