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: \( 28.3486863507 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.140801870\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.806668738\) \(a_{7}=+0.740059959\) \(a_{8}=+0.353553391\) \(a_{9}=+0.301428906\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.512139031\) \(a_{12}=+0.570400935\) \(a_{13}=+1.005614457\) \(a_{14}=+0.523301415\) \(a_{15}=+0.510182106\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.382661723\) \(a_{18}=+0.213142423\) \(a_{19}=-0.499963195\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.844261785\) \(a_{22}=-0.362136982\) \(a_{23}=+0.020426938\) \(a_{24}=+0.403334369\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.711076802\) \(a_{27}=-0.796931210\) \(a_{28}=+0.370029979\) \(a_{29}=+1.193127890\) \(a_{30}=+0.360753227\)
\(a_{31}=+1.179530914\) \(a_{32}=+0.176776695\) \(a_{33}=-0.584249164\) \(a_{34}=+0.270582699\) \(a_{35}=+0.330964875\)
\(a_{36}=+0.150714453\) \(a_{37}=-0.365080921\) \(a_{38}=-0.353527365\) \(a_{39}=+1.147206852\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.758964211\) \(a_{42}=+0.596983233\) \(a_{43}=-0.580017177\) \(a_{44}=-0.256069516\) \(a_{45}=+0.134803105\)
\(a_{46}=+0.014444027\) \(a_{47}=-0.708827304\) \(a_{48}=+0.285200467\) \(a_{49}=-0.452311258\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.436541209\) \(a_{52}=+0.502807228\) \(a_{53}=+0.285935446\) \(a_{54}=-0.563515463\) \(a_{55}=-0.229035537\)
\(a_{56}=+0.261650708\) \(a_{57}=-0.570358948\) \(a_{58}=+0.843668822\) \(a_{59}=+1.362002676\) \(a_{60}=+0.255091053\)
\(a_{61}=+1.298648581\) \(a_{62}=+0.834054308\) \(a_{63}=+0.223075464\) \(a_{64}=+0.125000000\) \(a_{65}=+0.449724457\)
\(a_{66}=-0.413126546\) \(a_{67}=+0.880109364\) \(a_{68}=+0.191330861\) \(a_{69}=+0.023303089\) \(a_{70}=+0.234027507\)
\(a_{71}=+0.518800549\) \(a_{72}=+0.106571212\) \(a_{73}=-1.125905532\) \(a_{74}=-0.258151195\) \(a_{75}=+0.228160374\)
\(a_{76}=-0.249981597\) \(a_{77}=-0.379013590\) \(a_{78}=+0.811197745\) \(a_{79}=-0.888672794\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.210569521\) \(a_{82}=+1.243775522\) \(a_{83}=+0.816937140\) \(a_{84}=+0.422130892\) \(a_{85}=+0.171131525\)
\(a_{86}=-0.410134079\) \(a_{87}=+1.361122528\) \(a_{88}=-0.181068491\) \(a_{89}=+1.693323769\) \(a_{90}=+0.095320190\)
\(a_{91}=+0.744214993\) \(a_{92}=+0.010213469\) \(a_{93}=+1.345611072\) \(a_{94}=-0.501216593\) \(a_{95}=-0.223590338\)
\(a_{96}=+0.201667185\) \(a_{97}=-1.170353472\) \(a_{98}=-0.319832357\) \(a_{99}=-0.154373508\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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