Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 15.9382784617 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.524544017\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.370908632\) \(a_{7}=+0.062661108\) \(a_{8}=-0.353553391\) \(a_{9}=-0.724853574\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.173934621\) \(a_{12}=+0.262272009\) \(a_{13}=-0.771201723\) \(a_{14}=-0.044308094\) \(a_{15}=+0.234583216\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.798685436\) \(a_{18}=+0.512548878\) \(a_{19}=+1.021174463\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.032868509\) \(a_{22}=-0.830097131\) \(a_{23}=+0.156308331\) \(a_{24}=-0.185454316\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.545321968\) \(a_{27}=-0.904761623\) \(a_{28}=+0.031330554\) \(a_{29}=-0.652147931\) \(a_{30}=-0.165875383\)
\(a_{31}=+0.613278818\) \(a_{32}=-0.176776695\) \(a_{33}=+0.615780382\) \(a_{34}=-0.564755888\) \(a_{35}=+0.028022899\)
\(a_{36}=-0.362426787\) \(a_{37}=-1.712917066\) \(a_{38}=-0.722079387\) \(a_{39}=-0.404529250\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.252094126\) \(a_{42}=-0.023241546\) \(a_{43}=+0.360471045\) \(a_{44}=+0.586967310\) \(a_{45}=-0.324164373\)
\(a_{46}=-0.110526681\) \(a_{47}=+1.686399294\) \(a_{48}=+0.131136004\) \(a_{49}=-0.996073586\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.418945667\) \(a_{52}=-0.385600861\) \(a_{53}=+1.161375555\) \(a_{54}=+0.639763079\) \(a_{55}=+0.524999523\)
\(a_{56}=-0.022154047\) \(a_{57}=+0.535650955\) \(a_{58}=+0.461138224\) \(a_{59}=+1.854077392\) \(a_{60}=+0.117291608\)
\(a_{61}=+1.124128932\) \(a_{62}=-0.433653611\) \(a_{63}=-0.045420128\) \(a_{64}=+0.125000000\) \(a_{65}=-0.344891895\)
\(a_{66}=-0.435422484\) \(a_{67}=+1.204664381\) \(a_{68}=+0.399342718\) \(a_{69}=+0.081990600\) \(a_{70}=-0.019815182\)
\(a_{71}=-0.245592261\) \(a_{72}=+0.256274439\) \(a_{73}=-0.765468546\) \(a_{74}=+1.211215273\) \(a_{75}=+0.104908803\)
\(a_{76}=+0.510587231\) \(a_{77}=+0.073560044\) \(a_{78}=+0.286045376\) \(a_{79}=+0.261450553\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.250266278\) \(a_{82}=+0.178257466\) \(a_{83}=-0.610734665\) \(a_{84}=+0.016434255\) \(a_{85}=+0.357182986\)
\(a_{86}=-0.254891520\) \(a_{87}=-0.342080296\) \(a_{88}=-0.415048566\) \(a_{89}=+0.116193008\) \(a_{90}=+0.229218826\)
\(a_{91}=-0.048324354\) \(a_{92}=+0.078154166\) \(a_{93}=+0.321691736\) \(a_{94}=-1.192464376\) \(a_{95}=+0.456683103\)
\(a_{96}=-0.092727158\) \(a_{97}=+0.674672474\) \(a_{98}=+0.704330387\) \(a_{99}=-0.850930703\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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