Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 32.8911702135 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.173574422\) \(a_{3}=-0.501552671\) \(a_{4}=-0.969871920\) \(a_{5}=+1.819336889\)
\(a_{6}=-0.087056715\) \(a_{7}=-0.548825853\) \(a_{8}=-0.341919380\) \(a_{9}=-0.748444919\) \(a_{10}=+0.315790349\)
\(a_{11}=-0.706741156\) \(a_{12}=+0.486441852\) \(a_{13}=+0.514547269\) \(a_{14}=-0.095262130\) \(a_{15}=-0.912493275\)
\(a_{16}=+0.910523461\) \(a_{17}=+0.537426668\) \(a_{18}=-0.129910894\) \(a_{19}=+0.058162976\) \(a_{20}=-1.764523761\)
\(a_{21}=+0.275265072\) \(a_{22}=-0.122672188\) \(a_{23}=+1.004242127\) \(a_{24}=+0.171490578\) \(a_{25}=+2.309986715\)
\(a_{26}=+0.089312245\) \(a_{27}=+0.876937218\) \(a_{28}=+0.532290784\) \(a_{29}=+0.995312525\) \(a_{30}=-0.158385493\)
\(a_{31}=-0.172313085\) \(a_{32}=+0.499962964\) \(a_{33}=+0.354467914\) \(a_{34}=+0.093283523\) \(a_{35}=-0.998499120\)
\(a_{36}=+0.725895710\) \(a_{37}=+0.241728483\) \(a_{38}=+0.010095605\) \(a_{39}=-0.258072557\) \(a_{40}=-0.622066541\)
\(a_{41}=+0.825727341\) \(a_{42}=+0.047778976\) \(a_{43}=-0.323062608\) \(a_{44}=+0.685448402\) \(a_{45}=-1.361673450\)
\(a_{46}=+0.174310747\) \(a_{47}=+1.395784489\) \(a_{48}=-0.456675474\) \(a_{49}=-0.698790183\) \(a_{50}=+0.400954609\)
\(a_{51}=-0.269547781\) \(a_{52}=-0.499044948\) \(a_{53}=+1.379517949\) \(a_{54}=+0.152213871\) \(a_{55}=-1.285800257\)
\(a_{56}=+0.187654195\) \(a_{57}=-0.029171796\) \(a_{58}=+0.172760796\) \(a_{59}=+0.238953728\) \(a_{60}=+0.885001604\)
\(a_{61}=-1.286782627\) \(a_{62}=-0.029909142\) \(a_{63}=+0.410765921\) \(a_{64}=-0.823742682\) \(a_{65}=+0.936134841\)
\(a_{66}=+0.061526563\) \(a_{67}=+0.400474440\) \(a_{68}=-0.521235035\) \(a_{69}=-0.503680321\) \(a_{70}=-0.173313908\)
\(a_{71}=+0.163890396\) \(a_{72}=+0.255907823\) \(a_{73}=+0.882930319\) \(a_{74}=+0.041957882\) \(a_{75}=-1.158580006\)
\(a_{76}=-0.056410637\) \(a_{77}=+0.387877818\) \(a_{78}=-0.044794795\) \(a_{79}=-1.059370905\) \(a_{80}=+1.656548921\)
\(a_{81}=+0.308614715\) \(a_{82}=+0.143325146\) \(a_{83}=-1.598808003\) \(a_{84}=-0.266971864\) \(a_{85}=+0.977760163\)
\(a_{86}=-0.056075405\) \(a_{87}=-0.499201655\) \(a_{88}=+0.241648498\) \(a_{89}=+1.084155568\) \(a_{90}=-0.236351682\)
\(a_{91}=-0.282396844\) \(a_{92}=-0.973986240\) \(a_{93}=+0.086424088\) \(a_{94}=+0.242272486\) \(a_{95}=+0.105818048\)
\(a_{96}=-0.250757760\) \(a_{97}=+1.222589760\) \(a_{98}=-0.121292102\) \(a_{99}=+0.528956827\) \(a_{100}=-2.240391251\)

Showing 100 of 5000 available coefficients

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