Properties

Level 1
Weight 0
Character 1.1
Symmetry even
Fricke sign +1

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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

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