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: \( 18.5038062187 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.818716774\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.286026964\) \(a_{7}=+1.218166233\) \(a_{8}=+0.353553391\) \(a_{9}=+2.307730704\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.545616765\) \(a_{12}=+0.909358387\) \(a_{13}=+1.541876863\) \(a_{14}=+0.861373604\) \(a_{15}=+0.813354868\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.169241822\) \(a_{18}=+1.631812030\) \(a_{19}=-1.692888548\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.215499362\) \(a_{22}=+0.385809315\) \(a_{23}=-0.659469811\) \(a_{24}=+0.643013482\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.090271586\) \(a_{27}=+2.378391767\) \(a_{28}=+0.609083117\) \(a_{29}=-0.943464697\) \(a_{30}=+0.575128742\)
\(a_{31}=-0.267701993\) \(a_{32}=+0.176776695\) \(a_{33}=+0.992322363\) \(a_{34}=-0.826778821\) \(a_{35}=+0.544780501\)
\(a_{36}=+1.153865352\) \(a_{37}=-0.261308215\) \(a_{38}=-1.197052972\) \(a_{39}=+2.804237314\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.109234391\) \(a_{42}=+1.566594623\) \(a_{43}=-0.640264099\) \(a_{44}=+0.272808383\) \(a_{45}=+1.032048546\)
\(a_{46}=-0.466315575\) \(a_{47}=-0.123181503\) \(a_{48}=+0.454679194\) \(a_{49}=+0.483928972\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.126519714\) \(a_{52}=+0.770938431\) \(a_{53}=-0.918882803\) \(a_{54}=+1.681776947\) \(a_{55}=+0.244007235\)
\(a_{56}=+0.430686802\) \(a_{57}=-3.078884798\) \(a_{58}=-0.667130285\) \(a_{59}=-1.396651528\) \(a_{60}=+0.406677434\)
\(a_{61}=+0.112165506\) \(a_{62}=-0.189293894\) \(a_{63}=+2.811199619\) \(a_{64}=+0.125000000\) \(a_{65}=+0.689548296\)
\(a_{66}=+0.701677872\) \(a_{67}=+0.259734581\) \(a_{68}=-0.584620911\) \(a_{69}=-1.199388806\) \(a_{70}=+0.385217987\)
\(a_{71}=+1.265682340\) \(a_{72}=+0.815906015\) \(a_{73}=-0.743427160\) \(a_{74}=-0.184772811\) \(a_{75}=+0.363743355\)
\(a_{76}=-0.846444274\) \(a_{77}=+0.664651920\) \(a_{78}=+1.982895221\) \(a_{79}=+1.262787309\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.017890299\) \(a_{82}=-0.077240379\) \(a_{83}=+0.117844241\) \(a_{84}=+1.107749681\) \(a_{85}=-0.522900839\)
\(a_{86}=-0.452735086\) \(a_{87}=-1.715895071\) \(a_{88}=+0.192904657\) \(a_{89}=+0.832978729\) \(a_{90}=+0.729768525\)
\(a_{91}=+1.878262330\) \(a_{92}=-0.329734905\) \(a_{93}=-0.486874105\) \(a_{94}=-0.087102476\) \(a_{95}=-0.757082774\)
\(a_{96}=+0.321506741\) \(a_{97}=+0.777368882\) \(a_{98}=+0.342189458\) \(a_{99}=+1.259136562\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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