Properties

Level $51$
Weight $0$
Character 51.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.4662620621 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.190713455\) \(a_{3}=-0.577350269\) \(a_{4}=-0.963628378\) \(a_{5}=-0.016452947\)
\(a_{6}=-0.110108464\) \(a_{7}=+0.929585089\) \(a_{8}=-0.374490352\) \(a_{9}=+0.333333333\) \(a_{10}=-0.003137798\)
\(a_{11}=+0.427532975\) \(a_{12}=+0.556351104\) \(a_{13}=+0.934419361\) \(a_{14}=+0.177284384\) \(a_{15}=+0.009499113\)
\(a_{16}=+0.892208029\) \(a_{17}=+0.242535625\) \(a_{18}=+0.063571152\) \(a_{19}=-0.413617119\) \(a_{20}=+0.015854527\)
\(a_{21}=-0.536696201\) \(a_{22}=+0.081536291\) \(a_{23}=+0.689375562\) \(a_{24}=+0.216212105\) \(a_{25}=-0.999729301\)
\(a_{26}=+0.178206345\) \(a_{27}=-0.192450090\) \(a_{28}=-0.895774571\) \(a_{29}=+0.298509923\) \(a_{30}=+0.001811609\)
\(a_{31}=+0.622799855\) \(a_{32}=+0.544646428\) \(a_{33}=-0.246836278\) \(a_{34}=+0.046254807\) \(a_{35}=-0.015294414\)
\(a_{36}=-0.321209459\) \(a_{37}=+1.632397507\) \(a_{38}=-0.078882350\) \(a_{39}=-0.539487270\) \(a_{40}=+0.006161470\)
\(a_{41}=+1.450041562\) \(a_{42}=-0.102355187\) \(a_{43}=+0.338786522\) \(a_{44}=-0.411982908\) \(a_{45}=-0.005484316\)
\(a_{46}=+0.131473195\) \(a_{47}=+0.426070166\) \(a_{48}=-0.515116546\) \(a_{49}=-0.135871563\) \(a_{50}=-0.190661829\)
\(a_{51}=-0.140028008\) \(a_{52}=-0.900433014\) \(a_{53}=+1.281561523\) \(a_{54}=-0.036702821\) \(a_{55}=-0.007034177\)
\(a_{56}=-0.348120647\) \(a_{57}=+0.238801955\) \(a_{58}=+0.056929859\) \(a_{59}=-0.483207482\) \(a_{60}=-0.009153615\)
\(a_{61}=-1.258591782\) \(a_{62}=+0.118776312\) \(a_{63}=+0.309861696\) \(a_{64}=-0.788336628\) \(a_{65}=-0.015373952\)
\(a_{66}=-0.047074999\) \(a_{67}=-1.517729796\) \(a_{68}=-0.233714211\) \(a_{69}=-0.398011166\) \(a_{70}=-0.002916851\)
\(a_{71}=+0.788985138\) \(a_{72}=-0.124830117\) \(a_{73}=+0.746238323\) \(a_{74}=+0.311320168\) \(a_{75}=+0.577193981\)
\(a_{76}=+0.398573194\) \(a_{77}=+0.397428279\) \(a_{78}=-0.102887481\) \(a_{79}=-0.558595606\) \(a_{80}=-0.014679451\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.276542436\) \(a_{83}=+1.600575062\) \(a_{84}=+0.517175690\) \(a_{85}=-0.003990426\)
\(a_{86}=+0.064611148\) \(a_{87}=-0.172344784\) \(a_{88}=-0.160106974\) \(a_{89}=-0.697762049\) \(a_{90}=-0.001045933\)
\(a_{91}=+0.868622305\) \(a_{92}=-0.664301855\) \(a_{93}=-0.359573664\) \(a_{94}=+0.081257313\) \(a_{95}=+0.006805220\)
\(a_{96}=-0.314451762\) \(a_{97}=-0.483225228\) \(a_{98}=-0.025912535\) \(a_{99}=+0.142510992\) \(a_{100}=+0.963367524\)

Showing 100 of 462 available coefficients

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