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: \( 24.0655991316 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.464521428\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.035573033\) \(a_{7}=-0.656644387\) \(a_{8}=+0.353553391\) \(a_{9}=+1.144823013\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.249617451\) \(a_{12}=+0.732260714\) \(a_{13}=-1.912152587\) \(a_{14}=-0.464317699\) \(a_{15}=-0.654953893\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.025161588\) \(a_{18}=+0.809512115\) \(a_{19}=-1.317267343\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.961669775\) \(a_{22}=+0.883612974\) \(a_{23}=-0.271129593\) \(a_{24}=+0.517786516\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.352096061\) \(a_{27}=+0.212096405\) \(a_{28}=-0.328322193\) \(a_{29}=+1.084267561\) \(a_{30}=-0.463122339\)
\(a_{31}=-1.528247545\) \(a_{32}=+0.176776695\) \(a_{33}=+1.830091534\) \(a_{34}=+0.017791930\) \(a_{35}=+0.293660297\)
\(a_{36}=+0.572411506\) \(a_{37}=+1.268273090\) \(a_{38}=-0.931448671\) \(a_{39}=-2.800388437\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.385924397\) \(a_{42}=-0.680003219\) \(a_{43}=-0.496194478\) \(a_{44}=+0.624808726\) \(a_{45}=-0.511980416\)
\(a_{46}=-0.191717574\) \(a_{47}=-0.776566707\) \(a_{48}=+0.366130357\) \(a_{49}=-0.568818150\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.036849685\) \(a_{52}=-0.956076294\) \(a_{53}=+0.888065518\) \(a_{54}=+0.149974806\) \(a_{55}=-0.558845913\)
\(a_{56}=-0.232158849\) \(a_{57}=-1.929166250\) \(a_{58}=+0.766692945\) \(a_{59}=-0.501648322\) \(a_{60}=-0.327476947\)
\(a_{61}=+0.278075635\) \(a_{62}=-1.080634202\) \(a_{63}=-0.751741605\) \(a_{64}=+0.125000000\) \(a_{65}=+0.855140634\)
\(a_{66}=+1.294070134\) \(a_{67}=-1.529536094\) \(a_{68}=+0.012580794\) \(a_{69}=-0.397075099\) \(a_{70}=+0.207649187\)
\(a_{71}=-1.156685313\) \(a_{72}=+0.404756058\) \(a_{73}=+0.039328370\) \(a_{74}=+0.896804502\) \(a_{75}=+0.292904286\)
\(a_{76}=-0.658633672\) \(a_{77}=-0.820554285\) \(a_{78}=-1.980173654\) \(a_{79}=+0.274828245\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.834203282\) \(a_{82}=-0.979996540\) \(a_{83}=+0.150496738\) \(a_{84}=-0.480834887\) \(a_{85}=-0.011252604\)
\(a_{86}=-0.350862480\) \(a_{87}=+1.587933076\) \(a_{88}=+0.441806487\) \(a_{89}=+0.323040920\) \(a_{90}=-0.362024824\)
\(a_{91}=+1.255604263\) \(a_{92}=-0.135564797\) \(a_{93}=-2.238151276\) \(a_{94}=-0.549115585\) \(a_{95}=+0.589099865\)
\(a_{96}=+0.258893258\) \(a_{97}=+1.464865037\) \(a_{98}=-0.402215171\) \(a_{99}=+1.430590815\) \(a_{100}=+0.099975586\)

Showing 100 of 221 available coefficients

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