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: \( 30.4874572847 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.710006194\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.209156975\) \(a_{7}=+1.943633899\) \(a_{8}=-0.353553391\) \(a_{9}=+1.924121182\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.221568843\) \(a_{12}=+0.855003097\) \(a_{13}=-0.670613703\) \(a_{14}=-1.374356710\) \(a_{15}=-0.764738018\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.298587493\) \(a_{18}=-1.360559136\) \(a_{19}=+1.251854116\) \(a_{20}=-0.223606798\)
\(a_{21}=+3.323626005\) \(a_{22}=-0.863779612\) \(a_{23}=+0.785068011\) \(a_{24}=-0.604578488\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.474195497\) \(a_{27}=+1.580252945\) \(a_{28}=+0.971816949\) \(a_{29}=+0.679237690\) \(a_{30}=+0.540751438\)
\(a_{31}=-0.712705663\) \(a_{32}=-0.176776695\) \(a_{33}=+2.088890287\) \(a_{34}=+0.918240022\) \(a_{35}=-0.869219504\)
\(a_{36}=+0.962060591\) \(a_{37}=-0.255802465\) \(a_{38}=-0.885194535\) \(a_{39}=-1.146753586\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.689011831\) \(a_{42}=-2.350158486\) \(a_{43}=-0.728547275\) \(a_{44}=+0.610784421\) \(a_{45}=-0.860493152\)
\(a_{46}=-0.555126915\) \(a_{47}=+1.461823720\) \(a_{48}=+0.427501548\) \(a_{49}=+2.777712732\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.220592656\) \(a_{52}=-0.335306852\) \(a_{53}=+0.495412832\) \(a_{54}=-1.117407573\) \(a_{55}=-0.546302194\)
\(a_{56}=-0.687178355\) \(a_{57}=+2.140678293\) \(a_{58}=-0.480293577\) \(a_{59}=-1.657850554\) \(a_{60}=-0.382369009\)
\(a_{61}=-0.534485082\) \(a_{62}=+0.503959007\) \(a_{63}=+3.739787155\) \(a_{64}=+0.125000000\) \(a_{65}=+0.299907565\)
\(a_{66}=-1.477068487\) \(a_{67}=+1.212275286\) \(a_{68}=-0.649293747\) \(a_{69}=+1.342471162\) \(a_{70}=+0.614631006\)
\(a_{71}=+0.260635279\) \(a_{72}=-0.680279568\) \(a_{73}=+0.505315288\) \(a_{74}=+0.180879658\) \(a_{75}=+0.342001239\)
\(a_{76}=+0.625927058\) \(a_{77}=+2.374282612\) \(a_{78}=+0.810877237\) \(a_{79}=-0.149109576\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.778121141\) \(a_{82}=-0.487204938\) \(a_{83}=+0.047103288\) \(a_{84}=+1.661813002\) \(a_{85}=+0.580745982\)
\(a_{86}=+0.515160718\) \(a_{87}=+1.161500657\) \(a_{88}=-0.431889806\) \(a_{89}=+0.747051096\) \(a_{90}=+0.608460543\)
\(a_{91}=-1.303427526\) \(a_{92}=+0.392534006\) \(a_{93}=-1.218731098\) \(a_{94}=-1.033665466\) \(a_{95}=-0.559846180\)
\(a_{96}=-0.302289244\) \(a_{97}=+0.834971213\) \(a_{98}=-1.964139509\) \(a_{99}=+2.350446485\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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