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: \( 21.2190521412 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.195167390\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.138004185\) \(a_{7}=-0.086483517\) \(a_{8}=-0.353553391\) \(a_{9}=-0.961909690\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.708479530\) \(a_{12}=+0.097583695\) \(a_{13}=-0.812751759\) \(a_{14}=+0.061153082\) \(a_{15}=-0.087281510\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.692606511\) \(a_{18}=+0.680172865\) \(a_{19}=-1.483795640\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.016878762\) \(a_{22}=+1.208077461\) \(a_{23}=-1.150001325\) \(a_{24}=-0.069002092\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.574702280\) \(a_{27}=-0.382900793\) \(a_{28}=-0.043241759\) \(a_{29}=+1.378953187\) \(a_{30}=+0.061717348\)
\(a_{31}=-0.932806683\) \(a_{32}=-0.176776695\) \(a_{33}=-0.333439490\) \(a_{34}=+0.489746761\) \(a_{35}=+0.038676605\)
\(a_{36}=-0.480954845\) \(a_{37}=+1.320481099\) \(a_{38}=+1.049201959\) \(a_{39}=-0.158622639\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.928986663\) \(a_{42}=+0.011935087\) \(a_{43}=-0.847236439\) \(a_{44}=-0.854239765\) \(a_{45}=+0.430179091\)
\(a_{46}=+0.813173735\) \(a_{47}=-1.736598924\) \(a_{48}=+0.048791847\) \(a_{49}=-0.992520601\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.135174205\) \(a_{52}=-0.406375879\) \(a_{53}=-1.083679283\) \(a_{54}=+0.270751747\) \(a_{55}=+0.764055273\)
\(a_{56}=+0.030576541\) \(a_{57}=-0.289588522\) \(a_{58}=-0.975067149\) \(a_{59}=+0.545076265\) \(a_{60}=-0.043640755\)
\(a_{61}=+0.315224336\) \(a_{62}=+0.659593931\) \(a_{63}=+0.083189333\) \(a_{64}=+0.125000000\) \(a_{65}=+0.363473636\)
\(a_{66}=+0.235777325\) \(a_{67}=-1.119969675\) \(a_{68}=-0.346303256\) \(a_{69}=-0.224442757\) \(a_{70}=-0.027348490\)
\(a_{71}=-1.313006197\) \(a_{72}=+0.340086432\) \(a_{73}=-0.517439077\) \(a_{74}=-0.933721140\) \(a_{75}=+0.039033478\)
\(a_{76}=-0.741897820\) \(a_{77}=+0.147755319\) \(a_{78}=+0.112163144\) \(a_{79}=+0.287346171\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.887179942\) \(a_{82}=-0.656892769\) \(a_{83}=-0.846350114\) \(a_{84}=-0.008439381\) \(a_{85}=+0.309743048\)
\(a_{86}=+0.599086631\) \(a_{87}=+0.269126694\) \(a_{88}=+0.604038731\) \(a_{89}=-0.764397526\) \(a_{90}=-0.304182552\)
\(a_{91}=+0.070289631\) \(a_{92}=-0.575000662\) \(a_{93}=-0.182053445\) \(a_{94}=+1.227960875\) \(a_{95}=+0.663573583\)
\(a_{96}=-0.034501046\) \(a_{97}=+1.770587105\) \(a_{98}=+0.701818048\) \(a_{99}=+1.643403015\) \(a_{100}=+0.099975586\)

Showing 100 of 206 available coefficients

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