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: \( 0.806534894318 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.988258675\) \(a_{3}=+0.577350269\) \(a_{4}=-0.023344791\) \(a_{5}=-1.315909813\)
\(a_{6}=+0.570571412\) \(a_{7}=+0.311274223\) \(a_{8}=-1.011329367\) \(a_{9}=+0.333333333\) \(a_{10}=-1.300459289\)
\(a_{11}=+1.778801645\) \(a_{12}=-0.013478121\) \(a_{13}=-0.179352670\) \(a_{14}=+0.307619451\) \(a_{15}=-0.759740885\)
\(a_{16}=-0.976110230\) \(a_{17}=-0.242535625\) \(a_{18}=+0.329419558\) \(a_{19}=-0.471027944\) \(a_{20}=+0.030719639\)
\(a_{21}=+0.179714257\) \(a_{22}=+1.757916157\) \(a_{23}=+0.316587219\) \(a_{24}=-0.583891282\) \(a_{25}=+0.731618636\)
\(a_{26}=-0.177246832\) \(a_{27}=+0.192450090\) \(a_{28}=-0.007266632\) \(a_{29}=-0.153899241\) \(a_{30}=-0.750820520\)
\(a_{31}=+0.193275314\) \(a_{32}=+0.046679964\) \(a_{33}=+1.026991609\) \(a_{34}=-0.239687936\) \(a_{35}=-0.409608805\)
\(a_{36}=-0.007781597\) \(a_{37}=+0.936713895\) \(a_{38}=-0.465497452\) \(a_{39}=-0.103549312\) \(a_{40}=+1.330818238\)
\(a_{41}=-0.541075881\) \(a_{42}=+0.177604173\) \(a_{43}=+0.008861308\) \(a_{44}=-0.041525752\) \(a_{45}=-0.438636604\)
\(a_{46}=+0.312870065\) \(a_{47}=-1.516242717\) \(a_{48}=-0.563557504\) \(a_{49}=-0.903108358\) \(a_{50}=+0.723028464\)
\(a_{51}=-0.140028008\) \(a_{52}=+0.004186951\) \(a_{53}=-0.209381196\) \(a_{54}=+0.190190471\) \(a_{55}=-2.340742540\)
\(a_{56}=-0.314800763\) \(a_{57}=-0.271948110\) \(a_{58}=-0.152092260\) \(a_{59}=+1.191216567\) \(a_{60}=+0.017735992\)
\(a_{61}=+0.778970309\) \(a_{62}=+0.191006006\) \(a_{63}=+0.103758074\) \(a_{64}=+1.022242110\) \(a_{65}=+0.236011938\)
\(a_{66}=+1.014933367\) \(a_{67}=-1.193792643\) \(a_{68}=+0.005661943\) \(a_{69}=+0.182781716\) \(a_{70}=-0.404799455\)
\(a_{71}=-1.144986079\) \(a_{72}=-0.337109789\) \(a_{73}=+0.349154665\) \(a_{74}=+0.925715633\) \(a_{75}=+0.422400216\)
\(a_{76}=+0.010996049\) \(a_{77}=+0.553695100\) \(a_{78}=-0.102333506\) \(a_{79}=+1.509298333\) \(a_{80}=+1.284473030\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.534722934\) \(a_{83}=+1.434619752\) \(a_{84}=-0.004195392\) \(a_{85}=+0.319155009\)
\(a_{86}=+0.008757264\) \(a_{87}=-0.088853768\) \(a_{88}=-1.798954342\) \(a_{89}=+0.797590353\) \(a_{90}=-0.433486430\)
\(a_{91}=-0.055827863\) \(a_{92}=-0.007390662\) \(a_{93}=+0.111587554\) \(a_{94}=-1.498440019\) \(a_{95}=+0.619830294\)
\(a_{96}=+0.026950690\) \(a_{97}=-0.289664005\) \(a_{98}=-0.892504670\) \(a_{99}=+0.592933882\) \(a_{100}=-0.017079484\)

Showing 100 of 408 available coefficients

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