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: \( 1.29657787881 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.317632273\) \(a_{3}=+0.577350269\) \(a_{4}=+0.736154806\) \(a_{5}=+0.971261146\)
\(a_{6}=-0.760735347\) \(a_{7}=+1.370690516\) \(a_{8}=+0.347650942\) \(a_{9}=+0.333333333\) \(a_{10}=-1.279765032\)
\(a_{11}=-0.519638488\) \(a_{12}=+0.425019176\) \(a_{13}=-0.883001832\) \(a_{14}=-1.806066060\) \(a_{15}=+0.560757884\)
\(a_{16}=-1.194230907\) \(a_{17}=-0.242535625\) \(a_{18}=-0.439210758\) \(a_{19}=+1.782933898\) \(a_{20}=+0.714998561\)
\(a_{21}=+0.791368539\) \(a_{22}=+0.684692442\) \(a_{23}=-1.167035397\) \(a_{24}=+0.200716365\) \(a_{25}=-0.056651785\)
\(a_{26}=+1.163471711\) \(a_{27}=+0.192450090\) \(a_{28}=+1.009040412\) \(a_{29}=-0.403962845\) \(a_{30}=-0.738872686\)
\(a_{31}=+0.409542727\) \(a_{32}=+1.225906243\) \(a_{33}=-0.300013421\) \(a_{34}=+0.319572767\) \(a_{35}=+1.331298442\)
\(a_{36}=+0.245384935\) \(a_{37}=-1.629604475\) \(a_{38}=-2.349251244\) \(a_{39}=-0.509801345\) \(a_{40}=+0.337659853\)
\(a_{41}=+0.035802557\) \(a_{42}=-1.042732726\) \(a_{43}=-0.588216875\) \(a_{44}=-0.382534370\) \(a_{45}=+0.323753715\)
\(a_{46}=+1.537723503\) \(a_{47}=-1.019873715\) \(a_{48}=-0.689489536\) \(a_{49}=+0.878792492\) \(a_{50}=+0.074646221\)
\(a_{51}=-0.140028008\) \(a_{52}=-0.650026043\) \(a_{53}=+1.021311940\) \(a_{54}=-0.253578449\) \(a_{55}=-0.504704674\)
\(a_{56}=+0.476521849\) \(a_{57}=+1.029377366\) \(a_{58}=+0.532274481\) \(a_{59}=+0.666276100\) \(a_{60}=+0.412804612\)
\(a_{61}=-1.071329450\) \(a_{62}=-0.539626715\) \(a_{63}=+0.456896839\) \(a_{64}=-0.421062721\) \(a_{65}=-0.857625372\)
\(a_{66}=+0.395307366\) \(a_{67}=+0.089757585\) \(a_{68}=-0.178543766\) \(a_{69}=-0.673788201\) \(a_{70}=-1.754161792\)
\(a_{71}=+0.133338060\) \(a_{72}=+0.115883647\) \(a_{73}=+1.117023791\) \(a_{74}=+2.147219448\) \(a_{75}=-0.032707924\)
\(a_{76}=+1.312515358\) \(a_{77}=-0.712263547\) \(a_{78}=+0.671730705\) \(a_{79}=+0.316412986\) \(a_{80}=-1.159910080\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.047174605\) \(a_{83}=-1.355724693\) \(a_{84}=+0.582569753\) \(a_{85}=-0.235565429\)
\(a_{86}=+0.775053538\) \(a_{87}=-0.233228057\) \(a_{88}=-0.180652810\) \(a_{89}=+0.491727190\) \(a_{90}=-0.426588344\)
\(a_{91}=-1.210322237\) \(a_{92}=-0.859118717\) \(a_{93}=+0.236449604\) \(a_{94}=+1.343818521\) \(a_{95}=+1.731694422\)
\(a_{96}=+0.707777299\) \(a_{97}=+0.861308443\) \(a_{98}=-1.157925348\) \(a_{99}=-0.173212829\) \(a_{100}=-0.041704484\)

Showing 100 of 432 available coefficients

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