The even Maass form of level 2 with the smallest eigenvalue (the 4th smallest overall of level 2).
Maass form invariants
| Level: | \( 2 \) |
| Weight: | \( 0 \) |
| Character: | 2.1 |
| Symmetry: | even |
| Fricke sign: | $+1$ |
| Spectral parameter: | \( 8.92287648699 \) |
Maass form coefficients
| \(a_{1}=+1.000000000\) | \(a_{2}=-0.707106781\) | \(a_{3}=+1.103788996\) | \(a_{4}=+0.500000000\) | \(a_{5}=+0.904174593\) |
| \(a_{6}=-0.780496684\) | \(a_{7}=+0.829342468\) | \(a_{8}=-0.353553391\) | \(a_{9}=+0.218350147\) | \(a_{10}=-0.639347986\) |
| \(a_{11}=+0.567236139\) | \(a_{12}=+0.551894498\) | \(a_{13}=-0.828347540\) | \(a_{14}=-0.586433683\) | \(a_{15}=+0.998017966\) |
| \(a_{16}=+0.250000000\) | \(a_{17}=-0.310250241\) | \(a_{18}=-0.154396870\) | \(a_{19}=-0.736937970\) | \(a_{20}=+0.452087296\) |
| \(a_{21}=+0.915419089\) | \(a_{22}=-0.401096520\) | \(a_{23}=-0.063502297\) | \(a_{24}=-0.390248342\) | \(a_{25}=-0.182468306\) |
| \(a_{26}=+0.585730163\) | \(a_{27}=-0.862776506\) | \(a_{28}=+0.414671234\) | \(a_{29}=+1.748708967\) | \(a_{30}=-0.705705271\) |
| \(a_{31}=-1.586616066\) | \(a_{32}=-0.176776695\) | \(a_{33}=+0.626109008\) | \(a_{34}=+0.219380049\) | \(a_{35}=+0.749870388\) |
| \(a_{36}=+0.109175073\) | \(a_{37}=-0.754632964\) | \(a_{38}=+0.521093836\) | \(a_{39}=-0.914320899\) | \(a_{40}=-0.319673993\) |
| \(a_{41}=+0.740022536\) | \(a_{42}=-0.647299046\) | \(a_{43}=+0.789726181\) | \(a_{44}=+0.283618069\) | \(a_{45}=+0.197426655\) |
| \(a_{46}=+0.044902905\) | \(a_{47}=-0.984144061\) | \(a_{48}=+0.275947249\) | \(a_{49}=-0.312191071\) | \(a_{50}=+0.129024575\) |
| \(a_{51}=-0.342450803\) | \(a_{52}=-0.414173766\) | \(a_{53}=+1.153805608\) | \(a_{54}=+0.610075113\) | \(a_{55}=+0.512880501\) |
| \(a_{56}=-0.293216841\) | \(a_{57}=-0.813424022\) | \(a_{58}=-1.236523969\) | \(a_{59}=-0.144663126\) | \(a_{60}=+0.499008983\) |
| \(a_{61}=+0.070461491\) | \(a_{62}=+1.121906980\) | \(a_{63}=+0.181087050\) | \(a_{64}=+0.125000000\) | \(a_{65}=-0.748970800\) |
| \(a_{66}=-0.442725925\) | \(a_{67}=+0.942457929\) | \(a_{68}=-0.155125120\) | \(a_{69}=-0.070093137\) | \(a_{70}=-0.530238436\) |
| \(a_{71}=-1.115327822\) | \(a_{72}=-0.077198435\) | \(a_{73}=+1.423475007\) | \(a_{74}=+0.533606086\) | \(a_{75}=-0.201406508\) |
| \(a_{76}=-0.368468985\) | \(a_{77}=+0.470433019\) | \(a_{78}=+0.646522508\) | \(a_{79}=-0.686599912\) | \(a_{80}=+0.226043648\) |
| \(a_{81}=-1.170673360\) | \(a_{82}=-0.523274954\) | \(a_{83}=+0.225461110\) | \(a_{84}=+0.457709544\) | \(a_{85}=-0.280520385\) |
| \(a_{86}=-0.558420738\) | \(a_{87}=+1.930205714\) | \(a_{88}=-0.200548260\) | \(a_{89}=+0.894534288\) | \(a_{90}=-0.139601726\) |
| \(a_{91}=-0.686983793\) | \(a_{92}=-0.031751151\) | \(a_{93}=-1.751289352\) | \(a_{94}=+0.695894943\) | \(a_{95}=-0.666320588\) |
| \(a_{96}=-0.195124180\) | \(a_{97}=+1.477250543\) | \(a_{98}=+0.220752424\) | \(a_{99}=+0.123856094\) | \(a_{100}=-0.091234153\) |
Showing 100 of 5000 available coefficients