The even Maass form on $SL(2, \Z)$ with the smallest eigenvalue.
Maass form invariants
| Level: | \( 1 \) |
| Weight: | \( 0 \) |
| Character: | 1.1 |
| Symmetry: | even |
| Fricke sign: | $+1$ |
| Spectral parameter: | \( 13.7797513519 \) |
Maass form coefficients
| \(a_{1}=+1.000000000\) | \(a_{2}=+1.549304478\) | \(a_{3}=+0.246899772\) | \(a_{4}=+1.400344365\) | \(a_{5}=+0.737060385\) |
| \(a_{6}=+0.382522923\) | \(a_{7}=-0.261420076\) | \(a_{8}=+0.620255318\) | \(a_{9}=-0.939040503\) | \(a_{10}=+1.141930962\) |
| \(a_{11}=-0.953564653\) | \(a_{12}=+0.345744705\) | \(a_{13}=+0.278827029\) | \(a_{14}=-0.405019294\) | \(a_{15}=+0.181980041\) |
| \(a_{16}=-0.439380024\) | \(a_{17}=+1.307341715\) | \(a_{18}=-1.454859655\) | \(a_{19}=+0.092558583\) | \(a_{20}=+1.032138358\) |
| \(a_{21}=-0.064544557\) | \(a_{22}=-1.477361986\) | \(a_{23}=+1.138068521\) | \(a_{24}=+0.153140897\) | \(a_{25}=-0.456741988\) |
| \(a_{26}=+0.431987965\) | \(a_{27}=-0.478748659\) | \(a_{28}=-0.366078130\) | \(a_{29}=+0.752113845\) | \(a_{30}=+0.281942493\) |
| \(a_{31}=+0.024851954\) | \(a_{32}=-1.300988756\) | \(a_{33}=-0.235434896\) | \(a_{34}=+2.025470373\) | \(a_{35}=-0.192682382\) |
| \(a_{36}=-1.314980076\) | \(a_{37}=+0.199265656\) | \(a_{38}=+0.143401426\) | \(a_{39}=+0.068842330\) | \(a_{40}=+0.457165624\) |
| \(a_{41}=-0.304032997\) | \(a_{42}=-0.099999172\) | \(a_{43}=+0.783239364\) | \(a_{44}=-1.335318888\) | \(a_{45}=-0.692129555\) |
| \(a_{46}=+1.763214656\) | \(a_{47}=+0.360568411\) | \(a_{48}=-0.108482828\) | \(a_{49}=-0.931659544\) | \(a_{50}=-0.707632408\) |
| \(a_{51}=+0.322782372\) | \(a_{52}=+0.390453860\) | \(a_{53}=+1.398065718\) | \(a_{54}=-0.741727442\) | \(a_{55}=-0.702834729\) |
| \(a_{56}=-0.162147187\) | \(a_{57}=+0.022852693\) | \(a_{58}=+1.165253349\) | \(a_{59}=-1.587730962\) | \(a_{60}=+0.254834726\) |
| \(a_{61}=+1.167275969\) | \(a_{62}=+0.038503243\) | \(a_{63}=+0.245484039\) | \(a_{64}=-1.576247682\) | \(a_{65}=+0.205512358\) |
| \(a_{66}=-0.364760338\) | \(a_{67}=-0.027093886\) | \(a_{68}=+1.830728604\) | \(a_{69}=+0.280988859\) | \(a_{70}=-0.298523677\) |
| \(a_{71}=-1.633423858\) | \(a_{72}=-0.582444865\) | \(a_{73}=+1.067847737\) | \(a_{74}=+0.308723173\) | \(a_{75}=-0.112769493\) |
| \(a_{76}=+0.129613889\) | \(a_{77}=+0.249280944\) | \(a_{78}=+0.106657730\) | \(a_{79}=-0.531173889\) | \(a_{80}=-0.323849610\) |
| \(a_{81}=+0.820837567\) | \(a_{82}=-0.471039683\) | \(a_{83}=-0.904532380\) | \(a_{84}=-0.090384607\) | \(a_{85}=+0.963589788\) |
| \(a_{86}=+1.213476253\) | \(a_{87}=+0.185696737\) | \(a_{88}=-0.591453547\) | \(a_{89}=-1.067353172\) | \(a_{90}=-1.072319418\) |
| \(a_{91}=-0.072890985\) | \(a_{92}=+1.593687841\) | \(a_{93}=+0.006135943\) | \(a_{94}=+0.558630251\) | \(a_{95}=+0.068221266\) |
| \(a_{96}=-0.321213823\) | \(a_{97}=-0.003257117\) | \(a_{98}=-1.443424306\) | \(a_{99}=+0.895435829\) | \(a_{100}=-0.639596071\) |
Showing 100 of 5000 available coefficients