Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: \(+1\)
Spectral parameter: \( 12.1730083247 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.289251871\) \(a_{3}=-1.201858761\) \(a_{4}=-0.916333355\) \(a_{5}=+0.039552707\)
\(a_{6}=-0.347639896\) \(a_{7}=+0.448133104\) \(a_{8}=-0.554303009\) \(a_{9}=+0.444464481\) \(a_{10}=+0.011440695\)
\(a_{11}=-0.691450783\) \(a_{12}=+1.101303271\) \(a_{13}=-0.802780003\) \(a_{14}=+0.129623339\) \(a_{15}=-0.047536768\)
\(a_{16}=+0.756000172\) \(a_{17}=-1.037675373\) \(a_{18}=+0.128562183\) \(a_{19}=+0.637178807\) \(a_{20}=-0.036243465\)
\(a_{21}=-0.538592698\) \(a_{22}=-0.200003433\) \(a_{23}=+0.508798692\) \(a_{24}=+0.666193928\) \(a_{25}=-0.998435583\)
\(a_{26}=-0.232205618\) \(a_{27}=+0.667675230\) \(a_{28}=-0.410639311\) \(a_{29}=+0.779996881\) \(a_{30}=-0.013750099\)
\(a_{31}=-1.598013584\) \(a_{32}=+0.772977474\) \(a_{33}=+0.831026182\) \(a_{34}=-0.300149544\) \(a_{35}=+0.017724878\)
\(a_{36}=-0.407277629\) \(a_{37}=-0.429215161\) \(a_{38}=+0.184305162\) \(a_{39}=+0.964828180\) \(a_{40}=-0.021924185\)
\(a_{41}=-0.548524188\) \(a_{42}=-0.155788946\) \(a_{43}=-0.489355022\) \(a_{44}=+0.633599416\) \(a_{45}=+0.017579773\)
\(a_{46}=+0.147170974\) \(a_{47}=+0.816868006\) \(a_{48}=-0.908605430\) \(a_{49}=-0.799176720\) \(a_{50}=-0.288799361\)
\(a_{51}=+1.247139239\) \(a_{52}=+0.735614092\) \(a_{53}=-0.978756048\) \(a_{54}=+0.193126314\) \(a_{55}=-0.027348764\)
\(a_{56}=-0.248401523\) \(a_{57}=-0.765798932\) \(a_{58}=+0.225615558\) \(a_{59}=+1.342931385\) \(a_{60}=+0.043559526\)
\(a_{61}=-0.451739346\) \(a_{62}=-0.462228420\) \(a_{63}=+0.199179248\) \(a_{64}=-0.532414991\) \(a_{65}=-0.031752122\)
\(a_{66}=+0.240375878\) \(a_{67}=+0.407059647\) \(a_{68}=+0.950856556\) \(a_{69}=-0.611504166\) \(a_{70}=+0.005126954\)
\(a_{71}=-1.218362390\) \(a_{72}=-0.246368000\) \(a_{73}=+0.847623229\) \(a_{74}=-0.124151289\) \(a_{75}=+1.199978553\)
\(a_{76}=-0.583868194\) \(a_{77}=-0.309861986\) \(a_{78}=+0.279078357\) \(a_{79}=-0.152197859\) \(a_{80}=+0.029901854\)
\(a_{81}=-1.246915806\) \(a_{82}=-0.158661648\) \(a_{83}=+1.512681486\) \(a_{84}=+0.493530454\) \(a_{85}=-0.041042870\)
\(a_{86}=-0.141546856\) \(a_{87}=-0.937446086\) \(a_{88}=+0.383273250\) \(a_{89}=-0.351411891\) \(a_{90}=+0.005084980\)
\(a_{91}=-0.359752294\) \(a_{92}=-0.466229212\) \(a_{93}=+1.920586625\) \(a_{94}=+0.236280601\) \(a_{95}=+0.025202147\)
\(a_{96}=-0.929009751\) \(a_{97}=-0.434877625\) \(a_{98}=-0.231163364\) \(a_{99}=-0.307325315\) \(a_{100}=+0.914899828\)

Showing 100 of 5000 available coefficients

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