Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 30.2650176797 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.226550670\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.867302297\) \(a_{7}=+0.133887811\) \(a_{8}=-0.353553391\) \(a_{9}=+0.504426547\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.106318717\) \(a_{12}=-0.613275335\) \(a_{13}=+0.610721884\) \(a_{14}=-0.094672979\) \(a_{15}=-0.548530135\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.155983011\) \(a_{18}=-0.356683432\) \(a_{19}=+0.882833906\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.164220184\) \(a_{22}=+0.075178685\) \(a_{23}=-0.726253914\) \(a_{24}=+0.433651148\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.431845586\) \(a_{27}=+0.607845951\) \(a_{28}=+0.066943906\) \(a_{29}=+0.145554245\) \(a_{30}=+0.387869378\)
\(a_{31}=-0.780858032\) \(a_{32}=-0.176776695\) \(a_{33}=+0.130405293\) \(a_{34}=-0.110296645\) \(a_{35}=+0.059876449\)
\(a_{36}=+0.252213274\) \(a_{37}=-1.044415784\) \(a_{38}=-0.624257841\) \(a_{39}=-0.749081336\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.053361105\) \(a_{42}=+0.116121206\) \(a_{43}=-0.306302173\) \(a_{44}=-0.053159358\) \(a_{45}=+0.225586410\)
\(a_{46}=+0.513539068\) \(a_{47}=-0.130274941\) \(a_{48}=-0.306637668\) \(a_{49}=-0.982074054\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.191321067\) \(a_{52}=+0.305360942\) \(a_{53}=-0.106106921\) \(a_{54}=-0.429811994\) \(a_{55}=-0.047547176\)
\(a_{56}=-0.047336490\) \(a_{57}=-1.082840519\) \(a_{58}=-0.102922393\) \(a_{59}=-1.886881664\) \(a_{60}=-0.274265068\)
\(a_{61}=-0.178501430\) \(a_{62}=+0.552150009\) \(a_{63}=+0.067536566\) \(a_{64}=+0.125000000\) \(a_{65}=+0.273123130\)
\(a_{66}=-0.092210467\) \(a_{67}=+1.837527656\) \(a_{68}=+0.077991506\) \(a_{69}=+0.890787225\) \(a_{70}=-0.042339043\)
\(a_{71}=+1.629147927\) \(a_{72}=-0.178341716\) \(a_{73}=+0.801638803\) \(a_{74}=+0.738513483\) \(a_{75}=-0.245310134\)
\(a_{76}=+0.441416953\) \(a_{77}=-0.014234780\) \(a_{78}=+0.529680493\) \(a_{79}=-0.307064473\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.249980406\) \(a_{82}=+0.037731999\) \(a_{83}=-0.012259485\) \(a_{84}=-0.082110092\) \(a_{85}=+0.069757723\)
\(a_{86}=+0.216588343\) \(a_{87}=-0.178529656\) \(a_{88}=+0.037589343\) \(a_{89}=+1.397511061\) \(a_{90}=-0.159513680\)
\(a_{91}=+0.081768216\) \(a_{92}=-0.363126957\) \(a_{93}=+0.957761942\) \(a_{94}=+0.092118294\) \(a_{95}=+0.394815325\)
\(a_{96}=+0.216825574\) \(a_{97}=-0.330516397\) \(a_{98}=+0.694431223\) \(a_{99}=-0.053629983\) \(a_{100}=+0.099975586\)

Showing 100 of 251 available coefficients

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