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: \( 13.5633748047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.354821340\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.958003357\) \(a_{7}=-1.011631704\) \(a_{8}=+0.353553391\) \(a_{9}=+0.835540864\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.400329452\) \(a_{12}=-0.677410670\) \(a_{13}=-1.225484392\) \(a_{14}=-0.715331638\) \(a_{15}=-0.605894523\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.065984088\) \(a_{18}=+0.590816611\) \(a_{19}=+1.061320883\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.370580222\) \(a_{22}=+0.283075670\) \(a_{23}=-1.208403211\) \(a_{24}=-0.479001678\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.866548324\) \(a_{27}=+0.222812748\) \(a_{28}=-0.505815852\) \(a_{29}=+1.400672868\) \(a_{30}=-0.428432126\)
\(a_{31}=+0.804696799\) \(a_{32}=+0.176776695\) \(a_{33}=-0.542374885\) \(a_{34}=-0.753764577\) \(a_{35}=-0.452415452\)
\(a_{36}=+0.417770432\) \(a_{37}=+1.735929519\) \(a_{38}=+0.750467193\) \(a_{39}=+1.660312406\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.297426119\) \(a_{42}=+0.969146569\) \(a_{43}=-0.043390078\) \(a_{44}=+0.200164726\) \(a_{45}=+0.373665234\)
\(a_{46}=-0.854470105\) \(a_{47}=+1.637120390\) \(a_{48}=-0.338705335\) \(a_{49}=+0.023398705\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.444217991\) \(a_{52}=-0.612742196\) \(a_{53}=+0.299257152\) \(a_{54}=+0.157552405\) \(a_{55}=+0.179032774\)
\(a_{56}=-0.357665819\) \(a_{57}=-1.437900180\) \(a_{58}=+0.990425283\) \(a_{59}=+1.950149427\) \(a_{60}=-0.302947261\)
\(a_{61}=+0.687672911\) \(a_{62}=+0.569006564\) \(a_{63}=-0.845259628\) \(a_{64}=+0.125000000\) \(a_{65}=-0.548053281\)
\(a_{66}=-0.383516959\) \(a_{67}=-1.491570415\) \(a_{68}=-0.532992044\) \(a_{69}=+1.637170458\) \(a_{70}=-0.319906034\)
\(a_{71}=+0.026275913\) \(a_{72}=+0.295408305\) \(a_{73}=-0.308705045\) \(a_{74}=+1.227487535\) \(a_{75}=-0.270964268\)
\(a_{76}=+0.530660441\) \(a_{77}=-0.404985966\) \(a_{78}=+1.174018161\) \(a_{79}=-0.802123749\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.137412329\) \(a_{82}=-0.210312026\) \(a_{83}=+1.653854955\) \(a_{84}=+0.685290111\) \(a_{85}=-0.476722577\)
\(a_{86}=-0.030681419\) \(a_{87}=-1.897661489\) \(a_{88}=+0.141537835\) \(a_{89}=-0.800028866\) \(a_{90}=+0.264221221\)
\(a_{91}=+1.239738863\) \(a_{92}=-0.604201606\) \(a_{93}=-1.090220404\) \(a_{94}=+1.157618930\) \(a_{95}=+0.474637128\)
\(a_{96}=-0.239500839\) \(a_{97}=-0.966729957\) \(a_{98}=+0.016545383\) \(a_{99}=+0.334491619\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

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