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: \( 45.2874384425 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.865036928\) \(a_{3}=+1.197858525\) \(a_{4}=+2.478362743\) \(a_{5}=+0.698535305\)
\(a_{6}=-2.234050383\) \(a_{7}=+0.300996050\) \(a_{8}=-2.757201108\) \(a_{9}=+0.434865046\) \(a_{10}=-1.302794140\)
\(a_{11}=+0.730975683\) \(a_{12}=+2.968727939\) \(a_{13}=+1.312860089\) \(a_{14}=-0.561368748\) \(a_{15}=+0.836746471\)
\(a_{16}=+2.663919142\) \(a_{17}=-0.209497529\) \(a_{18}=-0.811039369\) \(a_{19}=+1.179311325\) \(a_{20}=+1.731223876\)
\(a_{21}=+0.360550679\) \(a_{22}=-1.363296597\) \(a_{23}=+0.395808652\) \(a_{24}=-3.302736852\) \(a_{25}=-0.512048427\)
\(a_{26}=-2.448532547\) \(a_{27}=-0.676951723\) \(a_{28}=+0.745977395\) \(a_{29}=+0.087938048\) \(a_{30}=-1.560563067\)
\(a_{31}=+1.158307945\) \(a_{32}=-2.211106465\) \(a_{33}=+0.875605454\) \(a_{34}=+0.390720627\) \(a_{35}=+0.210256367\)
\(a_{36}=+1.077753327\) \(a_{37}=+0.528220887\) \(a_{38}=-2.199459171\) \(a_{39}=+1.572620649\) \(a_{40}=-1.926002318\)
\(a_{41}=-0.277626965\) \(a_{42}=-0.672440340\) \(a_{43}=-0.529822742\) \(a_{44}=+1.811622900\) \(a_{45}=+0.303768587\)
\(a_{46}=-0.738197752\) \(a_{47}=+1.260408620\) \(a_{48}=+3.190998254\) \(a_{49}=-0.909401378\) \(a_{50}=+0.954989225\)
\(a_{51}=-0.250948401\) \(a_{52}=+3.253743531\) \(a_{53}=-1.691977486\) \(a_{54}=+1.262539962\) \(a_{55}=+0.510612322\)
\(a_{56}=-0.829906642\) \(a_{57}=+1.412648125\) \(a_{58}=-0.164007707\) \(a_{59}=-1.187377828\) \(a_{60}=+2.073761278\)
\(a_{61}=+0.234217753\) \(a_{62}=-2.160287091\) \(a_{63}=+0.130892661\) \(a_{64}=+1.459876065\) \(a_{65}=+0.917079124\)
\(a_{66}=-1.633036502\) \(a_{67}=+0.251605416\) \(a_{68}=-0.519210858\) \(a_{69}=+0.474122763\) \(a_{70}=-0.392135954\)
\(a_{71}=+1.912985680\) \(a_{72}=-1.199010385\) \(a_{73}=-0.099789812\) \(a_{74}=-0.985151461\) \(a_{75}=-0.613361573\)
\(a_{76}=+2.922761251\) \(a_{77}=+0.220020793\) \(a_{78}=-2.932995585\) \(a_{79}=+0.474234141\) \(a_{80}=+1.860841572\)
\(a_{81}=-1.245757438\) \(a_{82}=+0.517784543\) \(a_{83}=-1.174733103\) \(a_{84}=+0.893575382\) \(a_{85}=-0.146341420\)
\(a_{86}=+0.988138978\) \(a_{87}=+0.105337340\) \(a_{88}=-2.015446965\) \(a_{89}=+0.806330707\) \(a_{90}=-0.566539633\)
\(a_{91}=+0.395165700\) \(a_{92}=+0.980957416\) \(a_{93}=+1.387489046\) \(a_{94}=-2.350708620\) \(a_{95}=+0.823790597\)
\(a_{96}=-2.648592728\) \(a_{97}=+1.435547262\) \(a_{98}=+1.696067153\) \(a_{99}=+0.317875774\) \(a_{100}=-1.269041744\)

Showing 100 of 5000 available coefficients

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