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: \( 31.7376827649 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.429149144\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.303454270\) \(a_{7}=-1.550145031\) \(a_{8}=+0.353553391\) \(a_{9}=-0.815831012\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.060998269\) \(a_{12}=+0.214574572\) \(a_{13}=+0.530357788\) \(a_{14}=-1.096118063\) \(a_{15}=-0.191921332\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.841248913\) \(a_{18}=-0.576879641\) \(a_{19}=-1.237917241\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.665243413\) \(a_{22}=+0.750239071\) \(a_{23}=-0.467674506\) \(a_{24}=+0.151727135\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.375019589\) \(a_{27}=-0.779262324\) \(a_{28}=-0.775072516\) \(a_{29}=+0.696414661\) \(a_{30}=-0.135708875\)
\(a_{31}=+1.260437494\) \(a_{32}=+0.176776695\) \(a_{33}=+0.455326499\) \(a_{34}=+1.301959592\) \(a_{35}=+0.693245933\)
\(a_{36}=-0.407915506\) \(a_{37}=-0.248966008\) \(a_{38}=-0.875339676\) \(a_{39}=+0.227602591\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.736145885\) \(a_{42}=-0.470398128\) \(a_{43}=-0.333352024\) \(a_{44}=+0.530499134\) \(a_{45}=+0.364850720\)
\(a_{46}=-0.330695815\) \(a_{47}=-0.595027280\) \(a_{48}=+0.107287286\) \(a_{49}=+1.402949618\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.790170395\) \(a_{52}=+0.265178894\) \(a_{53}=-0.483375021\) \(a_{54}=-0.551021674\) \(a_{55}=-0.474492851\)
\(a_{56}=-0.548059032\) \(a_{57}=-0.531251124\) \(a_{58}=+0.492439530\) \(a_{59}=-0.394428998\) \(a_{60}=-0.095960666\)
\(a_{61}=-0.878697316\) \(a_{62}=+0.891263899\) \(a_{63}=+1.264656390\) \(a_{64}=+0.125000000\) \(a_{65}=-0.237183213\)
\(a_{66}=+0.321964455\) \(a_{67}=-1.802532461\) \(a_{68}=+0.920624456\) \(a_{69}=-0.200702114\) \(a_{70}=+0.490198900\)
\(a_{71}=-1.288189350\) \(a_{72}=-0.288439821\) \(a_{73}=+1.045065813\) \(a_{74}=-0.176045552\) \(a_{75}=+0.085829829\)
\(a_{76}=-0.618958621\) \(a_{77}=-1.644701195\) \(a_{78}=+0.160939335\) \(a_{79}=-1.283629357\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.481411253\) \(a_{82}=+1.227640529\) \(a_{83}=+0.598972339\) \(a_{84}=-0.332621706\) \(a_{85}=-0.823431547\)
\(a_{86}=-0.235715476\) \(a_{87}=+0.298865756\) \(a_{88}=+0.375119535\) \(a_{89}=-0.819039574\) \(a_{90}=+0.257988418\)
\(a_{91}=-0.822131491\) \(a_{92}=-0.233837253\) \(a_{93}=+0.540915671\) \(a_{94}=-0.420747825\) \(a_{95}=+0.553613420\)
\(a_{96}=+0.075863567\) \(a_{97}=-0.066473171\) \(a_{98}=+0.992035188\) \(a_{99}=-0.865595292\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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