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: \( 8.58191066592 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.671011853\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.474477032\) \(a_{7}=-1.601546462\) \(a_{8}=-0.353553391\) \(a_{9}=-0.549743093\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.300924025\) \(a_{12}=-0.335505927\) \(a_{13}=+1.640227839\) \(a_{14}=+1.132464363\) \(a_{15}=+0.300085623\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.490792576\) \(a_{18}=+0.388727069\) \(a_{19}=-0.928652204\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.074656659\) \(a_{22}=+0.919892200\) \(a_{23}=+0.706928298\) \(a_{24}=+0.237238516\) \(a_{25}=+0.200000000\)
\(a_{26}=-1.159816227\) \(a_{27}=+1.039895985\) \(a_{28}=-0.800773231\) \(a_{29}=-0.213033269\) \(a_{30}=-0.212192579\)
\(a_{31}=-0.030961482\) \(a_{32}=-0.176776695\) \(a_{33}=+0.872935441\) \(a_{34}=-0.347042759\) \(a_{35}=+0.716233352\)
\(a_{36}=-0.274871546\) \(a_{37}=+0.232572114\) \(a_{38}=+0.656656268\) \(a_{39}=-1.100612319\) \(a_{40}=+0.158113890\)
\(a_{41}=+0.855725217\) \(a_{42}=-0.759897029\) \(a_{43}=+0.744504341\) \(a_{44}=-0.650461957\) \(a_{45}=+0.245852585\)
\(a_{46}=-0.499873794\) \(a_{47}=-1.409783877\) \(a_{48}=-0.167752963\) \(a_{49}=+1.564951069\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.329327636\) \(a_{52}=+0.820113919\) \(a_{53}=-0.405568670\) \(a_{54}=-0.735317503\) \(a_{55}=+0.581790911\)
\(a_{56}=+0.566232182\) \(a_{57}=+0.623136636\) \(a_{58}=+0.150637269\) \(a_{59}=+0.306443031\) \(a_{60}=+0.150042812\)
\(a_{61}=-1.754867961\) \(a_{62}=+0.021893074\) \(a_{63}=+0.880439105\) \(a_{64}=+0.125000000\) \(a_{65}=-0.733532189\)
\(a_{66}=-0.617258570\) \(a_{67}=+0.430658661\) \(a_{68}=+0.245396288\) \(a_{69}=-0.474357267\) \(a_{70}=-0.506453459\)
\(a_{71}=-0.588898229\) \(a_{72}=+0.194363536\) \(a_{73}=+0.072429826\) \(a_{74}=-0.164453320\) \(a_{75}=-0.134202370\)
\(a_{76}=-0.464326106\) \(a_{77}=+2.083490278\) \(a_{78}=+0.778250444\) \(a_{79}=+1.589410564\) \(a_{80}=-0.111803379\)
\(a_{81}=-0.148039435\) \(a_{82}=-0.605089071\) \(a_{83}=-1.007654193\) \(a_{84}=+0.537328319\) \(a_{85}=-0.219489160\)
\(a_{86}=-0.526444049\) \(a_{87}=+0.142947848\) \(a_{88}=+0.459946100\) \(a_{89}=-0.987160784\) \(a_{90}=-0.173844030\)
\(a_{91}=-2.626901091\) \(a_{92}=+0.353464149\) \(a_{93}=+0.020775520\) \(a_{94}=+0.996867740\) \(a_{95}=+0.415305892\)
\(a_{96}=+0.118619258\) \(a_{97}=+1.580473730\) \(a_{98}=-1.106587513\) \(a_{99}=+0.715173996\) \(a_{100}=+0.100000000\)

Showing 100 of 2000 available coefficients

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