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: \( 18.2771231012 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.055713773\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.039395587\) \(a_{7}=-0.799718604\) \(a_{8}=+0.353553391\) \(a_{9}=-0.996895975\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.176934349\) \(a_{12}=-0.027856887\) \(a_{13}=+0.456433439\) \(a_{14}=-0.565486448\) \(a_{15}=-0.024915957\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.499950449\) \(a_{18}=-0.704911904\) \(a_{19}=+1.867712140\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.044555341\) \(a_{22}=-0.832218259\) \(a_{23}=+0.196552962\) \(a_{24}=-0.019697793\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.322747180\) \(a_{27}=+0.111254610\) \(a_{28}=-0.399859302\) \(a_{29}=-0.052145668\) \(a_{30}=-0.017618242\)
\(a_{31}=-0.710216965\) \(a_{32}=+0.176776695\) \(a_{33}=+0.065571453\) \(a_{34}=+0.353518353\) \(a_{35}=-0.357645032\)
\(a_{36}=-0.498447988\) \(a_{37}=+1.578392875\) \(a_{38}=+1.320671920\) \(a_{39}=-0.025429629\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.707657276\) \(a_{42}=+0.031505384\) \(a_{43}=+1.073697390\) \(a_{44}=-0.588467175\) \(a_{45}=-0.445825434\)
\(a_{46}=+0.138983932\) \(a_{47}=+1.011519859\) \(a_{48}=-0.013928443\) \(a_{49}=-0.360450155\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.027854126\) \(a_{52}=+0.228216719\) \(a_{53}=-1.903934336\) \(a_{54}=+0.078668889\) \(a_{55}=-0.526341042\)
\(a_{56}=-0.282743224\) \(a_{57}=-0.104057291\) \(a_{58}=-0.036872555\) \(a_{59}=-0.766093964\) \(a_{60}=-0.012457978\)
\(a_{61}=+1.587583245\) \(a_{62}=-0.502199232\) \(a_{63}=+0.797236258\) \(a_{64}=+0.125000000\) \(a_{65}=+0.204123239\)
\(a_{66}=+0.046366019\) \(a_{67}=+1.875522342\) \(a_{68}=+0.249975225\) \(a_{69}=-0.010950707\) \(a_{70}=-0.252893228\)
\(a_{71}=-0.532742703\) \(a_{72}=-0.352455952\) \(a_{73}=+0.307848286\) \(a_{74}=+1.116092305\) \(a_{75}=-0.011142755\)
\(a_{76}=+0.933856070\) \(a_{77}=+0.941216295\) \(a_{78}=-0.017981463\) \(a_{79}=+0.928448462\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.990697561\) \(a_{82}=+0.500389259\) \(a_{83}=+0.548736628\) \(a_{84}=+0.022277670\) \(a_{85}=+0.223584638\)
\(a_{86}=+0.759218706\) \(a_{87}=+0.002905232\) \(a_{88}=-0.416109130\) \(a_{89}=-0.326775801\) \(a_{90}=-0.315246187\)
\(a_{91}=-0.365018312\) \(a_{92}=+0.098276481\) \(a_{93}=+0.039568867\) \(a_{94}=+0.715252552\) \(a_{95}=+0.835266262\)
\(a_{96}=-0.009848897\) \(a_{97}=-0.163204579\) \(a_{98}=-0.254876749\) \(a_{99}=+1.173281116\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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