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: \( 30.4710497659 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.561667442\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.397158857\) \(a_{7}=-0.729049735\) \(a_{8}=-0.353553391\) \(a_{9}=-0.684529685\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.035074744\) \(a_{12}=+0.280833721\) \(a_{13}=-1.163736565\) \(a_{14}=+0.515516011\) \(a_{15}=+0.251185316\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.347614165\) \(a_{18}=+0.484035582\) \(a_{19}=-1.052029670\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.409483499\) \(a_{22}=-0.731908370\) \(a_{23}=+1.384391615\) \(a_{24}=-0.198579428\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.822886017\) \(a_{27}=-0.946145479\) \(a_{28}=-0.364524867\) \(a_{29}=+1.503338041\) \(a_{30}=-0.177614840\)
\(a_{31}=+1.337587396\) \(a_{32}=-0.176776695\) \(a_{33}=+0.581367783\) \(a_{34}=+0.245800333\) \(a_{35}=-0.326040953\)
\(a_{36}=-0.342264842\) \(a_{37}=+1.222612172\) \(a_{38}=+0.743897314\) \(a_{39}=-0.653632939\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.499242713\) \(a_{42}=+0.289548559\) \(a_{43}=+1.227771472\) \(a_{44}=+0.517537372\) \(a_{45}=-0.306130982\)
\(a_{46}=-0.978912698\) \(a_{47}=-1.091545034\) \(a_{48}=+0.140416860\) \(a_{49}=-0.468486484\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.195243559\) \(a_{52}=-0.581868283\) \(a_{53}=+0.461081162\) \(a_{54}=+0.669025884\) \(a_{55}=+0.462899498\)
\(a_{56}=+0.257758006\) \(a_{57}=-0.590890814\) \(a_{58}=-1.063020523\) \(a_{59}=+0.966305617\) \(a_{60}=+0.125592658\)
\(a_{61}=-1.261057314\) \(a_{62}=-0.945817118\) \(a_{63}=+0.499056185\) \(a_{64}=+0.125000000\) \(a_{65}=-0.520438813\)
\(a_{66}=-0.411089102\) \(a_{67}=-0.383453462\) \(a_{68}=-0.173807082\) \(a_{69}=+0.777567697\) \(a_{70}=+0.230545769\)
\(a_{71}=+0.254029960\) \(a_{72}=+0.242017791\) \(a_{73}=+0.283808012\) \(a_{74}=-0.864517357\) \(a_{75}=+0.112333488\)
\(a_{76}=-0.526014835\) \(a_{77}=-0.754620967\) \(a_{78}=+0.462188284\) \(a_{79}=-1.127328359\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.153110574\) \(a_{82}=+0.353017908\) \(a_{83}=-1.799130020\) \(a_{84}=-0.204741750\) \(a_{85}=-0.155457780\)
\(a_{86}=-0.868165534\) \(a_{87}=+0.844376032\) \(a_{88}=-0.365954185\) \(a_{89}=-1.517400322\) \(a_{90}=+0.216467293\)
\(a_{91}=+0.848421834\) \(a_{92}=+0.692195807\) \(a_{93}=+0.751279291\) \(a_{94}=+0.771838896\) \(a_{95}=-0.470481971\)
\(a_{96}=-0.099289714\) \(a_{97}=+1.255968729\) \(a_{98}=+0.331269970\) \(a_{99}=-0.708539388\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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